# 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.

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 = $$\frac{1}{2}$$ hourTime taken to paint a chair = $$\frac{1}{3}$$ hourTotal 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:

= 3/5 × 75

= 45 pages.

= 30 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?

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