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## Adding fractions word problems

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## Fraction Addition Word Problems Worksheets

Let children work on our printable adding fractions word problems worksheets hammer and tongs! Whether it's sharing a meal with your friends or measuring the ingredients for a recipe, adding fractions is at the heart of it all, hence our worksheets. A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!

Adding Fractions with Whole Numbers

Dazzle 3rd grade kids with a gift of lifelike story problems! If you're a novice up against fraction addition, don't miss our pdf adding fractions word problems worksheets using whole numbers and fractions!

- Download the set

Adding Like Fractions Word Problems

Gerald ate 5/9 of an apple, and Garry ate 4/9 of it. How many apples did they eat in all? Good going! They both ate one whole apple. Simply combine the numerators and solve the like fraction word problems here!

Adding Unlike Fractions

A potpourri of word problems that involve adding unlike fractions, these pdfs mean that 4th grade and 5th grade students will breeze through addition of fractions with different denominators in their day-to-day lives.

Adding Mixed Numbers | Same Denominators

See in your mind's eye adding mixed numbers with same denominators riding on the several real-life scenarios in our printable worksheets! Convert the mixed numbers to fractions, and add them as usual.

Adding Mixed Numbers | Different Denominators

Steal a march on your 5th grade and 6th grade peers by getting your act together to power through the real-world situations featured in this set of printable adding mixed numbers word problems worksheets.

Related Worksheets

» Adding Like Fractions

» Adding Unlike Fractions

» Adding Mixed Numbers

» Adding Fractions with Whole Numbers

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## Adding Fractions

A fraction like 3 4 says we have 3 out of the 4 parts the whole is divided into.

## To add fractions there are Three Simple Steps:

- Step 1: Make sure the bottom numbers (the denominators ) are the same
- Step 2: Add the top numbers (the numerators ), put that answer over the denominator
- Step 3: Simplify the fraction (if possible)

Step 1 . The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2 . Add the top numbers and put the answer over the same denominator:

1 4 + 1 4 = 1 + 1 4 = 2 4

Step 3 . Simplify the fraction:

In picture form it looks like this:

... and do you see how 2 4 is simpler as 1 2 ? (see Equivalent Fractions .)

Step 1 : The bottom numbers are different. See how the slices are different sizes?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2 , like this:

Important: you multiply both top and bottom by the same amount, to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

The bottom numbers are now the same, so we can go to step 2.

Step 2 : Add the top numbers and put them over the same denominator:

2 6 + 1 6 = 2 + 1 6 = 3 6

Step 3 : Simplify the fraction:

In picture form the whole answer looks like this:

## With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

## A Rhyme To Help You Remember

♫ "If adding or subtracting is your aim, The bottom numbers must be the same! ♫ "Change the bottom using multiply or divide, But the same to the top must be applied, ♫ "And don't forget to simplify, Before its time to say good bye"

Again, the bottom numbers are different (the slices are different sizes)!

But let us try dividing them into smaller sizes that will each be the same :

The first fraction: by multiplying the top and bottom by 5 we ended up with 5 15 :

The second fraction: by multiplying the top and bottom by 3 we ended up with 3 15 :

The bottom numbers are now the same, so we can go ahead and add the top numbers:

The result is already as simple as it can be, so that is the answer:

1 3 + 1 5 = 8 15

## Making the Denominators the Same

In the previous example how did we know to cut them into 1 / 15 ths to make the denominators the same? We simply multiplied the two denominators together (3 × 5 = 15).

Read about the two main ways to make the denominators the same here:

- Common Denominator Method , or the
- Least Common Denominator Method

They both work, use which one you prefer!

## Example: Cupcakes

You want to make and sell cupcakes:

- A friend can supply the ingredients, if you give them 1 / 3 of sales
- And a market stall costs 1 / 4 of sales

How much is that altogether?

We need to add 1 / 3 and 1 / 4

First make the bottom numbers (the denominators) the same.

Multiply top and bottom of 1 / 3 by 4 :

And multiply top and bottom of 1 / 4 by 3 :

Now do the calculations:

Answer: 7 12 of sales go in ingredients and market costs.

## Adding Mixed Fractions

We have a special (more advanced) page on Adding Mixed Fractions .

## Adding Fractions

Learn about adding fractions., adding fractions lesson, how to add fractions.

To add fractions, we follow three simple steps. They are as follows:

- Make the denominators the same if they aren't already.
- Add the numerators, keeping the denominator the same.
- Simplify the resulting fraction.

The same three steps apply for adding mixed fractions (such as 4 1 / 2 + 1 2 / 3 ) except that we will simply add the whole number and fraction components separately.

In this lesson we will go through how to add fractions and show examples of adding fractions with like and unlike denominators.

## Adding Fractions with Like Denominators

Let's go through how to add fractions with like denominators first, since it is most simple type of fraction addition. Here's an example of adding fractions with like denominators, using the three steps from earlier.

Find the sum of 3 / 5 + 1 / 5 .

- The denominators are already the same, so we can skip step 1.
- Let's add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is 4 / 5 .
- 4 / 5 is already in its simplest form, so there is no simplifying needed here.

The solution is 3 / 5 + 1 / 5 = 4 / 5 .

## Adding Fractions with Unlike Denominators

Now let's go through another example but this time with unlike denominators. We will use the same exact three steps.

Find the sum of 1 / 4 + 2 / 3 .

- Let's find the lowest common denominator and convert these fractions to like denominators to make them addable. Multiplying the top and bottom of each fraction by the other fraction's denominator gives us 1 / 4 · 3 / 3 = 3 / 12 and 2 / 3 · 4 / 4 = 8 / 12 .
- Now let's add the numerators. 3 + 8 = 11, so the sum of our numerators is 11. The denominator is still 12, so our result is 11 / 12 .
- 11 / 12 is already in its simplest form, so there is no simplifying needed here.

