# Word Problems on Division of Mixed Fractions

We will discuss here how to solve the word problems on division of mixed fractions or division of mixed numbers.

Let us consider some of the examples.

1. The product of two numbers is 18. If one number is 8 2/5, find the other number.

Solution:

Product of two numbers = 18

One number = 8 2/5 = {(8 × 5) + 2}/5 = 42/5

The other number = 18 ÷ 42/5 = 18 × 5/42, (Because 18 ÷ 42/5 = 18/1 ÷ 42/5 = 18/1 × 5/42)

= 90/42

= 15/7

= 2 1/7

2. Ashish cut a 25 m long rope into pieces of 1 2/3 metres each. Find the total number of pieces he cut.

Solution:

Total number of pieces he cut = 25 ÷ 1 2/3

= 25 ÷ 5/3, (Because 25 ÷ 5/3 = 25/1 ÷ 5/3 = 25/1 × 3/5

= 25 × 3/5

= 75/5

= 15

So, Ashish cut 15 pieces.

3. A pole whose length is 10$$\frac{2}{3}$$ metres is cut into 16 equal pieces.

Solution:

What is the length of each piece?

Length of the pole = 10$$\frac{2}{3}$$ m

Number of pieces = 16

Length of each pieces = 10$$\frac{2}{3}$$ m ÷ 16

= $$\frac{32}{3}$$ ÷ $$\frac{16}{1}$$

= $$\frac{32}{3}$$ × $$\frac{1}{16}$$

= $$\frac{32}{3 × 16}$$

= $$\frac{\not 2 × \not 2 × \not 2 × \not 2 × 2}{3 × \not 2 × \not 2 × \not 2 × \not 2}$$

= $$\frac{2}{3}$$ m

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