problem solving using subtraction

Subtraction Worksheets

Welcome to the Subtraction Worksheets page at Math-Drills.com where you will get less of an experience than our other pages! This page includes Subtraction worksheets on topics such as five minute frenzies, one-, two-, three- and multi-digit subtraction and subtracting across zeros.

Subtraction has been around for several years now... well maybe more than a few, so it's probably a good thing for students to learn. People experience subtraction every minute of their lives from banks and the government taking away your money to the cookies in the jar mysteriously disappearing. With a good knowledge of subtraction, you can understand why your bank account reaches zero and do something to prevent it from happening.

Some students do have difficulty with subtraction, so take it easy on them. Help them to learn their addition facts first. Once they know those, they will need a few more strategies to successfully subtract. Teaching with manipulatives like base ten blocks or cereal or insects in the park can help students gain a deeper understanding of subtraction. The subtracting worksheets on this page are meant to support good teaching practices, so only use them for independent learning if students are practising skills they already know.

We use the words, minuend, subtrahend and difference on this page. Please refer to the following, so you know which word means which part of a subtraction question.

Minuend - Subtrahend = Difference

Most Popular Subtraction Worksheets this Week

Subtraction Facts Tables

Five minute subtraction frenzies are timed practice charts that help students develop subtraction fact recall speed. These charts are similar to the addition and multiplication frenzy charts, but due to the nature of how subtraction works, we could not focus solely on the single digit fact families. For example, you might get questions like 18 - 4 = 14. You also have to be aware that you must subtract the row number from the column number to get a positive number (or zero). Other than that, they should be a nice way to practice some mental subtraction. As with most of these pages, please only use them as a timed activity with students who will experience success. If a student does not have the necessary skills to complete a frenzy in under five minutes, you may need to take a different approach to how you deliver this page. For all others, students should be able to complete this page in under five minutes with a 98% or greater accuracy and improve their time as they get more practice.

• Five Minute Subtraction Frenzies Five Minute Subtraction Frenzy (Minuends 9 to 18; Subtrahends 0 to 9) Five Minute Subtraction Frenzy (Minuends 29 to 38; Subtrahends 10 to 19) Five Minute Subtraction Frenzy (Minuends 41 to 50; Subtrahends 16 to 25)

Most of the subtraction tables in this section are meant to be used as a reference for students learning their subtraction facts. After a while, most students will remember the facts and recall them easily when completing math problems.

• Subtraction Facts Tables 0 to 11 Subtraction Facts 0 to 11 in Grey Subtraction Facts 0 to 11 in Color Subtraction Facts 0 to 11 with Facts Highlighted Subtraction Facts 0 to 11 in Montessori Colors Subtraction Facts 0 to 11 in Montessori Colors with Facts Highlighted
• Subtraction Facts Tables 1 to 12 Subtraction Facts Tables in Gray 1 to 12 Subtraction Facts Tables in Color 1 to 12 Subtraction Facts Tables in Montessori Colors 1 to 12 Subtraction Facts 1 to 12 with Facts Highlighted Subtraction Facts 1 to 12 in Montessori Colors with Facts Highlighted
• Compact Subtraction Facts Tables Compact Subtraction Table (Filled) Compact Subtraction Table (Blank)

Single-Digit Subtraction Facts

Subtracting single-digit facts is a skill that students generally learn after or while they are learning single-digit addition facts. The subtraction worksheets in this section are meant to be used for practice, testing or with teacher guidance. They will not teach students how to subtract or what the connection is between addition and subtraction; for that, students require a teacher or parent.

Some students might find it easier to start with subtraction facts with minuends (the first number) limited to 9 or lower. This way, they don't need to count across 10 eliminating that extra pesky digit... for now.

• Subtracting Single-Digit from Single-Digit Numbers 100 Subtraction Questions with Minuends up to 9 64 Subtraction Questions with Minuends up to 9 25 Subtraction Questions with Minuends up to 9

In relation to addition facts, the following worksheets cover the facts from 0 to 9, and the worksheets after that cover the addition facts from 1 to 9. The minuends are the amounts to be subtracted from, so a minuend of 18 means that both the subtrahend (the amount being subtracted) and the difference will be 9. The worksheets marked with an asterisk (*) include all possible questions in a random order on each version of the worksheet.

• Subtraction Facts from (0 − 0) to (18 − 9) Subtraction Facts from (0 − 0) to (18 − 9) (100* Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (81 Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (64 Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (50 Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (25 Large Print Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (12 Very Large Print Questions) ✎
• Subtraction Facts from (2 − 1) to (18 − 9) (No Zeros) Subtraction Facts from (2 − 1) to (18 − 9) (100 Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (81* Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (64 Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (50 Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (25 Large Print Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (12 Very Large Print Questions) ✎
• Subtraction Facts with Minuends from 10 to 18 100 Subtraction Questions with Minuends from 10 to 18 and All Regrouping (100 Questions) 64 Subtraction Questions with Minuends from 10 to 18 and All Regrouping (64 Questions) 25 Subtraction Questions with Minuends from 10 to 18 and All Regrouping (25 Large Print Questions)

Sometimes students just need to reinforce a single number at a time which is where these worksheets come in. There are three sets of worksheets in this section, each with a different number of questions. The last set is the most interesting as there are no questions repeated. Eleven and Twelve have been included as they are essentially subtracting by 10 and 1 or 2 more.

• Subtracting Individual Focus or Target Facts (50 Questions per Page) Subtracting 0 (50 Questions) ✎ Subtracting 1 (50 Questions) ✎ Subtracting 2 (50 Questions) ✎ Subtracting 3 (50 Questions) ✎ Subtracting 4 (50 Questions) ✎ Subtracting 5 (50 Questions) ✎ Subtracting 6 (50 Questions) ✎ Subtracting 7 (50 Questions) ✎ Subtracting 8 (50 Questions) ✎ Subtracting 9 (50 Questions) ✎ Subtracting 10 (50 Questions) ✎ Subtracting 11 (50 Questions) ✎ Subtracting 12 (50 Questions) ✎
• Subtracting Individual Focus or Target Facts (25 Questions per Page) Subtracting Zero (0) (25 Large Print Questions) ✎ Subtracting One (1) (25 Large Print Questions) ✎ Subtracting Two (2) (25 Large Print Questions) ✎ Subtracting Three (3) (25 Large Print Questions) ✎ Subtracting Four (4) (25 Large Print Questions) ✎ Subtracting Five (5) (25 Large Print Questions) ✎ Subtracting Six (6) (25 Large Print Questions) ✎ Subtracting Seven (7) (25 Large Print Questions) ✎ Subtracting Eight (8) (25 Large Print Questions) ✎ Subtracting Nine (9) (25 Large Print Questions) ✎
• Subtracting Individual Focus or Target Facts with Differences of 0 to 99 (100 Unique Questions per Page) Subtracting One (1) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Two (2) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Three (3) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Four (4) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Five (5) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Six (6) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Seven (7) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Eight (8) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Nine (9) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Ten (10) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Eleven (11) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Twelve (12) with Differences 0 to 99 (100 Unique Questions) ✎
• Horizontally Arranged Subtraction Facts with Minuends to 18 Horizontal Subtraction Facts with Minuends to 18 (100 Questions) ✎ Horizontal Subtraction Facts with Minuends to 18 (50 Questions) ✎ Horizontal Subtraction Facts with Minuends to 18 (25 Questions; Large Print) ✎
• Horizontally Arranged Subtracting 1 to 5 from 1 to 10 Horizontal Subtracting 1 to 5 from 1 to 10 (100 Questions) ✎ Horizontal Subtracting 1 to 5 from 1 to 10 (50 Questions) ✎ Horizontal Subtracting 1 to 5 from 1 to 10 (25 Questions; Large Print) ✎
• Horizontally Arranged Subtracting 1s and 2s from Single-Digit Minuends Horizontal Subtracting Ones from Single-Digit Minuends (25 per page) ✎ Horizontal Subtracting Twos from Single-Digit Minuends (25 per page) ✎
• Horizontally Arranged Subtracting Individual Focus Facts Horizontal Subtracting 0s (100 per page) ✎ Horizontal Subtracting 1s (100 per page) ✎ Horizontal Subtracting 2s (100 per page) ✎ Horizontal Subtracting 3s (100 per page) ✎ Horizontal Subtracting 4s (100 per page) ✎ Horizontal Subtracting 5s (100 per page) ✎ Horizontal Subtracting 6s (100 per page) ✎ Horizontal Subtracting 7s (100 per page) ✎ Horizontal Subtracting 8s (100 per page) ✎ Horizontal Subtracting 9s (100 per page) ✎
• Horizontally Arranged Subtracting Pairs of Individual Focus Facts Horizontal Subtracting 0s and 1s (100 per page) ✎ Horizontal Subtracting 2s and 3s (100 per page) ✎ Horizontal Subtracting 4s and 5s (100 per page) ✎ Horizontal Subtracting 6s and 7s (100 per page) ✎ Horizontal Subtracting 8s and 9s (100 per page) ✎
• Subtracting a Number from Itself Subtracting a Number from Itself (Range 1 to 20)

The make ten subtraction strategy involves "spliting" the subtrahend (amount being subtracted) into two parts. The first part should be the exact amount that will reduce the minuend (the first number) to ten (or multiple of ten as the case may be) and the second part is the leftover amount. The strategy helps students internalize a mental strategy for subtracting across tens. For example, with the question 15 - 9, students first recognize that they need to subtract 5 to get 10, so they split the 9 into 5 and 4. Subtracting 5 from 15 results in 10 and subtracting 4 more results in 6, so 15 - 9 = 6. This strategy can be used any time students need to subtract "over" a multiple of ten and there are many worksheets in this section to practice it. For example, subtracting 84 - 8, students recognize that they must subtract 4 from 84 to get 80 which leaves 4 more to subtract from 80 to get 76.