The solution is 1 / 4 + 2 / 3 = 11 / 12 .

Learning math has never been easier. Get unlimited access to more than 168 personalized lessons and 73 interactive calculators. Join Voovers+ Today 100% risk free. Cancel anytime.

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## Fractions - Adding and Subtracting Fractions

Fractions -, adding and subtracting fractions, fractions adding and subtracting fractions.

## Fractions: Adding and Subtracting Fractions

Lesson 3: adding and subtracting fractions.

/en/fractions/comparing-and-reducing-fractions/content/

## Adding and subtracting fractions

In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water.

In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back? Or drained 1/4 of a quart of gas from a gas tank that had 3/4 of a quart in it? You probably didn't think about it at the time, but these are examples of adding and subtracting fractions.

Click through the slideshow to learn how to set up addition and subtraction problems with fractions.

Let's imagine that a cake recipe tells you to add 3/5 of a cup of oil to the batter.

You also need 1/5 of a cup of oil to grease the pan. To see how much oil you'll need total, you can add these fractions together.

When you add fractions, you just add the top numbers, or numerators .

That's because the bottom numbers, or denominators , show how many parts would make a whole.

We don't want to change how many parts make a whole cup ( 5 ). We just want to find out how many parts we need total.

So we only need to add the numerators of our fractions.

We can stack the fractions so the numerators are lined up. This will make it easier to add them.

And that's all we have to do to set up an addition example with fractions. Our fractions are now ready to be added.

We'll do the same thing to set up a subtraction example. Let's say you had 3/4 of a tank of gas when you got to work.

If you use 1/4 of a tank to drive home, how much will you have left? We can subtract these fractions to find out.

Just like when we added, we'll stack our fractions to keep the numerators lined up.

This is because we want to subtract 1 part from 3 parts.

Now that our example is set up, we're ready to subtract!

Try setting up these addition and subtraction problems with fractions. Don't try solving them yet!

You run 4/10 of a mile in the morning. Later, you run for 3/10 of a mile.

You had 7/8 of a stick of butter and used 2/8 of the stick while cooking dinner.

Your gas tank is 2/5 full, and you put in another 2/5 of a tank.

## Solving addition problems with fractions

Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers , you're ready to add fractions.

Click through the slideshow to learn how to add fractions.

Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.

Remember, when we add fractions, we don't add the denominators.

This is because we're finding how many parts we need total. The numerators show the parts we need, so we'll add 3 and 1 .

3 plus 1 equals 4 . Make sure to line up the 4 with the numbers you just added.

The denominators will stay the same, so we'll write 5 on the bottom of our new fraction.

3/5 plus 1/5 equals 4/5 . So you'll need 4/5 of a cup of oil total to make your cake.

Let's try another example: 7/10 plus 2/10 .

Just like before, we're only going to add the numerators. In this example, the numerators are 7 and 2 .

7 plus 2 equals 9 , so we'll write that to the right of the numerators.

Just like in our earlier example, the denominator stays the same.

So 7/10 plus 2/10 equals 9/10 .

Try solving some of the addition problems below.

## Solving subtraction problems with fractions

Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers , you can subtract fractions too!

Click through the slideshow to learn how to subtract fractions.

Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank.

Just like in addition, we're not going to change the denominators.

We don't want to change how many parts make a whole tank of gas. We just want to know how many parts we'll have left.

We'll start by subtracting the numerators. 3 minus 1 equals 2 , so we'll write 2 to the right of the numerators.

Just like when we added, the denominator of our answer will be the same as the other denominators.

So 3/4 minus 1/4 equals 2/4 . You'll have 2/4 of a tank of gas left when you get home.

Let's try solving another problem: 5/6 minus 3/6 .

We'll start by subtracting the numerators.

5 minus 3 equals 2 . So we'll put a 2 to the right of the numerators.

As usual, the denominator stays the same.

So 5/6 minus 3/6 equals 2/6 .

Try solving some of the subtraction problems below.

After you add or subtract fractions, you may sometimes have a fraction that can be reduced to a simpler fraction. As you learned in Comparing and Reducing Fractions , it's always best to reduce a fraction to its simplest form when you can. For example, 1/4 plus 1/4 equals 2/4 . Because 2 and 4 can both be divided 2 , we can reduce 2/4 to 1/2 .

## Adding fractions with different denominators

On the last page, we learned how to add fractions that have the same denominator, like 1/4 and 3/4 . But what if you needed to add fractions with different denominators? For example, our cake recipe might say to blend 1/4 cup of milk in slowly and then dump in another 1/3 of a cup.

In Comparing and Reducing Fractions , we compared fractions with a different bottom number, or denominator. We had to change the fractions so their denominators were the same. To do that, we found the lowest common denominator , or LCD .

We can only add or subtract fractions if they have the same denominators. So we'll need to find the lowest common denominator before we add or subtract these fractions. Once the fractions have the same denominator, we can add or subtract as usual.

Click through the slideshow to learn how to add fractions with different denominators.

Let's add 1/4 and 1/3 .

Before we can add these fractions, we'll need to change them so they have the same denominator .

To do that, we'll have to find the LCD , or lowest common denominator, of 4 and 3 .

It looks like 12 is the smallest number that can be divided by both 3 and 4, so 12 is our LCD .

Since 12 is the LCD, it will be the new denominator for our fractions.

Now we'll change the numerators of the fractions, just like we changed the denominators.

