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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