• Make Ten Strategy Worksheets with 10 and Multiples of 10 Make 10 Subtraction Strategy Make 20 Subtraction Strategy Make 30 Subtraction Strategy Make 40 Subtraction Strategy Make 50 Subtraction Strategy Make 60 Subtraction Strategy Make 70 Subtraction Strategy Make 80 Subtraction Strategy Make 90 Subtraction Strategy Make Multiples of 10 Subtraction Strategy

Long Subtraction Worksheets

Try teaching a mental math strategy for subtraction called counting up. Here is how it is done:

Start with the second number (the subtrahend) and count up by tens until you find the closest value to the first number (the minuend). Keep track of how many tens you counted. Add or subtract a single digit number to get the minuend exactly then adjust the tens by that amount. For the question, 84 - 35, start at 35, and count, 45, 55, 65, 75, 85 (five tens) and one down to get 84. Five tens minus one is 49. For the question 65 - 22, start at 22 and count, 32, 42, 52, 62 (four tens) and three up to get 65. Four tens and three is 43. The previous examples used two-digit numbers, but the strategy can swiftly be modified for larger numbers. How far can your students go with it? Here is an example with three-digit numbers:

Let's use the question 927 - 648. First, count up by hundreds to 948 (that's 300). Then count down by tens to 928 (that's -20). Finally count down by ones to 927 (that's one). 300 - 20 - 1 = 279. That's almost easier than adding!

The multi-digit or long subtraction worksheets in the first part of this section are classic long subtraction worksheets with randomly generated numbers. Regrouping should be necessary about half of the time. Versions with ALL regrouping and NO regrouping follow. If you would like to see numbers with thousands separators, look a little further down and choose the appropriate version for your location.

• Subtracting up to 3-Digit Numbers with Some Regrouping Subtracting 2-Digit from 2-Digit Numbers with Some Regrouping ✎ Subtracting 2-Digit from 3-Digit Numbers with Some Regrouping ✎ Subtracting 3-Digit from 3-Digit Numbers with Some Regrouping ✎ 3-Digit Expanded Form Subtraction Subtracting 3-Digit from 4-Digit Numbers with Some Regrouping ✎
• Subtracting up to 3-Digit Numbers with Some Regrouping (Large Print) Subtracting 1-Digit from 2-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 2-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 1-Digit from 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 1- to 3-Digit from 1- to 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 4-Digit Numbers with Some Regrouping ( Large Print ) ✎
• Subtracting 4- to 9-Digit Numbers with Some Regrouping Subtracting 4-Digit from 4-Digit Numbers with Some Regrouping ✎ Subtracting 4-Digit from 5-Digit Numbers with Some Regrouping ✎ Subtracting 5-Digit from 5-Digit Numbers with Some Regrouping ✎ Subtracting 5-Digit from 6-Digit Numbers with Some Regrouping ✎ Subtracting 6-Digit from 6-Digit Numbers with Some Regrouping ✎ Subtracting 6-Digit from 7-Digit Numbers with Some Regrouping ✎ Subtracting 7-Digit from 7-Digit Numbers with Some Regrouping ✎ Subtracting 7-Digit from 8-Digit Numbers with Some Regrouping ✎ Subtracting 8-Digit from 8-Digit Numbers with Some Regrouping ✎ Subtracting 8-Digit from 9-Digit Numbers with Some Regrouping ✎ Subtracting 9-Digit from 9-Digit Numbers with Some Regrouping ✎
• Subtracting 4- to 6-Digit Numbers with Some Regrouping (Large Print) Subtracting 4-Digit from 4-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 4-Digit from 5-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 5-Digit from 5-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 5-Digit from 6-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 6-Digit from 6-Digit Numbers with Some Regrouping ( Large Print ) ✎

For students who need a little extra help with lining things up, these long subtraction worksheets have the digits spaced farther apart on a grid. The answer keys also show the carrying values to help diagnose where things went wrong (but hopefully they won't).

• Long Subtraction Worksheets with Grid Support 2-Digit Minus 2-Digit Subtraction With Grid Support 3-Digit Minus 2-Digit Subtraction With Grid Support 3-Digit Minus 3-Digit Subtraction With Grid Support 4-Digit Minus 3-Digit Subtraction With Grid Support 4-Digit Minus 4-Digit Subtraction With Grid Support 5-Digit Minus 4-Digit Subtraction With Grid Support 5-Digit Minus 5-Digit Subtraction With Grid Support 6-Digit Minus 5-Digit Subtraction With Grid Support 6-Digit Minus 6-Digit Subtraction With Grid Support 2- to 4-Digit Minus 2- to 4-Digit Subtraction With Grid Support 3- to 6-Digit Minus 3- to 6-Digit Subtraction With Grid Support

The next long subtraction worksheets include questions that require regrouping at every step. They can be frustrating and difficult for students who are not familiar with the concept of subtraction. Try showing them with base ten blocks how regrouping works.

• Subtracting up to 3-Digit Numbers with All Regrouping Subtracting 1-Digit Numbers with ALL Regrouping ✎ Subtracting 2-Digit Numbers with ALL Regrouping ✎ Subtracting 3-Digit Numbers with ALL Regrouping ✎
• Subtracting up to 3-Digit Numbers with All Regrouping (Large Print) Subtracting 1-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 2-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 3-Digit Numbers with ALL Regrouping ( Large Print ) ✎
• Subtracting 4- to 8-Digit Numbers with All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping ✎ Subtracting 5-Digit Numbers with ALL Regrouping ✎ Subtracting 6-Digit Numbers with ALL Regrouping ✎ Subtracting 7-Digit Numbers with ALL Regrouping ✎ Subtracting 8-Digit Numbers with ALL Regrouping ✎
• Subtracting 4- to 6-Digit Numbers with All Regrouping (Large Print) Subtracting 4-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 5-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 6-Digit Numbers with ALL Regrouping ( Large Print ) ✎

Some students require a little extra help when learning to subtract large numbers. These subtraction worksheets include questions where the regrouping step has been eliminated. This might help students learn a subtraction algorithm before learning about regrouping.

• Subtracting up to 3-Digit Numbers with No Regrouping Subtracting 2-Digit from 2-Digit Numbers with NO Regrouping ✎ Subtracting 2-Digit from 3-Digit Numbers with NO Regrouping ✎ Subtracting 3-Digit from 3-Digit Numbers with NO Regrouping ✎ Subtracting 2-Digit from 4-Digit Numbers with NO Regrouping ✎ Subtracting 3-Digit from 4-Digit Numbers with NO Regrouping ✎
• Subtracting up to 3-Digit Numbers with No Regrouping (Large Print) Subtracting 2-Digit from 2-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 3-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 3-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 4-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 4-Digit Numbers with NO Regrouping ( Large Print ) ✎
• Subtracting 4- to 9-Digit Numbers with No Regrouping Subtracting 4-Digit from 4-Digit Numbers with NO Regrouping ✎ Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping ✎
• Subtracting 4- to 6-Digit Numbers with No Regrouping (Large Print) Subtracting 4-Digit from 4-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping ( Large Print ) ✎

Why horizontal subtraction worksheets? Students can show their understanding of place value and number sense if they do not already have the numbers lined up. Vertical subtraction is often learned based on a student's understanding of single-digit subtraction, but looking at the whole number is lost in the algorithm.

• Horizontally Arranged 2-Digit Minus 1-Digit Questions 2-digit Minus 1-Digit Horizontal Subtraction (100 Questions) ✎ 2-digit Minus 1-Digit Horizontal Subtraction (50 Questions) ✎ 2-digit Minus 1-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
• Horizontally Arranged 2-Digit Minus 2-Digit Questions 2-digit Minus 2-Digit Horizontal Subtraction (100 Questions) ✎ 2-digit Minus 2-Digit Horizontal Subtraction (50 Questions) ✎ 2-digit Minus 2-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
• Horizontally Arranged 3-Digit Minus 1-Digit Questions 3-digit Minus 1-Digit Horizontal Subtraction (100 Questions) ✎ 3-digit Minus 1-Digit Horizontal Subtraction (50 Questions) ✎ 3-digit Minus 1-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
• Horizontally Arranged 3-Digit Minus 2-Digit Questions 3-digit Minus 2-Digit Horizontal Subtraction (50 Questions) ✎ 3-digit Minus 2-Digit Horizontal Subtraction (25 Questions; Large Print) ✎ 3-Digit Minus 2-Digit Horizontal Subtraction ( All Regrouping ; 100 Questions)
• Horizontally Arranged 3-Digit Minus 3-Digit Questions 3-Digit Minus 3-Digit Horizontal Subtraction (50 Questions) ✎ 3-Digit Minus 3-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
• Horizontally Arranged Various-Digit Minus Various-Digit Questions Various-Digit Minus Various-Digit Horizontal Subtraction (50 Questions) ✎ Various-Digit Minus Various-Digit Horizontal Subtraction (25 Questions; Large Print) ✎

Many students in English-speaking countries are used to seeing numbers with comma-separated thousands.

• Long Subtraction Worksheets with Comma Separated Thousands Subtracting 2-Digit from 4-Digit Numbers (Comma Separated) ✎ Subtracting 3-Digit from 4-Digit Numbers (Comma Separated) ✎ Subtracting 4-Digit from 4-Digit Numbers (Comma Separated) ✎ Subtracting 2-Digit from 5-Digit Numbers (Comma Separated) ✎ Subtracting 3-Digit from 5-Digit Numbers (Comma Separated) ✎ Subtracting 4-Digit from 5-Digit Numbers (Comma Separated) ✎ Subtracting 5-Digit from 5-Digit Numbers (Comma Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 4 digits (Comma Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 5 digits (Comma Separated) ✎
• Long Subtraction Worksheets with Comma Separated Thousands and All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 5-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 6-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 7-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 8-Digit Numbers with ALL Regrouping (Comma Separated) ✎
• Long Subtraction Worksheets with Comma Separated Thousands and No Regrouping Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping (Comma Separated) ✎

Space-separated thousands are becoming more widely used, including in the United States. Canadian students have used both comma separated and space separated thousands for many years.

• Long Subtraction Worksheets with Space Separated Thousands Subtracting 2-Digit from 4-Digit Numbers (Space Separated) ✎ Subtracting 3-Digit from 4-Digit Numbers (Space Separated) ✎ Subtracting 4-Digit from 4-Digit Numbers (Space Separated) ✎ Subtracting 2-Digit from 5-Digit Numbers (Space Separated) ✎ Subtracting 3-Digit from 5-Digit Numbers (Space Separated) ✎ Subtracting 4-Digit from 5-Digit Numbers (Space Separated) ✎ Subtracting 5-Digit from 5-Digit Numbers (Space Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 4 digits (Space Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 5 digits (Space Separated) ✎
• Long Subtraction Worksheets with Space Separated Thousands and All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 5-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 6-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 7-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 8-Digit Numbers with ALL Regrouping (Space Separated) ✎
• Long Subtraction Worksheets with Space Separated Thousands and No Regrouping Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping (Space Separated) ✎

Even though period separated thousands are not common in the English-speaking world, we provide these for our friends in other countries who may find them useful.