First, let's look at the fraction on the left: 1/4 .

To change 4 into 12 , we multiplied it by 3 .

Since the denominator was multiplied by 3 , we'll also multiply the numerator by 3 .

1 times 3 equals 3 .

1/4 is equal to 3/12 .

Now let's look at the fraction on the right: 1/3 . We changed its denominator to 12 as well.

Our old denominator was 3 . We multiplied it by 4 to get 12.

We'll also multiply the numerator by 4 . 1 times 4 equals 4 .

So 1/3 is equal to 4/12 .

Now that our fractions have the same denominator, we can add them like we normally do.

3 plus 4 equals 7 . As usual, the denominator stays the same. So 3/12 plus 4/12 equals 7/12 .

Try solving the addition problems below.

## Subtracting fractions with different denominators

We just saw that fractions can only be added when they have the same denominator. The same thing is true when we're subtracting fractions. Before we can subtract, we'll have to change our fractions so they have the same denominator.

Click through the slideshow to learn how to subtract fractions with different denominators.

Let's try subtracting 1/3 from 3/5 .

First, we'll change the denominators of both fractions to be the same by finding the lowest common denominator .

It looks like 15 is the smallest number that can be divided evenly by 3 and 5 , so 15 is our LCD.

Now we'll change our first fraction. To change the denominator to 15 , we'll multiply the denominator and the numerator by 3 .

5 times 3 equals 15 . So our fraction is now 9/15 .

Now let's change the second fraction. To change the denominator to 15 , we'll multiply both numbers by 5 to get 5/15 .

Now that our fractions have the same denominator, we can subtract like we normally do.

9 minus 5 equals 4 . As always, the denominator stays the same. So 9/15 minus 5/15 equals 4/15 .

Try solving the subtraction problems below.

## Adding and subtracting mixed numbers

Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below?

In Introduction to Fractions , you learned about mixed numbers . A mixed number has both a fraction and a whole number . An example is 2 1/2 , or two-and-a-half . Another way to write this would be 5/2 , or five-halves . These two numbers look different, but they're actually the same.

5/2 is an improper fraction . This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first.

Let's add these two mixed numbers: 2 3/5 and 1 3/5 .

We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5 .

As you learned in Lesson 2 , we'll multiply the whole number, 2 , by the bottom number, 5 .

2 times 5 equals 10 .

Now, let's add 10 to the numerator, 3 .

10 + 3 equals 13 .

Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5 .

Now we'll need to convert our second mixed number: 1 3/5 .

First, we'll multiply the whole number by the denominator. 1 x 5 = 5 .

Next, we'll add 5 to the numerators. 5 + 3 = 8 .

Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5 .

Now that we've changed our mixed numbers to improper fractions, we can add like we normally do.

13 plus 8 equals 21 . As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5 .

Because we started with a mixed number, let's convert this improper fraction back into a mixed number.

As you learned in the previous lesson , divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1 .

The answer, 4, will become our whole number.

And the remainder , 1, will become the numerator of the fraction.

So 2 3/5 + 1 3/5 = 4 1/5 .

/en/fractions/multiplying-and-dividing-fractions/content/

## Addition and Subtraction of Fraction: Methods, Examples, Facts, FAQs

What is addition and subtraction of fractions, methods of addition and subtraction of fractions, addition and subtraction of mixed numbers, solved examples on addition and subtraction of fractions, practice problems on addition and subtraction of fractions, frequently asked questions on addition and subtraction of fractions.

Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases:

- Addition and subtraction of like fractions (fractions with same denominators)
- Addition and subtraction of unlike fractions (fractions with different denominators)

A fraction represents parts of a whole. For example, the fraction 37 represents 3 parts out of 7 equal parts of a whole. Here, 3 is the numerator and it represents the number of parts taken. 7 is the denominator and it represents the total number of parts of the whole.

Adding and subtracting fractions is simple and straightforward when it comes to like fractions. In the case of unlike fractions, we first need to make the denominators the same. Let’s take a closer look at both these cases.

Before adding and subtracting fractions, we first need to make sure that the fractions have the same denominators.

When the denominators are the same, we simply add the numerators and keep the denominator as it is. To add or subtract unlike fractions, we first need to learn how to make the denominators alike. Let’s learn how to add fractions and how to subtract fractions in both cases.

## Related Worksheets

## Addition and Subtraction of Like Fractions

The rules for adding fractions with the same denominator are really simple and straightforward.

Let’s learn with the help of examples and visual bar models.

Addition of Like Fractions

Here are the steps to add fractions with the same denominator:

Step 1: Add the numerators of the given fractions.

Step 2: Keep the denominator the same.

Step 3: Simplify.

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$ …$c \neq 0$

Example 1: Find $\frac{1}{4} + \frac{2}{4}$ .

$\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$

We can visualize this addition using a bar model:

Example 2: $\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}$

Subtraction of Like Fractions

Here are the steps to subtract fractions with the same denominator:

Step 1: Subtract the numerators of the given fractions.

Step 3: Simplify.

$\frac{a}{c}\;-\;\frac{b}{c} = \frac{a \;-\; b}{c}$ …$c \neq 0$

Example 1: Find $\frac{4}{6} \;-\; \frac{1}{6}$.

$\frac{4}{6}\;-\;\frac{1}{6} = \frac{4-1}{6} = \frac{3}{6} = \frac{1}{2}$

## Addition and Subtraction of Unlike Fractions

Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not the same. So, we need to first convert the unlike fractions into like fractions. Let’s look at a few ways to do this!

Addition of Unlike Fractions

We can make the denominators the same by finding the LCM of the two denominators. Once we calculate the LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator.

