Problems on Division of Fractional Numbers

Problems on division of fractional numbers will give idea how to
solve different types of word problems.

1. In a school 2/7 of the students are boys. If there are 280 girls, find the number of boys.

Solution:

Suppose the number of students = 1

Number of boys = 1 × 2/7 = 2/7

Number of girls = 1 – 2/7 = 5/7

5/7 of the students = 280

Therefore, total number of students = 280 ÷ 5/7

= 280 × 7/5

= 392 students

Number of boys = 392 – 280 = 112 boys

2. Ron has 5 ¼ m
long  ribbon. She cuts it into three
equal pieces. What is the length of each piece of ribbon?

Solution:

Length of the ribbon = 5
¼ m

Number of equal pieces cut out = 3

Length of each piece of ribbon = 5 ¼ ÷ 3

= 21/4 ÷ 3

= 21/4 × 1/3

= 21 × 1/4 × 3

= 7/4 metre

= 1 ¾ metre

Therefore, length of each piece of ribbon is 1 ¾ metre.

3. The cost of 4  ½ m
cloth is $ 60  ¾. Find the cost of 1 m
cloth.

Solution:

Cost of 4 ½ m cloth =
$ 60  ¾

Cost of 1 m cloth = $ (60 ¾ ÷ 4 ½)

= $ (243/4 × 2/9)

= $ 27/2

= $ 13 ½

4. Sam paid $ 45 for 3 ¾ kg of sugar. How much did he pay
for 1 kg of sugar?

Solution:

Cost of 3 ¾ kg of sugar = $ 45

Cost of 1 kg of sugar = 45 ÷ 3 ¾

= 45 ÷ 15/4

= 45/1 × 4/15

= $ 12

Therefore, cost of 1 kg of sugar is $ 12.