• Long Subtraction Worksheets with Period Separated Thousands Subtracting 2-Digit from 4-Digit Numbers (Period Separated) ✎ Subtracting 3-Digit from 4-Digit Numbers (Period Separated) ✎ Subtracting 4-Digit from 4-Digit Numbers (Period Separated) ✎ Subtracting 2-Digit from 5-Digit Numbers (Period Separated) ✎ Subtracting 3-Digit from 5-Digit Numbers (Period Separated) ✎ Subtracting 4-Digit from 5-Digit Numbers (Period Separated) ✎ Subtracting 5-Digit from 5-Digit Numbers (Period Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 4 digits (Period Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 5 digits (Period Separated) ✎
• Long Subtraction Worksheets with Period Separated Thousands and All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 5-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 6-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 7-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 8-Digit Numbers with ALL Regrouping (Period Separated) ✎
• Long Subtraction Worksheets with Period Separated Thousands and No Regrouping Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping (Period Separated) ✎

Various Other Long Subtraction Worksheets

Generally, a student would not regroup to determine the complements of 10, 100, 1000, etc. One strategy that could be used is as follows: working from left to right, a student would take each digit in the subtrahend and figure out its nines complement. If the digit was 3, for example, the nines complement of 3 is 6. For the last digit (ones), the student would use the tens complement. For example, a typical question is 1000 - 456. The nines complement of 4 is 5, the nines complement of 5 is 4 and the tens complement of 6 is 4. Putting it all together, the student would get 5 4 4 or 544 = 1000 - 456.

• Calculating Complements of Powers of Ten (Subtracting Across Zeros) Complements of 10 Complements of 100 Complements of 1000 Complements of 10000 Complements of 100 and 1000 Complements of 1000 and 10000 Complements of 100, 1000 and 10000

A similar strategy is employed with the next worksheets except students must adapt to calculating the largest place value number.

• Calculating Complements of Multiples of Powers of Ten (Subtracting Across Zeros) Subtracting from multiples of 10 Subtracting from multiples of 100 Subtracting from multiples of 1000 Subtracting from multiples of 10000 Subtracting from a mixture of multiples of 100 and 1000 Subtracting from a mixture of multiples of 1000 and 10000 Subtracting from a mixture of multiples of 100, 1000 and 10000

These worksheets are meant to give students practice dealing with 0's in the middles of subtraction questions. Whether using pencil and paper or mental arithmetic, it is always a good idea to make sure students know what to do when they encounter zeros.

• Subtracting Across Zeros in the Middle (Ones Always Need Regrouping) 3-Digit Subtraction across zeros in the middle ( Ones always need regrouping ) 4-Digit Subtraction across zeros in the middle ( Ones always need regrouping ) 5-Digit Subtraction across zeros in the middle ( Ones always need regrouping )
• Subtracting Across Zeros in the Middle (Ones Sometimes Need Regrouping) 3-Digit Subtraction across zeros in the middle ( Ones sometimes need regrouping ) 4-Digit Subtraction across zeros in the middle ( Ones sometimes need regrouping ) 5-Digit Subtraction across zeros in the middle ( Ones sometimes need regrouping )

Subtracting numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.

• Subtracting in Other Base Number Systems Subtracting Binary Numbers (Base 2) Subtracting Ternary Numbers (Base 3) Subtracting Quaternary Numbers (Base 4) Subtracting Quinary Numbers (Base 5) Subtracting Senary Numbers (Base 6) Subtracting Octal Numbers (Base 8) Subtracting Duodecimal Numbers (Base 12) Subtracting Hexadecimal Numbers (Base 16) Subtracting Vigesimal Numbers (Base 20) Subtracting Hexatrigesimal Numbers (Base 36) Subtracting Various Numbers (Various Bases)

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Subtraction Word Problem Worksheets

The extensive set of subtraction word problems featured here will require the learner to find the difference between minuends and subtrahends, which includes problems with regrouping and without regrouping. This large collection of printable word problem worksheets, ideal for children in kindergarten through grade 4 features scenarios that involve single-digit subtraction, two-digit subtraction, three-digit subtraction, and subtraction of large numbers up to six digits. Give yourself a head-start with our free subtraction worksheets!

Word Problems for Beginners: 0 to 10

Find the difference between the numbers that ranges from 0 to 10 in the set of kindergarten worksheets featured here. Use the answer key to verify your responses.

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Subtraction within 20

Ascend from a beginner to a proficient in performing subtraction up to 20 as you explore this bunch of well-researched word problems and work out the difference within 20.

Two-digit Subtraction: No Regrouping (No Borrowing)

The series of worksheets for grade 1 and grade 2 presented here involve two-digit subtraction word problems that do not require regrouping. Find the differences between the two-digit subtrahends and minuends featured here.

Two-digit Subtraction: Regrouping (Borrowing)

The two-digit subtraction word problems presented in the 2nd grade worksheets here require regrouping (borrowing). Determine the difference between the two-digit numbers by following the place value columns correctly.

Theme based Subtraction Problems

The colorful theme-based worksheet pdfs for kids in 1st grade through 3rd grade are based on three engaging real-life themes - Beach, Italian Ice and Birthday Party.

Three-digit and Two-digit Subtraction

The set of subtraction word problem pdfs featured here will require grade 3 student to find the difference between three-digit minuends and two-digit subtrahends. Use the answer keys to verify your responses.

Three-digit Subtraction Word Problems

Each printable worksheet contains five word problems finding difference between three-digit numbers. Some problems may require regrouping.

Four-digit Subtraction Word Problems

This section contains subtraction word problems on finding the difference between four-digit numbers. Both borrowing and no borrowing problems are included. Some problems may involve subtraction across zero.

Advanced: Large Number Subtraction

The word problems featured in the 4th grade pdf worksheets here include large numbers with minuends and subtrahends up to six digits. Determine the difference between the large numbers by following the place value columns correctly.

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Problem Solving on Subtraction

Problem solving on subtraction will help us to get the idea on how to solve the basic subtraction statement problems.

1.  Eight birds sat on a wire. Three birds flew away. How many were left?

Total number of birds sat on a wire = 8

Number of birds flew away = 3

Therefore, number of birds left = 8 - 3 = 5

2.  Sam had 7 dollars. He spent 4 dollars. How many dollars is he left with?

Total amount of money Sam had = $7

He spent = $4

Therefore, amount of money left with him = $7 - $4 = $3

3. Five boats were tied up. Four of the boats sailed away. How many were left?

Total number of boats tied up = 5

Number of boats sailed away = 4

Therefore, number of boats were left = 5 - 4 = 1

4. Ron had 10 stamps. His father took 2 stamps. How many stamps does Ron have now?

Total number of stamps Ron had = 10

Number of stamps his father took = 2

Therefore, number of stamps he have now = 10 - 2 = 8

5. Diana had 18 toffees. She gave 5 toffees to her friend. How many toffees left with her?

Total number of toffees Diana had = 18

Number of toffees she gave to her friend = 5

Therefore, number of toffees left = 18 - 5 = 13

More examples on statement problem solving on subtraction:

6. Mr. Daniel had 39 goats in a pasture. When he opened the pasture gate, 13 goats went out. How many goats remained in? 

Total number of goats in a pasture Mr. Daniel had = 39

Number of goats went out = 13

Therefore, number of goats remained in = 39 - 13 = 26

7. Derek’s father is 47 years old. His mother is 35 years old. What is the difference of their ages?

Age of Derek’s father = 47 years

Age of his mother = 35 years

Therefore, difference of their ages = 47 - 35 = 12 years

2nd Grade Math Practice From Problem Solving on Subtraction to HOME PAGE

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Subtraction

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

What Is Subtraction?

Subtraction is an operation used to find the difference between numbers . When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two". When we subtract 7 from 9, (9 - 7) we get 2. Here, we performed the subtraction operation on two numbers 9 and 7 to get the difference of 2.

Subtraction Symbol

In mathematics, we have different symbols. The subtraction symbol is one of the important math symbols that we use while performing subtraction. In the above section, we read about subtracting two numbers 9 and 7. If we observe this subtraction: (9 - 7 = 2), the symbol (-) connects the two numbers and completes the given expression. This symbol is also known as the minus sign.

Subtraction Formula

When we subtract two numbers, we use some terms which are used in the subtraction expression:

• Minuend: The number from which the other number is subtracted.
• Subtrahend: The number which is to be subtracted from the minuend.
• Difference: The final result after subtracting the subtrahend from the minuend.

The subtraction formula is written as: Minuend - Subtrahend = Difference

Let us understand the subtraction formula or the mathematical equation of subtraction with an example.

Here, 9 is the minuend, 7 is the subtrahend, and 2 is the difference.

How To Solve Subtraction Problems?

While solving subtraction problems, one-digit numbers can be subtracted in a simple way, but for larger numbers, we split the numbers into columns using their respective place values , like Ones, Tens, Hundreds, Thousands, and so on. While solving such problems we may encounter some cases with borrowing and some without borrowing. Subtraction with borrowing is also known as subtraction with regrouping. When the minuend is smaller than the subtrahend, we use the regrouping method. While regrouping, we borrow 1 number from the preceding column to make the minuend bigger than the subtrahend. Let us understand this with the help of a few examples.

Subtraction Without Regrouping

Example: Subtract 25632 from 48756.

Note: In subtraction, we always subtract the smaller number from the larger number to get the correct answer.

Solution: Follow the given steps and try to relate them with the following figure.

Step 1: Start with the digit at ones place. (6 - 2 = 4) Step 2: Move to the tens place. (5 - 3 = 2) Step 3: Now subtract the digits at hundreds place. (7 - 6 = 1) Step 4: Now subtract the digits at thousands place. (8 - 5 = 3) Step 5: Finally, subtract the digits at ten thousands place. (4 - 2 = 2) Step 6: Therefore, the difference between the two given numbers is: 48756 - 25632 = 23124.