Example: $\frac{3}{5} + \frac{3}{2}$

Step 1: Find the LCM (Least Common Multiple) of the two denominators.

The LCM of 5 and 2 is 10.

Step 2: Convert both the fractions into like fractions by making the denominators same.

$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$

$\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$

Step 3: Add the numerators. The denominator stays the same.

$\frac{6}{10} + \frac{15}{10} = \frac{21}{10}$

Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1.

In this case, GCF (21,10) $= 1$

The fraction $\frac{21}{10}$ is already in its simplest form.

Thus, $\frac{3}{5} + \frac{3}{2} = \frac{21}{10}$

Subtraction of Unlike Fractions

Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method. The process is similar to what we discussed in the previous example.

Example: $\frac{5}{6} \;-\; \frac{2}{9}$

Step 1: Find the LCM of the two denominators.

LCM of 6 and $9 = 18$

Step 2: Convert both the fractions into like fractions by making the denominators same.

$\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$

$\frac{2 \times 2}{9 \times 2} = \frac{4}{18}$

Step 3: Subtract the numerators. The denominator stays the same.

$\frac{15}{18} \;-\; \frac{4}{18} = \frac{11}{18}$

In this case, the GCF (11,18) $= 1$

So, it is already in its simplest form.

Thus, $\frac{5}{6}\;-\; 29 = \frac{11}{18}$

A mixed number is a type of fraction that has two parts: a whole number and a proper fraction. It is also known as a mixed fraction. Any mixed number can be written in the form of an improper fraction and vice-versa.

Adding and subtracting mixed fractions is done by converting mixed numbers into improper fractions .

Addition and Subtraction of Mixed Fractions with Same Denominators

The steps of adding and subtracting mixed numbers with the same denominators are the same. The only difference is the operation.

Step 1: Convert the given mixed fractions to improper fractions.

Step 2: Add/Subtract the like fractions obtained in step 1.

Step 3: Reduce the fraction to its simplest form.

Step 4: Convert the resulting fraction into a mixed number.

Example 1: $2\frac{1}{5} + 1\frac{3}{5}$

$2\frac{1}{5} = \frac{(5 \times 2) + 1}{5} = \frac{11}{5}$

$1\frac{3}{5} = \frac{(5 \times 1) + 3}{5} = \frac{8}{5}$

Thus, $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} + \frac{8}{5} = \frac{19}{5}$

Converting $\frac{19}{5}$ into a mixed number, we get

$\frac{19}{5} = 3\frac{4}{5}$

Example 2: $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} \;-\; \frac{8}{5} = \frac{3}{5}$

Addition and Subtraction of Mixed Fractions with Unlike Denominators

Step 2: Convert both the fractions into like fractions by finding the least common denominator.

Step 3: Add the fractions. (or subtract the fractions.)

Step 4: Reduce the fraction if possible or convert back to a mixed number

Let us understand the addition of mixed numbers with unlike denominators with the help of an example.

Example 1: Find the value of $1\frac{3}{5} + 2\frac{1}{2}$.

Convert the given mixed fractions to improper fractions.

$1\frac{3}{5} = \frac{8}{5}$ and $2\frac{1}{2} = \frac{5}{2}$

Step 2: Convert both the fractions into like fractions by making the denominators the same.

Here, LCM of 5 and 2 is 10.

Thus, $\frac{8 \times 2}{5 \times 2} = \frac{16}{10}$ and $\frac{5\times 5}{2 \times 5} = \frac{25}{10}$

Step 3: Add the fractions by adding the numerators.

$\frac{16}{10} + \frac{25}{10} = \frac{41}{10}$

Step 4: Convert back into a mixed number.

Thus, $\frac{41}{10}$ will become $4\frac{1}{10}$

Therefore, $1\frac{3}{5} + 2\frac{1}{2} = 4\frac{1}{10}$

Here’s an example for subtraction. It follows the same steps.

Example 2 : $6\frac{1}{2} \;-\; 1\frac{3}{4}$

Step 1: Convert the mixed numbers into improper fractions.

$6\frac{1}{2} \;-\; 1\frac{3}{4} = \frac{13}{2} \;-\; \frac{7}{4}$

Step 2: Make the denominators equal.

LCM of 2 and 4 is 4.

$\frac{13 \times 2}{2 \times 2} = \frac{26}{4}$

Step 3: Subtract the fractions.

$\frac{26}{4} \;-\; \frac{7}{4} = \frac{19}{4}$

Step 4: Convert the fraction as a mixed number.

$\frac{19}{4} = 4\frac{3}{4}$

Thus, $6\frac{1}{2} \;-\; 1\frac{3}{4} = 4\frac{3}{4}$

## Facts about Addition and Subtraction of Fractions

- We cannot add or subtract fractions without converting them into like fractions.
- Like fractions are fractions that have the same denominator, and unlike fractions are fractions that have different denominators.
- Equivalent fractions are two different fractions that represent the same value.
- The LCD (least common denominator) of two fractions is the LCM of the denominators.

In this article, we have learned about addition and subtraction of fractions (like fractions, unlike fractions, mixed fractions), methods of addition and subtraction of these fractions along with the steps. Let’s solve some examples on adding and subtracting fractions to understand the concept better.

- Solve: $\frac{2}{4} + \frac{1}{4}$ .

Solution:

Here, the denominators are the same.

Thus, we add the numerators by keeping the denominators as it is.

$\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4}$

$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

2. Find the sum of the fractions $\frac{3}{5}$ and $\frac{5}{2}$ by using the LCM method.

$\frac{3}{5}$ and $\frac{5}{2}$ are unlike fractions.

