Word Problems on Fraction
In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.
I. Word Problems on Addition of Fractions:
1. Nairitee took \(\frac{7}{8}\) hour to paint a table and \(\frac{2}{3}\) hour to paint a chair. How much time did he take in painting both items?
Total time taken in painting both items = \(\frac{7}{8}\) h + \(\frac{2}{3}\) h = (\(\frac{7}{8}\) + \(\frac{2}{3}\)) h
= (\(\frac{21 + 16}{24}\)) h
= \(\frac{37}{24}\) h
= 1\(\frac{13}{24}\) h
Therefore, Nairitee took 1\(\frac{13}{24}\) hours in painting both items.
2. Nitheeya and Nairitee \(\frac{3}{10}\) and \(\frac{1}{6}\) of a cake respectively. What portion of the cake did they eat together?
The portion of cake ate by Nitheeya = \(\frac{3}{10}\)
The portion of cake ate by Nitheeya = \(\frac{1}{6}\) The portion they ate together = \(\frac{3}{10}\) + \(\frac{1}{6}\)
= \(\frac{9}{30}\) + \(\frac{5}{30}\); [Since, LCM of 10 and 6 = 30]
= \(\frac{9 + 5}{30}\)
= \(\frac{14}{30}\)
= \(\frac{7}{15}\)
Therefore, together Nitheeya and Nairitee ate \(\frac{7}{15}\) of the cake.
3. Rachel took \(\frac{1}{2}\) hour to paint a table and \(\frac{1}{3}\) hour to paint a chair. How much time did she take in all?
II. Word Problems on Subtraction of Fractions:
1. Out of \(\frac{12}{17}\) m of cloth given to a tailor, \(\frac{1}{5}\) m were used. Find the length of cloth unused.
Length of the cloth given to the tailors = \(\frac{12}{17}\) m
Length of cloth used = \(\frac{1}{5}\) m
Length of the unused cloth = \(\frac{12}{17}\) m - \(\frac{1}{5}\) m
= (\(\frac{12}{17}\) - \(\frac{1}{5}\)) m
= (\(\frac{12 × 5}{17 × 5}\) - \(\frac{1 × 17}{5 × 17}\)) m; [Since, LCM of 17 and 5 = 85]
= (\(\frac{60}{85}\) - \(\frac{17}{85}\)) m
= (\(\frac{60 - 17}{85}\) m
= (\(\frac{43}{85}\) m
2. Nairitee has $6\(\frac{4}{7}\). She gives $4\(\frac{2}{3}\) to her mother. How much money does she have now?
Money with Nairitee = $6\(\frac{4}{7}\)
Money given to her mother = $4\(\frac{2}{3}\)
Money left with Nairitee = $6\(\frac{4}{7}\) - $4\(\frac{2}{3}\)
= $(6\(\frac{4}{7}\) - 4\(\frac{2}{3}\))
= $(\(\frac{46}{7}\) - \(\frac{14}{3}\))
= $(\(\frac{46 × 3}{7 × 3}\) - \(\frac{14 × 7}{3 × 7}\)) ; [Since, LCM of 7 and 3 = 21]
= $(\(\frac{138}{21}\) - \(\frac{98}{21}\))
= $\(\frac{40}{21}\)
= $1\(\frac{19}{21}\)
Therefore, Nairitee has $1\(\frac{19}{21}\).
3. If 3\(\frac{1}{2}\) m of wire is cut from a piece of 10 m long wire, how much of wire is left?
Total length of the wire = 10 m
Fraction of the wire cut out = 3\(\frac{1}{2}\) m = \(\frac{7}{2}\) m
Length of the wire left = 10 m – 3\(\frac{1}{2}\) m
= [\(\frac{10}{1}\) - \(\frac{7}{2}\)] m, [L.C.M. of 1, 2 is 2]
= [\(\frac{20}{2}\) - \(\frac{7}{2}\)] m, [\(\frac{10}{1}\) × \(\frac{2}{2}\)]
= [\(\frac{20 - 7}{2}\)] m
= \(\frac{13}{2}\) m
= 6\(\frac{1}{2}\) m
III. Word Problems on Multiplication of Fractions:
1. \(\frac{4}{7}\) of a number is 84. Find the number. Solution: According to the problem, \(\frac{4}{7}\) of a number = 84 Number = 84 × \(\frac{7}{4}\) [Here we need to multiply 84 by the reciprocal of \(\frac{4}{7}\)]
= 21 × 7 = 147 Therefore, the number is 147.
2. One half of the students in a school are girls, \(\frac{3}{5}\) of these girls are studying in lower classes. What fraction of girls are studying in lower classes?
Fraction of girls studying in school = \(\frac{1}{2}\)
Fraction of girls studying in lower classes = \(\frac{3}{5}\) of \(\frac{1}{2}\)
= \(\frac{3}{5}\) × \(\frac{1}{2}\)
= \(\frac{3 × 1}{5 × 2}\)
= \(\frac{3}{10}\)
Therefore, \(\frac{3}{10}\) of girls studying in lower classes.
3. Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson? Solution: Maddy reads = \(\frac{3}{5}\) of 75 = \(\frac{3}{5}\) × 75
= 45 pages. Maddy has to read = 75 – 45. = 30 pages. Therefore, Maddy has to read 30 more pages.
IV. Word Problems on Division of Fractions:
1. A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd?
Solution: A herd of cows gives 4 litres of milk each day. Each cow gives one-third of total milk each day = \(\frac{1}{3}\) of 4 Therefore, each cow gives \(\frac{4}{3}\) of milk each day. Total no. of cows = 4 ÷ \(\frac{4}{3}\) = 4 × \(\frac{3}{4}\) = 3 Therefore there are 3 cows in the herd.
Worksheet on Word problems on Fractions:
1. Shelly walked \(\frac{1}{3}\) km. Kelly walked \(\frac{4}{15}\) km. Who walked farther? How much farther did one walk than the other?
2. A frog took three jumps. The first jump was \(\frac{2}{3}\) m long, the second was \(\frac{5}{6}\) m long and the third was \(\frac{1}{3}\) m long. How far did the frog jump in all?
3. A vessel contains 1\(\frac{1}{2}\) l of milk. John drinks \(\frac{1}{4}\) l of milk; Joe drinks \(\frac{1}{2}\) l of milk. How much of milk is left in the vessel?
4. Between 4\(\frac{2}{3}\)and 3\(\frac{2}{3}\) which is greater and by how much?
5. What must be subtracted from 5\(\frac{1}{6}\) to get 2\(\frac{1}{8}\)?
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● Multiplication of Fractional Number by a Whole Number.
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● Division of a Fractional Number.
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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
» Fraction Word Problems
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