Subtraction With Regrouping

Example: Subtract 3678 from 8162.

Solution: Follow the given steps and try to relate them with the following figure. We need to solve: 8162 - 3678 Step 1: Start subtracting the digits at ones place. We can see that 8 is greater than 2. So, we will borrow 1 from the tens column which will make it 12. Now, 12 - 8 = 4 ones. Step 2: After giving 1 to the ones column in the previous step, 6 becomes 5. Now, let us subtract the digits at the tens place (5 - 7). Here, 7 is greater than 5, so we will borrow 1 from the hundreds column. This will make it 15. So,15 - 7 = 8 tens. Step 3: In step 2 we had given 1 to the tens column, so we are left with 0 at the hundreds place. To subtract the digits on the hundreds place, i.e., (0 - 6) we will borrow 1 from the thousands column. This will make it 10. So, 10 - 6 = 4 hundreds. Step 4: Now, let us subtract the digits at the thousands place. After giving 1 to the hundreds column, we have 7. So, 7 - 3 = 4 Step 5: Therefore, the difference between the two given numbers is: 8162 - 3678 = 4484

Subtraction Using Number Line

A number line is a visual aid that helps us understand subtraction because it allows us to jump backward and forward on each number. To understand how this works, let us explore subtraction using a number line. Let us subtract 4 from 9 using a number line. We will start by marking the number 9 on the number line. When we subtract using a number line, we count by moving one number at a time towards the left-hand side. Since we are subtracting 4 from 9, we will move 4 times to the left. The number on which you land after 4 backward jumps, is the answer. Thus, 9 - 4 = 5.

Real Life Subtraction Word Problems

The concept of subtraction is often used in our day-to-day activities. Let us understand how to solve real-life subtraction word problems with the help of an interesting example.

Example: A soccer match had a total of 4535 spectators. After the first innings, 2332 spectators left the stadium. Find the number of remaining spectators.

Solution: Given: The total number of spectators present in the first innings = 4535; The number of spectators who left the stadium after the first innings = 2332 Here, 4535 is the minuend and 2332 is the subtrahend.

Th H T O 4 5 3 5 -2 3 3 2 2 2 0 3

Therefore, the number of remaining spectators = 2203.

Important Notes on Subtraction:

Here are a few important notes that you can follow while performing subtraction in your everyday life.

• Any subtraction problem can be transformed into an addition problem and vice-versa.
• Subtracting 0 from any number gives the number itself as the difference.
• When 1 is subtracted from any number, the difference equals the predecessor of the number.
• Words like "Minus", "Less", "Difference", "Decrease", "Take Away" and "Deduct" indicate that you need to subtract one number from another.

Topics Related to Subtraction

Check out these interesting articles to know about subtraction and its related topics.

• Binary Subtraction
• Subtraction Calculator
• Addition and Subtraction of Fractions
• Subtraction of Complex Numbers
• Subtraction of Fractions

Subtraction Examples

Example 1: In an International cricket match, Sri Lanka scored 236 runs and India scored 126 runs. How many more runs should India score to be equal to the number of runs scored by Sri Lanka?

Runs scored by Sri Lanka = 236; Runs scored by India = 126 To find the number of runs that India should score more to be equal to the number of runs scored by Sri Lanka, we will subtract 126 from 236.

H T O 2 3 6 - 1 2 6 1 1 0

Therefore, India must score 110 more runs to be equal to Sri Lanka's runs.

Example 2: Jerry collected 189 seashells and Eva collected 54 shells. Who collected more seashells and by how much?

Number of shells collected by Jerry = 189; Number of shells collected by Eva = 54

This shows that Jerry collected more seashells. Let us subtract 189 - 54 to get the difference.

H T O 1 8 9 - 0 5 4 1 3 5

Therefore, Jerry collected 135 seashells more than Eva.

Example 3: During an annual Easter egg hunt, the participants found 2469 eggs in the clubhouse, out of which 54 Easter eggs were broken. Can you find out the number of unbroken eggs?

The number of easter eggs found in the Clubhouse = 2469; Number of easter eggs that were broken = 54; The total number of unbroken eggs=?

Now, we will subtract the number of broken eggs from the total number of eggs.

Th H T O 2 4 6 9 - 5 4 2 4 1 5

Therefore, the number of unbroken eggs are 2415.

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Practice Questions on Subtraction

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FAQs on Subtraction

Where do we use subtraction.

Subtraction is used in our day-to-day life. For example, if we want to know how much money we spent on the items that we bought, or, how much money is left with us, or, if we want to calculate the time left in finishing a task, we use subtraction.

What Are the Types of Subtraction?

The types of subtraction mean the various methods used in subtraction. For example, subtraction with and without regrouping, subtraction using number charts, subtraction using number line, the subtraction of small numbers using you fingers, and so on.

What Are Subtraction Strategies?

Subtraction strategies are different ways in which subtraction can be learned. For example, using a number line, with the help of a Place Value Chart, separating the Tens and Ones and then subtracting them separately, and many others.

Give Some Subtraction Examples.

There can be various real-life examples of subtraction. For example, if you have 5 apples and your friend ate 3 apples. Using subtraction, we can find out the number of remaining apples: 5 - 3 = 2. So, 2 apples are left with you. Similarly, if there are 16 students in a class, out of which 9 are girls, then we can find out the number of boys in the class by subtracting 9 from 16. (16 - 9 = 7). So, we know that there are 7 boys in the class.

What Are the Three Parts of Subtraction?

The 3 parts of subtraction are named as follows:

• Minuend: The number from which we subtract the other number is known as the minuend.
• Subtrahend: The number which is subtracted from the minuend is known as the subtrahend.
• Difference: The final result obtained after performing subtraction is known as the difference.

How Do You Write a Subtraction?

While writing subtraction, the two important symbols are '-' (minus) and '=' (equal to). The minus sign means when one number is being subtracted from the other number. And the equal to sign delivers the final result.

Subtraction Word Problems (1-step word problems)

These lessons look at some examples of subtraction word problems that can be solved in one step, illustrating the use of bar models or block diagrams in the solution process.

Related Pages 2-step Subtraction Word Problems Using Bar Models Solving Word Problems Using Bar Models Singapore Math More Word Problems

We will illustrate how block diagrams can be used to help you to visualize the subtraction word problems in terms of the information given and the data that needs to be found. The block diagrams or block modeling method is used in Singapore Math.

Example: Jessica has 1135 beads. 604 beads are red and the rest are blue. How many blue beads does she have?

1135 – 604 = 531

She has 531 blue beads.

Example: James and Ken donated $2300 to a charitable organization. Ken donated $658. How much did James donate?

2300 – 658 = 1642 James donated $1642.

Example: The price of a car is $2795 and the price of a motorbike is $1063. What is the difference between the prices of the 2 vehicles?

Solution: 2795 – 1063 = 1732

The difference between the prices of the 2 vehicles is $1732.

Example: There are 967 chairs in a hall. During an event, 761 chairs were occupied. How many chairs were not occupied?

967 – 761 = 206 206 chairs were not occupied.

Examples of subtraction word problems

134 girls and 119 boys took part in an art competition. How many more girls than boys were there?

Mei Lin saved $184. She saved $63 more than Betty. How much did Betty saved?

John read 32 pages in the morning. He read 14 pages less in the afternoon. a) How many pages did he read in the afternoon? b) How many pages did they read altogether?

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model.

Example: Mr. Oliver bought 88 pencils. he sold 26 of them. How many pencils did he have left?

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model. Because the part is missing, this is a subtraction problem.

Example: There are 98 hats, 20 of them are pink and the rest are yellow. How many yellow hats are there?

Example: Cayla did 88 sit-ups in the morning. Nekira did 32 sit-ups at night. How many more sit-ups did Cayla do than Nekira?

How to use bar modeling in Singapore math to solve word problems that deal with comparing?

Example: Adam has 11 fewer lollipops than Hope. If Adam has 16 lollipops, how many lollipop does Hope have?

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Solving Equations Using Subtraction

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Subtraction Word Problems

Subtraction helps us to find the difference. Subtraction can tell us how many are left.

Subtraction is easy to do! Subtraction is the opposite of addition. We can use subtraction in word, or story, problems. Subtraction skills can help us solve correctly!

For example:

Let’s take a look at the example above. We are subtracting because some of the dolphins swim away. There are 10 dolphins to start with and 5 swim away. We need to figure out how many are left. We can do this by subtracting 10 – 5 to get our answer.

We write it like this:

10 – 5 = 5

There are 5 dolphins left!

Let’s look at another problem!

Let’s take a look at the example above. We are subtracting because some of the butterflies fly away. There are 11 butterflies to start with and 4 fly away. We need to figure out how many are left. We can do this by subtracting 11 – 4 to get our answer.

11 – 4 = 7

There are 7 butterflies left!

Amazing work! Let’s look at another problem together.

This time we will subtract strawberries. We are SUBTRACTING to find out how many are left because some have been eaten. We can see that there were nine strawberries to start with. Six of them have been eaten When we SUBTRACT 9 minus 6 , we have 3 left. We say: NINE minus SIX equals THREE. We write it like this:

9 – 6 = 3

Let’s try one more together!

This time we will subtract donuts. We are SUBTRACTING to find out how many are left because some have been eaten. We can see that there were ten donuts to start with. Six of them have been eaten When we SUBTRACT 10 minus 6 , we have 4 left. We say: TEN minus SIX equals FOUR. We write it like this:

10 – 6 = 4

There are many different words that are used to describe subtraction. For example, we can find out HOW MANY MORE there are or how many ARE LEFT. Here are several other examples:

Knowing these keywords will help you understand that in order to solve some problems, you must subtract. You might see these keywords in math story problems.

There are many strategies you can use to help you subtract correctly. We will learn about these in other lessons.

Now, let’s practice!

• Subtraction
• Subtraction By 1
• Subtraction By 10
• Adding Doubles
• Adding by 10
• Even Numbers
• Mass (Weight)

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Practice Question 1

Find the difference to solve.

REVEAL THE ANSWER 13 - 8 = 5 SANDCASTLES

Practice Question 2

Solve the subtraction problem below.