The LCM of 2 and 5 is 10.

Thus, we can write

$\frac{3}{5} + \frac{5}{2} = \frac{3 \times 2}{5 \times 2} + \frac{5 \times 5}{2 \times 5}$

$= \frac{6}{10} + \frac{25}{10}$

$= \frac{6}{10} + \frac{25}{10}$

$= \frac{31}{10}$

Thus, $\frac{3}{5} + \frac{5}{2} = \frac{31}{10}$

3. Find $\frac{4}{16} + \frac{5}{8}$.

Solution:

To add two fractions with different denominators, we first need to find the LCM of the denominators.

The LCM of 16 and 8 is 16.

$\frac{4}{16} + \frac{5}{8} = \frac{4 \times 1}{16\times 1} + \frac{5 \times 2}{8 \times 2}$

$= \frac{10}{16} + \frac{4}{16}$

$= \frac{14}{16}$

$= \frac{7}{8}$

4. From a rope $12\frac{1}{2}$ ft. long, a $7 \frac{6}{8}\;-$ ft-long piece is cut off. Find the length of the remaining rope.

Total length of the rope $= 12\frac{1}{2}$ ft.

Length of the rope that was cut off $= 7 \frac{6}{8}$ ft.

The length of the remaining rope $= 12\frac{1}{2} \;-\; 7 \frac{6}{8}$

$12\frac{1}{2} \;-\; 7 \frac{6}{8} = \frac{25}{2} \;-\; \frac{62}{8}$

$= \frac{25 \times 4}{2 \times 4} \;-\; \frac{62 \times 1}{8\times 1}$

$= \frac{100}{8} \;-\; \frac{62}{8}$

$= \frac{38}{8}$

$= \frac{19}{4}$

Converting it into a mixed fraction, $\frac{19}{4}$ becomes $4 \frac{3}{4}$.

Thus, the length of the remaining rope is $4\frac{3}{4}$ ft.

Attend this quiz & Test your knowledge.

## Find $\frac{2}{4} + \frac{2}{4}$.

$\frac{7}{24} + \frac{5}{16} =$, what is the least common denominator of $\frac{1}{2}$ and $\frac{1}{3}$, $\frac{3}{6} \;-\; \frac{1}{6} =$, what equation does the following figure represent.

How do we add and subtract negative fractions?

Negative fractions are simply fractions with a negative sign. The steps to add and subtract the negative fractions remain the same. We need to follow the rules for addition/subtraction with negative signs.

How can we convert an improper fraction into a mixed number?

To convert an improper fraction into a mixed number, we divide the numerator by the denominator. The denominator stays the same. The quotient represents the whole number part. The remainder represents the numerator of the mixed number.

Example: $\frac{14}{3} = 4\; \text{R}\; 2$

Quotient $= 4$

Remainder $= 2$

$\frac{14}{3} = 4\frac{2}{3}$

How do we divide two fractions?

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.

$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$

For example, $\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$

What are the rules of adding and subtracting fractions?

- Before adding or subtracting, we check if the fractions have the same denominator.
- If the denominators are equal, then we add/subtract the numerators keeping the common denominator.
- If the denominators are different, then we make the denominators equal by using the LCM method. Once the fractions have the same denominator, we can add/subtract the numerators keeping the common denominator as it is.

How do we add and subtract fractions with whole numbers?

- Convert the whole number to a fraction. To do this, give the whole number a denominator of 1.
- Convert to fractions of like denominators.
- Add/subtract the numerators. Now that the fractions have the same denominators, you can treat the numerators as a normal addition/subtraction problem.

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## Add & subtract fractions word problems

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## Word Problems - Fraction Addition (different denominators)

Description : This packet helps students practice solving word problems that require addition with fractions with different denominators. Each page contains 6 problems. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems. After doing all 12 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them.

Claudia ordered pizza. So far, she has eaten $\dfrac{3}{9}$ of the large pizza. Her dad has eaten $\dfrac{1}{6}$ of the large pizza. How much of the pizza has been eaten so far?

Practice problems require knowledge of how to add, subtract, and multiply whole numbers

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## Word Problems on Addition of Mixed Fractions | Adding Mixed Numbers Word Problems

Mixed Fractions are the ones having a Whole Number and a Fraction. Learn how to solve problems on adding mixed fractions by availing our quick resource on Word Problems on Addition of Mixed Fractions. Try to solve the Questions on Adding Mixed Numbers available on your own before you cross-check with the respective Solutions and explanations. For better understanding, we have provided the Examples on Mixed Numbers Addition step by step. Understand the Problem Solving Strategy Used and Solve the Related Problems on your own.

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- Addition of Mixed Fractions

## Addition of Mixed Fractions Word Problems with Answers

Example 1. Ram walked 1\(\frac { 3 }{ 5 } \) km on Monday, 3 \(\frac { 1 }{ 6 } \) km on Tuesday, and 2 \(\frac { 1 }{ 12 } \) km on Wednesday. Find out the distance he walked in all? Solution: Ram walked on monday= 1 \(\frac { 3 }{ 5 } \) Ram walked on tuesday=3 \(\frac { 1 }{ 6 } \) Ram walked on wednesday=2 \(\frac { 1 }{ 12 } \) The distance he walked in all days= 1 \(\frac { 3 }{ 5 } \) + 3\(\frac { 1 }{ 6 } \) + 2 \(\frac { 1 }{ 12 } \) =\(\frac { 8 }{ 5 } \) +\(\frac { 19 }{ 6 } \) + \(\frac { 25 }{ 12 } \) =\(\frac {8 × 12 }{ 5 ×12 } \) +\(\frac {19 × 10 }{ 6 ×10 } \) +\(\frac {25 ×5 }{ 12 ×5 } \) ( LCM of 5,6,12 is 60) = \(\frac { 96 }{ 60 } \)+\(\frac { 190 }{ 60 } \)1 +\(\frac { 125 }{ 60 } \) =\(\frac { 411 }{ 60 } \) =\(\frac { 137 }{ 20 } \) =6 \(\frac { 17 }{ 20 } \) Hence, Ram walked 6 \(\frac { 17 }{ 20 } \) km.

