In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.
1. 4/7 of a number is 84. Find the number.
Solution:
According to the problem,
4/7 of a number = 84
Number = 84 × 7/4
[Here we need to multiply 84 by the reciprocal of 4/7]
= 21 × 7
= 147
Therefore, the number is 147.
2. 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?
Time taken to paint a table = \(\frac{1}{2}\) hour Time taken to paint a chair = \(\frac{1}{3}\) hour Total time taken = \(\frac{1}{2}\) hour + \(\frac{1}{3}\) hour = \(\frac{5}{6}\) hour |
\(\frac{1}{2}\) + \(\frac{1}{3}\) L.C.M. of 2, 3 is 6. = \(\frac{3}{6}\) + \(\frac{2}{6}\) \(\frac{1 × 3}{2 × 3}\) = \(\frac{3}{6}\) \(\frac{1 × 2}{3 × 2}\) = \(\frac{2}{6}\) |
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
4. One half of the students in a school are girls, 3/5 of
these girls are studying in lower classes. What fraction of girls are studying
in lower classes?
Solution:
Fraction of girls studying in school = 1/2
Fraction of girls studying in lower classes = 3/5 of 1/2
= 3/5 × 1/2
= (3 × 1)/(5 × 2)
= 3/10
Therefore, 3/10 of girls studying in lower classes.
5. Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson?
Solution:
Maddy reads = 3/5 of 75
= 3/5 × 75
= 45 pages.
Maddy has to read = 75 – 45.
= 30 pages.
Therefore, Maddy has to read 30 more pages.
6. 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 = 1/3 of 4
Therefore, each cow gives 4/3 of milk each day.
Total no. of cows = 4 ÷ 4/3
= 4 × ¾
= 3
Therefore there are 3 cows in the herd.
Questions and Answers 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?
● Multiplication is Repeated Addition.
● Multiplication of Fractional Number by a Whole Number.
● Multiplication of a Fraction by Fraction.
● Properties of Multiplication of Fractional Numbers.
● Worksheet on Multiplication on Fraction.
● Division of a Fraction by a Whole Number.
● Division of a Fractional Number.
● Division of a Whole Number by a Fraction.
● Properties of Fractional Division.
● Worksheet on Division of Fractions.
● Simplification of Fractions.
● Worksheet on Simplification of Fractions.
● Worksheet on Word Problems on Fractions.
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