REVEAL THE ANSWER 7 - 4 = 3 BALLOONS

Practice Question 3

Use the key words to help you solve.

REVEAL THE ANSWER 20 - 5 = 15 SANDWICHES

Practice Question 4

Find out how many are left.

REVEAL THE ANSWER 16 - 11 = 5 BUGS

Practice Question 5

Solve by subtracting.

REVEAL THE ANSWER 17 - 9 = 8 FISH

Now you’re ready to take a quick quiz on adding with subtraction word problems! Click below!

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Subtraction Word Problems — Examples & Practice - Expii

Subtraction word problems — examples & practice, explanations (3).

Words to Math: Subtraction

In this section, we will learn to translate phrases into a mathematical expression by identifying key words that indicate subtraction .

When talking about subtraction, you will most likely see the terms " subtract ", " less than ", " minus ", " difference ", and " decreased by ". There are different such terms for addition , multiplication , and division .

Let’s take a look at an example.

Sam has 6 pencils. His friend, Jack, has 3 pencils less than Sam. How many pencils does Jack have?

We know that the term " less than " often refers to subtraction, so the operator ‘−’ is required.

Since Sam has 6 pencils and Jack had 3 less than Sam, we can rewrite this as a mathematical expression.

Jack = Sam (6 Pencils) − 3 Pencils = 3 Pencils

When talking about equality, you will most likely see the terms " equal to ", " is ", " the same as ", and " amounts to ".

Here are some phrases about subtraction translated into a mathematical expression.

• 2 less than 6 is 4→6−2=4
• 13 minus 1 equals to 12→13−1=12
• The difference between 10 and 7 is 3→10−7=3

This technique is useful for solving equations too. In that case, we're subtracting the same number from both sides of an equation.

We are now going to take a look at some of the types of problems you might encounter about subtraction word problems.

Example 1 Translate the following into a mathematical expression: 15 minus 8 is 7.

Related Lessons

Word problems with subtraction.

The key to solving word problems is to translate them into mathematical expressions. This is made easier if you can pick out key phrases that tell you what type of operation the problem is asking for. We'll call these signal words .

Image source: By OpenClipartVectors CC0 , via pixabay.com

Which subtraction signal word is included in this word problem?

(Video) Writing an Algebraic Expression from a Word Problem

by mrmaisonet

This video by mrmaisonet works through a few word problem examples with an identification of key words.

The problem he looks at is:

Katie has 12 fewer dollars than Julia has. If d equals the amount of money Julia has, write an expression for the amount of money Katie has.

Here d is a variable . Our expression will have the variable in it somewhere. The key phrase is 12 fewer. This means Katie has the same as Julia minus 12. Therefore, we can say Katie has: d−12

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8.2: Solve Equations Using the Subtraction and Addition Properties of Equality

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Learning Objectives

By the end of this section, you will be able to:

• Solve equations using the Subtraction and Addition Properties of Equality
• Solve equations that need to be simplified
• Translate an equation and solve
• Translate and solve applications

Be Prepared 8.1

Before you get started, take this readiness quiz.

Solve: n − 12 = 16 . n − 12 = 16 . If you missed this problem, review Example 2.33.

Be Prepared 8.2

Translate into algebra ‘five less than x .’ x .’ If you missed this problem, review Example 2.24.

Be Prepared 8.3

Is x = 2 x = 2 a solution to 5 x − 3 = 7 ? 5 x − 3 = 7 ? If you missed this problem, review Example 2.28.

We are now ready to “get to the good stuff.” You have the basics down and are ready to begin one of the most important topics in algebra: solving equations. The applications are limitless and extend to all careers and fields. Also, the skills and techniques you learn here will help improve your critical thinking and problem-solving skills. This is a great benefit of studying mathematics and will be useful in your life in ways you may not see right now.

Solve Equations Using the Subtraction and Addition Properties of Equality

We began our work solving equations in previous chapters. It has been a while since we have seen an equation , so we will review some of the key concepts before we go any further.

We said that solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle.

Solution of an Equation

A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.

In the earlier sections, we listed the steps to determine if a value is a solution. We restate them here.

Determine whether a number is a solution to an equation.

• Step 1. Substitute the number for the variable in the equation.
• Step 2. Simplify the expressions on both sides of the equation.
• If it is true, the number is a solution.
• If it is not true, the number is not a solution.

Example 8.1

Determine whether y = 3 4 y = 3 4 is a solution for 4 y + 3 = 8 y . 4 y + 3 = 8 y .

Since y = 3 4 y = 3 4 results in a true equation, 3 4 3 4 is a solution to the equation 4 y + 3 = 8 y . 4 y + 3 = 8 y .

Is y = 2 3 y = 2 3 a solution for 9 y + 2 = 6 y ? 9 y + 2 = 6 y ?

Is y = 2 5 y = 2 5 a solution for 5 y − 3 = 10 y ? 5 y − 3 = 10 y ?

We introduced the Subtraction and Addition Properties of Equality in Solving Equations Using the Subtraction and Addition Properties of Equality. In that section, we modeled how these properties work and then applied them to solving equations with whole numbers. We used these properties again each time we introduced a new system of numbers. Let’s review those properties here.

Subtraction and Addition Properties of Equality

Subtraction Property of Equality

For all real numbers a , b , a , b , and c , c , if a = b , a = b , then a − c = b − c . a − c = b − c .

Addition Property of Equality

For all real numbers a , b , a , b , and c , c , if a = b , a = b , then a + c = b + c . a + c = b + c .

When you add or subtract the same quantity from both sides of an equation, you still have equality.

We introduced the Subtraction Property of Equality earlier by modeling equations with envelopes and counters. Figure 8.2 models the equation x + 3 = 8 . x + 3 = 8 .

The goal is to isolate the variable on one side of the equation. So we ‘took away’ 3 3 from both sides of the equation and found the solution x = 5 . x = 5 .

Some people picture a balance scale, as in Figure 8.3, when they solve equations.

The quantities on both sides of the equal sign in an equation are equal, or balanced. Just as with the balance scale, whatever you do to one side of the equation you must also do to the other to keep it balanced.

Let’s review how to use Subtraction and Addition Properties of Equality to solve equations. We need to isolate the variable on one side of the equation. And we check our solutions by substituting the value into the equation to make sure we have a true statement.

Example 8.2

Solve: x + 11 = −3 . x + 11 = −3 .

To isolate x , x , we undo the addition of 11 11 by using the Subtraction Property of Equality.

Since x = −14 x = −14 makes x + 11 = −3 x + 11 = −3 a true statement, we know that it is a solution to the equation.

Solve: x + 9 = −7 . x + 9 = −7 .

Solve: x + 16 = −4 . x + 16 = −4 .

In the original equation in the previous example, 11 11 was added to the x x , so we subtracted 11 11 to ‘undo’ the addition. In the next example, we will need to ‘undo’ subtraction by using the Addition Property of Equality .

Example 8.3

Solve: m + 4 = −5 . m + 4 = −5 .

Solve: n − 6 = −7 . n − 6 = −7 .

Solve: x − 5 = −9 . x − 5 = −9 .

Now let’s review solving equations with fractions.

Example 8.4

Solve: n − 3 8 = 1 2 . n − 3 8 = 1 2 .

Solve: p − 1 3 = 5 6 . p − 1 3 = 5 6 .

Solve: q − 1 2 = 1 6 . q − 1 2 = 1 6 .

In Solve Equations with Decimals, we solved equations that contained decimals. We’ll review this next.

Example 8.5

Solve a − 3.7 = 4.3 . a − 3.7 = 4.3 .

Solve: b − 2.8 = 3.6 . b − 2.8 = 3.6 .

Try It 8.10

Solve: c − 6.9 = 7.1 . c − 6.9 = 7.1 .

Solve Equations That Need to Be Simplified

In the examples up to this point, we have been able to isolate the variable with just one operation. Many of the equations we encounter in algebra will take more steps to solve. Usually, we will need to simplify one or both sides of an equation before using the Subtraction or Addition Properties of Equality. You should always simplify as much as possible before trying to isolate the variable.

Example 8.6

Solve: 3 x − 7 − 2 x − 4 = 1 . 3 x − 7 − 2 x − 4 = 1 .

The left side of the equation has an expression that we should simplify before trying to isolate the variable.

The solution checks.

Try It 8.11

Solve: 8 y − 4 − 7 y − 7 = 4 . 8 y − 4 − 7 y − 7 = 4 .

Try It 8.12

Solve: 6 z + 5 − 5 z − 4 = 3 . 6 z + 5 − 5 z − 4 = 3 .

Example 8.7

Solve: 3 ( n − 4 ) − 2 n = −3 . 3 ( n − 4 ) − 2 n = −3 .

The left side of the equation has an expression that we should simplify.

Try It 8.13

Solve: 5 ( p − 3 ) − 4 p = −10 . 5 ( p − 3 ) − 4 p = −10 .

Try It 8.14

Solve: 4 ( q + 2 ) − 3 q = −8 . 4 ( q + 2 ) − 3 q = −8 .

Example 8.8

Solve: 2 ( 3 k − 1 ) − 5 k = −2 − 7 . 2 ( 3 k − 1 ) − 5 k = −2 − 7 .

Both sides of the equation have expressions that we should simplify before we isolate the variable.

Try It 8.15

Solve: 4 ( 2 h − 3 ) − 7 h = −6 − 7 . 4 ( 2 h − 3 ) − 7 h = −6 − 7 .

Try It 8.16

Solve: 2 ( 5 x + 2 ) − 9 x = −2 + 7 . 2 ( 5 x + 2 ) − 9 x = −2 + 7 .

Translate an Equation and Solve

In previous chapters, we translated word sentences into equations. The first step is to look for the word (or words) that translate(s) to the equal sign. Table 8.1 reminds us of some of the words that translate to the equal sign.

Let’s review the steps we used to translate a sentence into an equation.

Translate a word sentence to an algebraic equation.

• Step 1. Locate the "equals" word(s). Translate to an equal sign.
• Step 2. Translate the words to the left of the "equals" word(s) into an algebraic expression.
• Step 3. Translate the words to the right of the "equals" word(s) into an algebraic expression.

Now we are ready to try an example.