Example 2. Laxman bought 2 \(\frac { 1 }{ 2 } \) kg wheat, 4\(\frac { 1 }{ 4 } \) of sugar, 10 \(\frac { 1 }{ 2 } \) kg rice. How many kg of items did he buy? Solution: Laxman bought wheat= 2 \(\frac { 1 }{ 2 } \) kg Laxman bought sugar=4 \(\frac { 1 }{ 4 } \) kg Laxman bought rice=10 \(\frac { 1 }{ 2 } \) kg Total no. of kg of items Laxman bought = 2 \(\frac { 1 }{ 2 } \) + 4 \(\frac { 1 }{ 4 } \) + 10 \(\frac { 1 }{ 2 } \) =\(\frac { 5 }{ 2 } \) +\(\frac { 17 }{ 4 } \) +\(\frac { 21 }{ 2 } \) =\(\frac { 5 ×2}{ 2×2 } \) + \(\frac { 17}{ 4 } \) +\(\frac { 21 ×2 }{ 2×2 } \) = \(\frac { 10 }{ 4 } \) +\(\frac { 17 }{ 4 } \) + \(\frac { 42 }{ 4 } \) = \(\frac { 69 }{ 4 } \) =17 \(\frac { 1 }{ 4 } \) . Therefore, Laxman bought 17 \(\frac { 1 }{ 4 } \) kg of items.

Example 3. Rajesh donated 19 \(\frac { 1 }{ 2 } \) kg of rice, 25 \(\frac { 1 }{ 4 } \) kg of wheat, and 11 \(\frac { 3 }{ 4 } \) of oil. Find how many kgs of groceries he donated? Solution: Rajesh donated rice=19 \(\frac { 1 }{ 2 } \) Rajesh donated wheat=25 \(\frac { 1 }{ 4 } \) Rajesh donated oil=11\(\frac { 3}{ 4 } \) Total no. of kg of groceries Rajesh donated =19 \(\frac { 1 }{ 2 } \)+ 25 \(\frac { 1 }{ 4 } \) + 11 \(\frac { 3 }{ 4 } \) =\(\frac { 39 }{ 2 } \)+\(\frac { 101 }{ 4 } \)+\(\frac { 47 }{ 4 } \) = \(\frac { 39 × 2 }{ 2 × 2 } \)+\(\frac { 101 }{ 4 } \)+ \(\frac { 47 }{ 4 } \) =\(\frac { 78 }{ 4 } \)+\(\frac { 101 }{ 4 } \)+ \(\frac { 47 }{ 4 } \)47/4 =\(\frac { 226 }{ 4 } \)=\(\frac { 113 }{ 2 } \)=56\(\frac {1 }{ 2 } \) Hence, Rajesh donated 56 \(\frac {1 }{ 2 } \) kgs of groceries.

Example 4. Giri went on walking 3 \(\frac {1 }{ 2 } \) km, and then cycling by 4 \(\frac {1 }{ 4 } \) km and then he took a lift and traveled 8 \(\frac {3 }{ 8 } \) km. Find out how much distance he traveled? Solution: Giri went on walking =3 \(\frac {1 }{ 2 } \) km Giri went on cycling=4 \(\frac {1 }{ 4 } \) km Giri took a lift and travelled=8 \(\frac {3}{ 8 } \) km The total distance he travelled= 3 \(\frac {1 }{ 2 } \)+4 \(\frac {1 }{ 4 } \) + 8 \(\frac {3}{ 8 } \) =\(\frac {7}{ 2 } \)+\(\frac {9 }{ 4 } \)+\(\frac {67 }{ 8 } \) =\(\frac {7 × 4 }{ 2 ×4 } \) + \(\frac {9 × 2 }{ 4 × 2} \) + \(\frac {67}{ 8 } \) (LCM of 2,4,8 is 8) =\(\frac {28}{ 8 } \)+\(\frac {18}{ 8 } \)+ \(\frac {67}{ 8 } \) =\(\frac {113}{ 8 } \)=14 \(\frac {1}{ 8 } \)

Example 5. Sameera went to a market and bought mangoes 3 \(\frac {3}{ 4 } \) and her sister bought 4 \(\frac {5}{ 8 } \) mangoes. Find how many kgs of mangoes bought by Sameera and her sister? Solution: Sameera bought mangoes= 3 \(\frac {3}{ 4 } \) Sameera sister bought mangoes=4 \(\frac {5}{ 8 } \) Total no. of kg of mangoes bought by Sameera and her sister=3 \(\frac {3}{ 4 } \) + 4 \(\frac {5}{ 8 } \) = \(\frac {15}{ 4 } \) + \(\frac {29}{ 8 } \) = \(\frac {15 × 2}{ 4× 2} \)+\(\frac {29}{ 8 } \) = \(\frac {30}{ 8 } \)+\(\frac {29}{ 8 } \)=\(\frac {59}{ 8 } \) =7\(\frac {3}{ 8 } \) Therefore, Sameera and her sister bought 7\(\frac {3}{ 8 } \) kg of mangoes.