Example 8.9

Translate and solve: five more than x x is equal to 26 . 26 .

Try It 8.17

Translate and solve: Eleven more than x x is equal to 41 . 41 .

Try It 8.18

Translate and solve: Twelve less than y y is equal to 51 . 51 .

Example 8.10

Translate and solve: The difference of 5 p 5 p and 4 p 4 p is 23 . 23 .

Try It 8.19

Translate and solve: The difference of 4 x 4 x and 3 x 3 x is 14 . 14 .

Try It 8.20

Translate and solve: The difference of 7 a 7 a and 6 a 6 a is −8 . −8 .

Translate and Solve Applications

In most of the application problems we solved earlier, we were able to find the quantity we were looking for by simplifying an algebraic expression. Now we will be using equations to solve application problems. We’ll start by restating the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve. When assigning a variable, choose a letter that reminds you of what you are looking for.

Example 8.11

The Robles family has two dogs, Buster and Chandler. Together, they weigh 71 71 pounds.

Chandler weighs 28 28 pounds. How much does Buster weigh?

Try It 8.21

Translate into an algebraic equation and solve: The Pappas family has two cats, Zeus and Athena. Together, they weigh 13 13 pounds. Zeus weighs 6 6 pounds. How much does Athena weigh?

Try It 8.22

Translate into an algebraic equation and solve: Sam and Henry are roommates. Together, they have 68 68 books. Sam has 26 26 books. How many books does Henry have?

Devise a problem-solving strategy.

• Step 1. Read the problem. Make sure you understand all the words and ideas.
• Step 2. Identify what you are looking for.
• Step 3. Name what you are looking for. Choose a variable to represent that quantity.
• Step 4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.
• Step 5. Solve the equation using good algebra techniques.
• Step 6. Check the answer in the problem and make sure it makes sense.
• Step 7. Answer the question with a complete sentence.

Example 8.12

Shayla paid $24,575 $24,575 for her new car. This was $875 $875 less than the sticker price. What was the sticker price of the car?

Try It 8.23

Translate into an algebraic equation and solve: Eddie paid $19,875 $19,875 for his new car. This was $1,025 $1,025 less than the sticker price. What was the sticker price of the car?

Try It 8.24

Translate into an algebraic equation and solve: The admission price for the movies during the day is $7.75 . $7.75 . This is $3.25 $3.25 less than the price at night. How much does the movie cost at night?

ACCESS ADDITIONAL ONLINE RESOURCES

• Solving One Step Equations By Addition and Subtraction
• Solve One Step Equations By Add and Subtract Whole Numbers (Variable on Left)
• Solve One Step Equations By Add and Subtract Whole Numbers (Variable on Right)

Section 8.1 Exercises

Practice makes perfect.

In the following exercises, determine whether the given value is a solution to the equation.

Is y = 1 3 y = 1 3 a solution of 4 y + 2 = 10 y ? 4 y + 2 = 10 y ?

Is x = 3 4 x = 3 4 a solution of 5 x + 3 = 9 x ? 5 x + 3 = 9 x ?

Is u = − 1 2 u = − 1 2 a solution of 8 u − 1 = 6 u ? 8 u − 1 = 6 u ?

Is v = − 1 3 v = − 1 3 a solution of 9 v − 2 = 3 v ? 9 v − 2 = 3 v ?

In the following exercises, solve each equation.

x + 7 = 12 x + 7 = 12

y + 5 = −6 y + 5 = −6

b + 1 4 = 3 4 b + 1 4 = 3 4

a + 2 5 = 4 5 a + 2 5 = 4 5

p + 2.4 = −9.3 p + 2.4 = −9.3

m + 7.9 = 11.6 m + 7.9 = 11.6

a − 3 = 7 a − 3 = 7

m − 8 = −20 m − 8 = −20

x − 1 3 = 2 x − 1 3 = 2

x − 1 5 = 4 x − 1 5 = 4

y − 3.8 = 10 y − 3.8 = 10

y − 7.2 = 5 y − 7.2 = 5

x − 15 = −42 x − 15 = −42

z + 5.2 = −8.5 z + 5.2 = −8.5

q + 3 4 = 1 2 q + 3 4 = 1 2

p − 2 5 = 2 3 p − 2 5 = 2 3

y − 3 4 = 3 5 y − 3 4 = 3 5

Solve Equations that Need to be Simplified

c + 3 − 10 = 18 c + 3 − 10 = 18

m + 6 − 8 = 15 m + 6 − 8 = 15

9 x + 5 − 8 x + 14 = 20 9 x + 5 − 8 x + 14 = 20

6 x + 8 − 5 x + 16 = 32 6 x + 8 − 5 x + 16 = 32

−6 x − 11 + 7 x − 5 = −16 −6 x − 11 + 7 x − 5 = −16

−8 n − 17 + 9 n − 4 = −41 −8 n − 17 + 9 n − 4 = −41

3 ( y − 5 ) − 2 y = −7 3 ( y − 5 ) − 2 y = −7

4 ( y − 2 ) − 3 y = −6 4 ( y − 2 ) − 3 y = −6

8 ( u + 1.5 ) − 7 u = 4.9 8 ( u + 1.5 ) − 7 u = 4.9

5 ( w + 2.2 ) − 4 w = 9.3 5 ( w + 2.2 ) − 4 w = 9.3

−5 ( y − 2 ) + 6 y = −7 + 4 −5 ( y − 2 ) + 6 y = −7 + 4

−8 ( x − 1 ) + 9 x = −3 + 9 −8 ( x − 1 ) + 9 x = −3 + 9

3 ( 5 n − 1 ) − 14 n + 9 = 1 − 2 3 ( 5 n − 1 ) − 14 n + 9 = 1 − 2

2 ( 8 m + 3 ) − 15 m − 4 = 3 − 5 2 ( 8 m + 3 ) − 15 m − 4 = 3 − 5

− ( j + 2 ) + 2 j − 1 = 5 − ( j + 2 ) + 2 j − 1 = 5

− ( k + 7 ) + 2 k + 8 = 7 − ( k + 7 ) + 2 k + 8 = 7

6 a − 5 ( a − 2 ) + 9 = −11 6 a − 5 ( a − 2 ) + 9 = −11

8 c − 7 ( c − 3 ) + 4 = −16 8 c − 7 ( c − 3 ) + 4 = −16

8 ( 4 x + 5 ) − 5 ( 6 x ) − x = 53 8 ( 4 x + 5 ) − 5 ( 6 x ) − x = 53

6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

Five more than x x is equal to 21 . 21 .

The sum of x x and −5 −5 is 33 . 33 .

Ten less than m m is −14 . −14 .

Three less than y y is −19 . −19 .

The sum of y y and −3 −3 is 40 . 40 .

Eight more than p p is equal to 52 . 52 .

The difference of 9 x 9 x and 8 x 8 x is 17 . 17 .

The difference of 5 c 5 c and 4 c 4 c is 60 . 60 .

The difference of n n and 1 6 1 6 is 1 2 . 1 2 .

The difference of f f and 1 3 1 3 is 1 12 . 1 12 .

The sum of −4 n −4 n and 5 n 5 n is −32 . −32 .

The sum of −9 m −9 m and 10 m 10 m is −25 . −25 .

In the following exercises, translate into an equation and solve.

Pilar drove from home to school and then to her aunt’s house, a total of 18 18 miles. The distance from Pilar’s house to school is 7 7 miles. What is the distance from school to her aunt’s house?

Jeff read a total of 54 54 pages in his English and Psychology textbooks. He read 41 41 pages in his English textbook. How many pages did he read in his Psychology textbook?

Pablo’s father is 3 3 years older than his mother. Pablo’s mother is 42 42 years old. How old is his father?

Eva’s daughter is 5 5 years younger than her son. Eva’s son is 12 12 years old. How old is her daughter?

Allie weighs 8 8 pounds less than her twin sister Lorrie. Allie weighs 124 124 pounds. How much does Lorrie weigh?

For a family birthday dinner, Celeste bought a turkey that weighed 5 5 pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed 16 16 pounds. How much did the Thanksgiving turkey weigh?

The nurse reported that Tricia’s daughter had gained 4.2 4.2 pounds since her last checkup and now weighs 31.6 31.6 pounds. How much did Tricia’s daughter weigh at her last checkup?

Connor’s temperature was 0.7 0.7 degrees higher this morning than it had been last night. His temperature this morning was 101.2 101.2 degrees. What was his temperature last night?

Melissa’s math book cost $22.85 $22.85 less than her art book cost. Her math book cost $93.75 . $93.75 . How much did her art book cost?

Ron’s paycheck this week was $17.43 $17.43 less than his paycheck last week. His paycheck this week was $103.76 . $103.76 . How much was Ron’s paycheck last week?

Everyday Math

Baking Kelsey needs 2 3 2 3 cup of sugar for the cookie recipe she wants to make. She only has 1 4 1 4 cup of sugar and will borrow the rest from her neighbor. Let s s equal the amount of sugar she will borrow. Solve the equation 1 4 + s = 2 3 1 4 + s = 2 3 to find the amount of sugar she should ask to borrow.

Construction Miguel wants to drill a hole for a 5 8 -inch 5 8 -inch screw. The screw should be 1 12 1 12 inch larger than the hole. Let d d equal the size of the hole he should drill. Solve the equation d + 1 12 = 5 8 d + 1 12 = 5 8 to see what size the hole should be.

Writing Exercises

Is −18 −18 a solution to the equation 3 x = 16 − 5 x ? 3 x = 16 − 5 x ? How do you know?

Write a word sentence that translates the equation y − 18 = 41 y − 18 = 41 and then make up an application that uses this equation in its solution.

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

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Subtraction Worksheets

Subtraction worksheets for kindergarten through grade 5.

Our free subtraction worksheets start with subtracting small numbers by counting objects and progresses to subtracting large numbers in columns.  An emphasis is placed on practicing mental subtraction so as to improve numeracy.

Choose your grade / topic:

Kindergarten subtraction worksheets, grade 1 subtraction worksheets, grade 2 subtraction worksheets, grade 3 subtraction worksheets, grade 4 subtraction worksheets, grade 5 subtraction worksheets.

Subtraction facts: drills and practice

Multi-digit subtraction: drills and practice

Subtraction flashcards

Subtraction videos

Topics include:

• Subtracting numbers within 10 by counting objects
• Counting down and subtraction
• Subtraction equations in pictures
• Add or subtracts 1s and 2s
• Subtract within 5
• Subtract single digit numbers (up to 10, 20)
• Subtract vertically
• Simple subtraction word problems
• Subtraction using objects (up to 10, 20)
• Subtract using number lines
• Subtraction sentences and number lines
• Subtracting within 0 - 10, 0-20
• Missing minuend or subtrahend (0-10)
• Subtracting a single digit number from a 2-digit number (no regrouping)
• Subtracting whole tens
• Subtracting from a whole ten
• Subtracting 1 and 2 digit numbers in columns (no regrouping)
• Mixed addition - subtraction with 3-4 single digit numbers
• Subtraction word problems
• Mixed addition and subtraction word problems
• Subtraction sentences
• Subtracting within 0-10
• Subtracting within 10-19
• Subtracting a 1-digit number from a 2-digit number (no crossing the ten)
• Subtracting a 1-digit number from a whole ten
• Subtracting a 1-digit number from a 2-digit number (some regrouping)
• Subtracting a 1-digit number from a 3-digit number (some regrouping)
• Subtracting whole tens from whole tens (0-1,000)
• Subtracting whole tens from 2 or 3 digit numbers with / without regrouping
• Subtracting whole hundreds
• Subtracting 2-digit numbers from whole hundreds
• Missing minuend or subtrahend questions
• Subtracting 2 or 3 digit numbers in columns (no regrouping)
• Subtracting 2 or 3 digit numbers in columns (with regrouping)
• Borrowing across zeros
• Fact families
• Mixed addition and subtraction of 3-4 single digit numbers
• Subtract 1-digit from 2-digit numbers mentally
• Subtract whole tens from 2 and 3 digit numbers
• Subtract whole hundreds from 3 digit numbers
• Subtract 2-digit numbers from 100
• Subtract whole hundreds from 3 and 4 digit numbers
• Subtracting whole hundreds from whole hundreds
• Subtracting whole tens from 1,000
• Subtracting 3-digit numbers from whole thousands
• Missing minuend / subtrahend questions
• Subtracting 3-4 digit numbers in columns
• Borrowing across 2 or 3 zeros
• Subtracting within 100
• Subtracting whole tens and whole hundreds
• Missing minuend problems
• Subtract any number from 1,000
• Subtract any 3-digit number from whole thousands
• Subtract 3, 4, 5 and 6 digit numbers in columns
• Regrouping across 2 or 3 zeros
• Mixed 4 operations word problems
• Missing minuend and subtrahend problems with large numbers
• Subtracting large numbers in columns

Related topics

Addition worksheets

Multiplication worksheets

Sample Subtraction Worksheet

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Problem Structures for Addition & Subtraction

Quick pop quiz. How many problem structures are there for addition and subtraction problems?

If you said somewhere around 15 structures, you’re in the right ballpark. Unfortunately, students are often exposed to only the simplest structures. As teachers, we need to have an understanding of all the structures and teach them to our students in a methodical way.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.

“…teachers who are not aware of the variety of situations and corresponding structures may randomly offer problems to students without the proper sequencing to support students; full grasp of the meaning of the operations.” (Van de Walle et al)

The charts below were adapted from Elementary and Middle School Mathematics: Teaching Developmentally (Van de Walle et al), a phenomenal book for developing your own understanding of math.

The addition/subtraction structures are grouped into three main types: Change, Part/Part/Whole, and Comparison. For each type, there are multiple structures, depending on what information is known and unknown.

Change Problems

One of the first things you might notice is that the structures are not designated as addition or subtraction. While we typically think of  joining as addition and  separating as subtraction, you’ll see from the chart that is not always the case.  Result Unknown is the simplest and most familiar structure. You might think of these as classic addition and subtraction problems. As we move across the chart, the problems become increasingly complex, and we see that the Change Unknown and  Start Unknown structures can be interpreted as either addition or subtraction.

An appropriate way to introduce the problems is to start with the simplest,  Result Unknown , problems. Start with Join problems and allow students to practice solving just that type of problem. Help students focus on the meaning of each number in the problem, in terms of Change , Start , or Result . Drawing models is a good strategy for helping students analyze and visualize each problem. Next, introduce Separate problems, again giving them practice with just that type. Then it’s time to mix them up, so students have to determine the appropriate structure, based on the problem.

Now start to move across the chart, using the same process. Introduce the next structure (Join, Change Unknown ), practice the structure, and then mix it in with the others they already know. Keep in mind that this process takes time. If you’re a second-grade teacher, make a schedule for introducing the structures throughout the school year. Use numbers appropriate to the students’ computation skills.

Part-Part-Whole

Part-Part-Whole problems are very similar to Change. The subtle difference is that often there is no action in these problems, which makes them a little more abstract for students. The Whole Unknown structure is a very simple addition problem. In the One Part Unknown structure, we know the total and one of the parts, but we are missing the other part. This is also commonly called a Missing Addend problem. We often solve this type of problem using subtraction, but a counting-up strategy works well also. A really interesting structure is Both Parts Unknown. It’s a word problem application of knowing all the combinations for a number !

As students are introduced to more of the structures, remember that it’s just as important that they generate problems as solve them. I love an activity I call You Write the Story . Give students an equation and have them write a story to go with it and draw a model for their story.

One other note about Change and Part-Part-Whole problems, while these examples all have two addends, you can also use more than two addends to provide more of a challenge. Think: There are 425 students in the cafeteria. One hundred twenty-seven students are 5th graders, 146 are 4th graders, and the rest are 3rd graders. How many 3rd graders are in the cafeteria?

Finally, we have Comparison problems, which involve comparing two quantities–a larger quantity and a smaller one. They can also be written using either more or  fewer.  Fewer is by far more difficult for students. We want to make sure we introduce comparison subtraction using manipulatives to help students understand the structure. See this pos t for more information.

There you have it! All the structures for addition and subtraction problems. You can download your own copy of the tables showing the structures using the button below.

I look forward to hearing how you will teach these structures in your classroom, so be sure to leave a comment!

Resources for problem structures

Morrow-Leong, K., Moore, S. D., & Gojak, L. (2021). Mathematize it!: Going beyond key words to make sense of word problems , grades K-2 or grades 3-5 . Thousand Oaks, CA: Corwin.

Carpenter, Thomas P., et al. (2015) Children’s Mathematics: Cognitively Guided Instruction . Heinemann.

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Great post! I’ve been reading the Mathematize IT: Making Sense books also.

Do you have a post for Problem Structures of multiplication and division?I saw the book, but I was hoping you had something more like this post for multiplication and division.

I follow all your posts! Thank you for helping me become a better teacher❤️

Thanks for your kind comments! I don’t have a post, but I do have a document with all the structures for all operations . Enjoy!

This is a great visual! Thanks for sharing.

Awesome blog and charts! I did notice that “amount” is misspelled in the last chart in the red boxes.

Well, yes it is! Thanks so much for calling it to my attention. I’ll get it corrected straight away.

Late to the game but I LOVE THIS!

What are your thoughts on multistep problems as it relates to these structures?

That would be another, and trickier, step! Being able to comprehend what’s happening in the problem is key. Check out this post on the 3 Reads Protocol for a great strategy for improving comprehension.

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Problem Solving on Subtraction | Learn How to Solve Subtraction Problems | Subtraction Word Problems with Answers

Subtraction is one of the basic arithmetic operations in mathematics. Subtraction means removing the specified number from the minuend or bottom number. We can observe the use of Subtraction in our everyday life in different ways. In subtraction, we will subtract numbers and find the difference between them. In Subtraction the numbers in both the minuend and subtrahend have the same digit numbers. Go through the complete article to be aware of the terms associated with subtraction and therefore the symbol used etc.

You can use and download without any charge, for more practicing purposes. On this page, you will learn the subtraction definition, solved problems on subtraction, and so on.

Also, Read Some More:

• Subtracting 2-digit numbers with Borrowing
• Subtraction without Regrouping
• Subtracting Numbers in Expanded Form 

Subtraction – Definition | What is meant by Subtraction?

In Mathematics, Subtraction is required for removal from a bunch or number of things. On Subtracting the number of things within the group decreases or reduces. The symbol ‘–’ is named the minus and therefore the number after the symbol must be subtracted from the number before it.

Terms utilized in the Subtraction are Minuend, Subtrahend, Difference. For Example: In 8-3, 8 is the minuend and 3 is the subtrahend and 5 is the difference.

Subtraction Word Problems with Answers

Example 1:  Sita had 20 pens. She gave 3pens to her friend. How many pens left with her? Solution: As given in the question, The total number of pens Sita had = 20 pens The number of pens she gave to her friend = 3 pens Now, we can calculate how many pens left with her. Using subtraction law, we get the value So, subtract the values i.e., 20 – 3 = 17 Therefore, the number of pens she has left is 17.

Example 2: Dinny’s mother is 48 years old. His father is 51 years old. What is the difference between their ages? Solution:  In the given question, father age and mother age is given. Now, we are going to find the difference in their ages. Using the Subtraction law, we can find the difference then we will get the value easily. So, the difference of their age is, 51 years – 48 years = 3 years. Therefore, the difference between the father’s age and the mother’s age is 3 years.

Example 3: There are 8 parrots and 6 pigeons. How many fewer pigeons are there than parrots? Solution: As given in the question, The number of Parrots is 8. The number of Pigeons is 6. Now, to find the number of fewer pigeons. We use the subtraction law, we get the value, So, 8 – 6 = 2 Therefore, compared to parrots the number of lesser pigeons is 2.

Therefore, the difference value of the two given numbers  8451 and 5263 is 3188.

Example 7: Subtract the value 648 from 837. Write the difference value. Solution: In the given question, the numbers are 648 and 837. Now, we want to find the difference value of the given two numbers. By using the Subtraction method, we can get the difference value, The numbers are 648 and 837, 837 – 648 = 189 ( 8 is not subtracted from 7. So, take a regroup from the following number 3, then the value changes to 17. Now subtract 17 – 8 = 9. After taking borrow the value 3 is reduces to 2, so 2- 4 is not subtracted. So, take a borrow from the following number 8, the value will be 12 – 4 = 8. Next 7-6 =1) Therefore, after subtracting 648 from 837, we get the difference value is 189.