Example 6. For a birthday party, Akhil distributed 14 \(\frac {1}{ 2 } \) liters of Pepsi, 10 \(\frac {3}{ 4 } \) liters of sprite, and 12 \(\frac {5}{ 8 } \) liters of thum sup. Find how many liters of cool drinks he distributed at the birthday party? Solution: Akhil distributed pepsi= 14 \(\frac {1}{ 2 } \) Akhil distributed sprite=10 \(\frac {3}{ 4 } \) Akhil distributed thums up=12 \(\frac {5}{ 8 } \) Total no. of liters of cool drinks Akhil distributed in the party=14 \(\frac {1}{ 2 } \) +10 \(\frac {3}{ 4 } \) +12 \(\frac {5}{ 8 } \) =\(\frac {29}{ 2 } \)+\(\frac {43}{ 4 } \)+\(\frac {101}{ 8 } \) =\(\frac {29 ×4}{ 2 ×4 } \)+\(\frac {43 ×2}{ 4 ×2 } \)+\(\frac {101}{ 8 } \) =\(\frac {116}{ 8 } \)+ \(\frac {86}{ 8 } \)+\(\frac {101}{ 8 } \) =\(\frac {303}{ 8 } \)=37 \(\frac {7}{ 8 } \) Akhil distributed 37 \(\frac {7}{ 8 } \) liters of cool drinks at the birthday party.

Example 7. In a competition between two friends, Anjana prepared 20 \(\frac {1}{ 2 } \) lit of orange juice and Sanjana prepared 22 \(\frac {5}{ 8 } \) of orange juice. Find how many liters of juice are prepared by both of them? Solution: Anjana prepared orange juice= 20 \(\frac {1}{ 2 } \) Sanjana prepared orange juice=22 \(\frac {5}{ 8} \) No. of liters of juice prepared by both of them= 20 \(\frac {1}{ 2 } \) + 22 \(\frac {5}{ 8 } \) = \(\frac {41}{ 2 } \)+ \(\frac {181}{ 8 } \) =\(\frac {41 ×4}{ 2 ×4 } \) +\(\frac {181}{ 8 } \) =\(\frac {164}{ 8 } \)+\(\frac {181}{ 8 } \)=\(\frac {345}{ 8 } \) =43\(\frac {1}{ 8 } \) Anjana and sanjana both prepared 43 \(\frac {1}{ 8 } \) liters of juice.

Example 8. Sriram has wires of length 6 \(\frac {3}{ 4 } \) m, 10 \(\frac {5}{ 8 } \). Find the length of both the wires? Solution: First wire length= 6 \(\frac {3}{ 4 } \) Second wire length=10 \(\frac {5}{ 8 } \) Length of both the wires= 6 \(\frac {3}{ 4 } \) +10 \(\frac {5}{ 8 } \) =\(\frac {27}{ 4 } \) +\(\frac {85}{ 8 } \) = \(\frac {27 × 2}{ 4 × 2 } \) +\(\frac {85}{ 8 } \) =\(\frac {54}{ 8 } \) +\(\frac {85}{ 8 } \) =\(\frac {139}{ 8 } \) =17 \(\frac {3}{ 8 } \) The length of both wires is 17 \(\frac {3}{ 8 } \) .

Example 9. Bhaskar spent 8 \(\frac {1}{ 2 } \) hours on work, 2 \(\frac {1}{ 2} \) hours on the playground. He spent 1 \(\frac {3}{ 4 } \)on walking. Find how much time he spent on the day? Solution: Bhaskar spent on work=8 \(\frac {1}{ 2 } \) Bhaskar spent on playground=2 \(\frac {1}{ 2 } \) Bhaskar spent on walking=1 \(\frac {3}{ 4} \) Bhaskar spent on the day= 8 \(\frac {1}{ 2 } \) + 2 \(\frac {1}{ 2 } \) + 1\(\frac {3}{ 4 } \) = \(\frac {17}{ 2 } \) +\(\frac {5}{ 2 } \) +\(\frac {7}{ 4 } \) = \(\frac {17 × 2}{ 2 ×2 } \) + \(\frac { 5× 2}{ 2 ×2 } \) +\(\frac {7}{ 4 } \) =\(\frac {34}{ 4 } \) + \(\frac {10}{ 4 } \) +\(\frac {7}{ 4 } \) =\(\frac {51}{ 4 } \) =12 \(\frac {3}{ 4 } \) Therefore, Bhaskar spent 12 \(\frac {3}{ 4 } \) hours a day.

Example 10. Srikrishna bought 5 \(\frac {1}{ 4 } \) of vegetables, 20 \(\frac {3}{ 4 } \) kg of groceries, and 1 \(\frac {1}{ 2} \) kg of chicken. Find how many kgs he bought? Solution: Srikrishna bought vegetables= 5 \(\frac {1}{ 4 } \) kg Srikrishna bought groceries=20 \(\frac {3}{ 4 } \) kg Srikrishna bought chicken= 1 \(\frac {1}{ 2 } \) kg Srikrishna bought all=5 \(\frac {1}{ 4 } \) +20 \(\frac {3}{ 4 } \) +1 \(\frac {1}{ 2 } \) = \(\frac {21}{ 4 } \) +\(\frac {83}{ 4 } \) +\(\frac {3}{ 2 } \) =\(\frac {21}{ 4 } \) +\(\frac {83}{ 4 } \)+ \(\frac {3 ×2}{ 2 × 2 } \) =\(\frac {21}{ 4 } \) +\(\frac {83}{ 4 } \) + \(\frac {6}{ 4 } \) =\(\frac {110}{ 4 } \)=\(\frac {55}{ 2 } \)=27 \(\frac {1}{ 2 } \) Srikrishna bought 27 \(\frac {1}{ 2 } \) kg.