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Addition and Subtraction Word Problems Learning Resources

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Addition Word Problems

Represent 'Add To' Scenarios Game

Learn to solve math problems through our 'Represent 'Add To' Scenarios' game.

Solve 'Add To' Scenarios Game

Add more arrows to your child’s math quiver by solving 'Add To' scenarios.

Find the Sum Using Part-Part-Whole Model Worksheet

Combine math learning with adventure by solving to find the sum using 'Part-Part-Whole' model.

Write Equations Using Part-Part-Whole Model Worksheet

Learn number sense at the speed of lightning by writing equations using 'Part-Part-Whole' model.

Subtraction Word Problems

Represent 'Take Apart' Scenarios Game

Kids must represent 'Take Apart' scenarios to practice subtraction.

Solve 'Take Apart' Scenarios Game

Take the pressure off by simplifying subtraction by solving 'Take Apart' scenarios.

Subtract Using Part-Part-Whole Model Worksheet

Combine math learning with adventure by solving to subtract using 'Part-Part-Whole' model.

Solve Using Part-Part-Whole Model Worksheet

Learn subtraction at the speed of lightning by practicing to solve using 'Part-Part-Whole' model.

All Addition and Subtraction Word Problems Resources

Add within 5: Summer Word Problems Worksheet

Engaging summer-themed worksheet with word problems to enhance addition skills within 5.

Subtract within 5: Summer Word Problems Worksheet

A fun, summer-themed worksheet designed to enhance students' subtraction skills with problems up to 5.

Add within 5: Halloween Word Problems Worksheet

Spooky-themed worksheet for practicing addition within 5 through Halloween word problems.

Subtract within 5: Halloween Word Problems Worksheet

Spooky themed worksheet to master subtraction within 5 through fun Halloween word problems!

Represent 'Put Together' Scenarios Game

Have your own math-themed party by learning how to represent 'Put Together' scenarios.

Change Unknown Scenarios Game

Shine bright in the math world by learning how to change unknown scenarios.

Add within 5: Christmas Word Problems Worksheet

Engage in festive math fun with this Christmas-themed worksheet, adding numbers within 5.

Subtract within 5: Christmas Word Problems Worksheet

Engaging Christmas-themed worksheet for students to master subtraction within 5 through word problems.

Solve 'Put Together' Scenarios Game

Shine bright in the math world by learning how to solve 'Put Together' scenarios.

Word Problems to Subtract Multiples of 10 Game

Help your child take flight by learning how to solve word problems to subtract multiples of 10.

Add within 5: Shopping Word Problems Worksheet

Engaging worksheet with a shopping theme to help students master addition within 5 through word problems.

Subtract within 5: Shopping Word Problems Worksheet

Engaging subtraction worksheet with a shopping theme, helping students solve problems within 5.

Solve Count On Scenarios Game

Begin the exciting journey of becoming a math wizard by learning how to solve count on scenarios.

Solve Word Problems on Take From Scenarios Game

Enjoy the marvel of math-multiverse by learning to solve word problems on "Take From" scenarios.

Add within 5: Travel Word Problems Worksheet

This worksheet combines fun travel-themed scenarios with math problems, requiring students to add numbers within 5.

Subtract within 5: Travel Word Problems Worksheet

Travel-themed worksheet to enhance students' subtraction skills within 5 through word problems.

Solve 'Change Unknown' Scenarios Game

Begin the exciting journey of becoming a math wizard by solving 'Change Unknown' scenarios.

Solve Difference Unknown Scenarios Game

Kids must solve difference unknown scenarios to practice subtraction.

Add within 5: Sports Word Problems Worksheet

Engaging sports-themed worksheet designed to strengthen students' ability to add within 5.

Subtract within 5: Sports Word Problems Worksheet

Sports-themed worksheet designed to engage students in solving subtraction problems within 5.

Solve 'Count On' Word Problems Game

Take the first step towards building your math castle by solving 'Count On' word problems.

Solve Scenarios with 'Difference Unknown' Game

Shine bright in the math world by learning how to solve scenarios with 'Difference Unknown'.

Add within 5: Cooking Word Problems Worksheet

A fun, cooking-themed worksheet for students to practice addition within 5 with word problems.

Subtract within 5: Cooking Word Problems Worksheet

Whip up your subtraction skills with this cooking-themed worksheet, subtracting within 5!

Represent 'Add To' Word Problems Game

Take a deep dive into the world of math with our 'Represent 'Add To' Word Problems' game.

Solve Subtraction Word Problems Game

Enjoy the marvel of mathematics by exploring how to solve subtraction word problems.

Add within 5: Winter Word Problems Worksheet

Engage students with this Winter-themed worksheet, solving fun addition problems within 5.

Subtract within 5: Winter Word Problems Worksheet

Engaging winter-themed worksheet to practice subtraction within 5 through word problems.

Solve 'Add To' Word Problems Game

Unearth the wisdom of mathematics by learning how to solve 'Add To' word problems.

Represent 'Put Together' Word Problems Game

Unearth the wisdom of mathematics by learning how to represent 'Put Together' word problems.

Add within 5: Easter Word Problems Worksheet

Engaging Easter-themed worksheet focused on solving addition problems up to the number 5.

Subtract within 5: Easter Word Problems Worksheet

Engage in this Easter-themed worksheet, subtracting numbers within 5 through fun word problems.

Solve 'Put Together' Word Problems Game

Let your child see the world through math-colored shades by solving 'Put Together' word problems!

Word Problems to Add Multiples of 10 Game

Learn to solve word problems to add multiples of 10.

Add within 5: Thanksgiving Word Problems Worksheet

Thanksgiving-themed worksheet helping students solve word problems by adding within 5.

Subtract within 5: Thanksgiving Word Problems Worksheet

Engaging worksheet for students to solve Thanksgiving-themed subtraction problems within 5.

Word Problems to Add Tens to a 2-digit number Game

Make math learning fun by solving word problems to add tens to a 2-digit number.

Solve Word Problems on Add to Scenarios Game

Ask your little one to solve word problems on "Add to" scenarios to play this game.

Create and Solve Your Own Story Problem Worksheet

Help your child revise subtraction by creating and solving your own story problem.

Solve Word Problems on Put together Scenarios Game

Practice the superpower of addition by learning to solve word problems on "Put together" scenarios.

Subtract to Compare Game

Let your child see the world through math-colored shades by subtracting to compare.

Solve Addition Word Problems Worksheet

Assess your math skills by solving addition word problems in this worksheet.

Your one stop solution for all grade learning needs.

Minecraft Math Activities for Elementary and Middle School

Multiply the excitement about math by using Minecraft! Your students will love these Minecraft math activities.

Doing Math with Minecraft

Unlike other video games, Minecraft works well as an educational platform. (It’s not all fighting Endermen!)

With its block design and the ability to build whatever you imagine, Minecraft works exceptionally well for math activities.

Check out these Minecraft math activities for elementary and middle school.

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Minecraft Math Activities for Elementary

Whether you are teaching counting, shapes, or basic operations, Minecraft has activities to reinforce learning.

Counting and Number Recognition

The blocks in Minecraft are virtual manipulatives.

Practice counting blocks and recognizing numbers.

You can even build numbers out of blocks.

Basic Addition and Subtraction Tasks

Use in-game items to solve simple addition and subtraction problems.

How many lumps of coal did you find? Dig more. How many do you have now?

How many sheep do you have in your farm? If you take some away, how many are left?

Shape Identification and Sorting

Identify and sort different shapes found in Minecraft structures.

You can build a structure for your students to take apart.

Pattern Recognition Exercises

Practice recognizing and extending patterns seen in Minecraft builds.

Can you make a wall with blocks in a pattern (by color, number, or shape)?

Can students extend the wall by identifying and replicating the pattern?

Measurement Activities

You may not have a ruler in Minecraft, but the world is made of unit cubes.

Measure distances, heights, and sizes of objects using Minecraft blocks.

Time Telling Challenges

Make clocks using the crafting system in the game.

Then, you can associate in-game events with telling time on analog clocks.

Skip Counting Drills

Practice skip counting by twos, fives, or tens using in-game elements like crops, ore, gems, and animals.

Word Problems with Visual Aids

Word problems come to life in Minecraft!

Solve word problems with visual representations using Minecraft scenes.

Minecraft Math Activities for Middle School

Middle school math concepts are easily depicted and practiced in Minecraft.

Area and Perimeter Challenges

Calculating the area and perimeter of structures built in Minecraft.

You can even have students build their own structures (as long as the structure has a basic footprint).

This combines math and art; this strategy interests a broader group of students.

Volume and Surface Area Calculations

Since blocks are three-dimensional, you can also calculate the volume of 3D structures in the game.

Few people like to find the volume of a rectangular prism.

But if that rectangular prism is a Minecraft treasure chamber…that’s another story.

You can even make this challenge like an escape room. Once your students find the volume, they can open the chamber.

Fraction Representation

You can represent fractions using blocks or resources in Minecraft builds.

Check out this lesson on fractions in Minecraft Education.

Coordinate Plane Exploration

Plot coordinates to navigate and locate specific points within the game world.

This lesson teaches students the basics of the Minecraft coordinate system.

Ratio and Proportion Tasks

Create proportional structures or designs using blocks in Minecraft.

Create a small structure. Can the students replicate it on a bigger scale?

Use proportions and ratios to make it accurate!

Decimal Operations Practice

In Minecraft scenarios, perform addition, subtraction, multiplication, and division with decimals.

For example, you can create a 10 x 10 garden with 100 crops.

What portion of the garden is sunflowers? (0.30)

Try it out with this lesson .

Data Analysis Challenges

Collect and analyze in-game data to create graphs and interpret results.

Decide what data you want to count (Endermen?), fill out a table, and convert it to a graph.

You can even make an in-game bar graph out of blocks!

Learning with Minecraft Math Activities

Math exercises are much more appealing when you practice them in Minecraft.

Let technology boost your students’ enthusiasm for learning.

You May Also Like:

• 10 Fun Facts About Minecraft
• 100 Minecraft Activities and Resources for Kids
• Helping Kids Overcome Math Anxiety

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