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Solution. This word problem requires addition of fractions. Choosing a common denominator of 4, we get. 1/2 + 3/4 = 2/4 + 3/4 = 5/4. So, John walked a total of 5/4 miles. Example #2: Mary is preparing a final exam. She study 3/2 hours on Friday, 6/4 hours on Saturday, and 2/3 hours on Sunday. How many hours she studied over the weekend.

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators. Solution: Answer: The warehouse has 21 and one-half meters of tape in all. Example 8: An electrician has three and seven-sixteenths cm of wire. He needs only two and five-eighths cm of wire for a job.

A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!

Adding Fractions. A fraction like 3 4 says we have 3 out of the 4 parts the whole is divided into. To add fractions there are Three Simple Steps: Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators ), put that answer over the denominator. Step 3: Simplify the fraction (if possible)

Solved Examples. Let us solve some problems based on adding fractions. Q. 1: Add 1/2 and 7/2. Solution: Given fractions: 1/2 and 7/2 Since the denominators are the same, hence we can just add the numerators here, keeping the denominator as it is.

Here's an example of adding fractions with like denominators, using the three steps from earlier. Find the sum of 3 / 5 + 1 / 5. Solution: The denominators are already the same, so we can skip step 1. Let's add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is 4 / 5.

Problem nº 1. Problem nº 2. Problem nº 3. Solution to Problem nº 1. This is an example of a problem involving the addition of a whole number and a fraction. The simplest way to show the number of cookies I ate is to write it as a mixed number. And the data given in the word problem gives us the result: 9 biscuits and 5 / 6 of a biscuit = 9 ...

Add and subtract fractions word problems. Google Classroom. Amir is sorting his stamp collection. He made a chart of the fraction of stamps from each country in his collection. 7 12 of Amir's stamps are from either Morocco or Spain. Country. Fraction of stamps. France. 1 3.

Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers, you're ready to add fractions. Click through the slideshow to learn how to add fractions. Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.

Add and subtract fractions word problems (same denominator) The table shows the amount of apples three friends collected. How many buckets of apples did Fred and Taylor pick combined? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.

Here are the steps to add fractions with the same denominator: Step 1: Add the numerators of the given fractions. Step 2: Keep the denominator the same. Step 3: Simplify. a c + b c = a + b c … c ≠ 0. Example 1: Find 1 4 + 2 4. 1 4 + 2 4 = 1 + 2 4 = 3 4. We can visualize this addition using a bar model:

Description: This packet helps students practice doing word problems using addition of fractions with like denominators.Each page has a speed and accuracy guide, to help students see how fast and how accurately they should be doing these problems. After doing all 23 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them.

Step Three: Add the numerators and find the sum. The final step is to add the numerators and keep the denominator the same: 2/9 + 4/9 = (2+4)/9 = 6/9. In this case, 6/9 is the correct answer, but this fraction can actually be reduced. Since both 6 and 9 are divisible by 3, 6/9 can be reduced to 2/3. Final Answer: 2/3.

Word problems with fractions: involving a fraction and a whole number. Finally, we are going to look at an example of a word problem with a fraction and a whole number. Now we will have to convert all the information into a fraction with the same denominator (as we did in the example above) in order to calculate. This morning Miguel bought 1 ...

Like & unlike denominators. Below are our grade 5 math word problem worksheet on adding and subtracting fractions. The problems include both like and unlike denominators, and may include more than two terms. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.

The way of solving the problems, however, always stayed the same. To summarize, the steps for adding fractions are: Find the GCM of the two denominators. Divide the GCM by the denominator and multiply that by the numerator to convert each fraction into a fraction that has the GCM as the new denominator. When we've done the two previous steps ...

Step 2: For the addition and subtraction of fractions, all fractions must have the same denominator. If your fractions already have the same denominator, you can skip to Step 3. The fractions 3 20 ...

College Math; History; Games; MAIN MENU; 1 Grade. Adding and subtracting up to 10; Comparing numbers up to 10; Adding and subtracting up to 20; ... Fraction Addition and Subtraction: Problems with Solutions. Problem 1. Calculate the sum of the fractions: [tex]\frac{1}{5}+\frac{2}{5}[/tex] [tex]\frac{2}{5}[/tex]

Addition of Fractions with Same Denominators. Step 1: Make sure the fractions' denominators are the same. If so, move on to step 2. Step 2: Add the numerators and divide by the common denominator to get the total. Step 3: If necessary, simplify the fraction to its simplest form. 1.

A mixed number or a mixed fraction is a type of fraction which is a combination of both a whole number and a proper fraction. We express improper fractions as mixed numbers. For example, 5\(\frac{1}{3}\), 1\(\frac{4}{9}\), 13\(\frac{7}{8}\) are mixed fractions. Unit fraction. A unit fraction is a fraction with a numerator equal to one.

A fraction is the ratio of two numbers.Most commonly, we consider rational numbers, those fractions which are the ratio of two integers or decimals.. An example of a fraction is .In the example, the numerator is and represents the number of individual parts of a given fraction, and the denominator is and represents the individual parts needed for the fraction to be one whole.

12 practice problems and an answer key. Description: This packet helps students practice solving word problems that require addition with fractions with different denominators. Each page contains 6 problems. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems.

Try to solve the Questions on Adding Mixed Numbers available on your own before you cross-check with the respective Solutions and explanations. For better understanding, we have provided the Examples on Mixed Numbers Addition step by step. Understand the Problem Solving Strategy Used and Solve the Related Problems on your own. Also, Refer ...