# Division in Terms of Reciprocal

We will learn division in terms of reciprocal.

Let us divide $$\frac{1}{4}$$ into 2 parts. In the following figure A the colored part represents $$\frac{1}{4}$$ of the whole figure. Now, we divide each part into two equal parts. The colored part in the figure B represents $$\frac{1}{8/}$$.

Therefore, $$\frac{1}{4}$$ ÷ 2 is equal to $$\frac{1}{8}$$. We know that the reciprocal or the multiplicative inverse of 2 is $$\frac{1}{2}$$.

So, if we multiply $$\frac{1}{4}$$ by the reciprocal of 2, we get $$\frac{1}{4}$$ × $$\frac{1}{2}$$ = $$\frac{1}{8}$$.

To divide a fraction or a whole number by a fraction or a whole number, we multiply the reciprocal of the divisor.

Solved Examples on Division in Terms of Reciprocal:

1. Divide 15 by $$\frac{3}{7}$$

Solution:

Reciprocal of $$\frac{3}{7}$$ is $$\frac{7}{3}$$. Thus 15 ÷ $$\frac{3}{7}$$ = $$\frac{15}{1}$$ × $$\frac{7}{3}$$ = $$\frac{105}{3}$$ = 35

2. Divide $$\frac{4}{9}$$ by 8

Solution:

$$\frac{4}{9}$$ ÷ 8 = $$\frac{4}{9}$$ ÷ $$\frac{8}{1}$$

= $$\frac{4}{9}$$ × $$\frac{1}{8}$$

= $$\frac{4}{72}$$

= $$\frac{1}{18}$$

3. Divide 13$$\frac{3}{5}$$ by 13

Solution:

We first convert the mixed number into improper fraction.

13$$\frac{3}{5}$$ = $$\frac{13 × 5 + 3}{5}$$ = $$\frac{68}{5}$$

Now, $$\frac{68}{5}$$ ÷ 13 = $$\frac{68}{5}$$ ÷ $$\frac{13}{1}$$

= $$\frac{68}{5}$$ × $$\frac{1}{13}$$

= $$\frac{68}{65}$$

= 1$$\frac{3}{65}$$

4. Divide 4$$\frac{1}{2}$$ by $$\frac{3}{4}$$

Solution:

We first convert the mixed number into improper fraction.

4$$\frac{1}{2}$$ = $$\frac{4 × 2 + 1}{2}$$ = $$\frac{9}{2}$$

Now, $$\frac{9}{2}$$ ÷ $$\frac{3}{4}$$ = $$\frac{9}{2}$$ × $$\frac{4}{3}$$

= $$\frac{36}{6}$$

= 6

5. How many pieces measuring $$\frac{5}{6}$$ m can be cut from a thread of length 150 m?

Solution:

Length of one piece = $$\frac{5}{6}$$ m

Length of the thread = 150 m

Number of pieces = 150 ÷ $$\frac{5}{6}$$

= 150 × $$\frac{6}{5}$$

= 180

Questions and Answers on Division in Terms of Reciprocal:

I. Fill in the blanks:

(i) $$\frac{3}{16}$$ ÷ 1

(ii) $$\frac{8}{15}$$ ÷ $$\frac{15}{8}$$

(iii) $$\frac{5}{9}$$ ÷ $$\frac{1}{9}$$

(iv) $$\frac{3}{10}$$ ÷ $$\frac{12}{10}$$

(v) 5 ÷ $$\frac{20}{7}$$

(vi) $$\frac{15}{8}$$ ÷ 45

(vii) $$\frac{11}{21}$$ ÷ $$\frac{33}{28}$$

(viii) $$\frac{2}{9}$$ ÷ $$\frac{16}{27}$$

(ix) $$\frac{5}{2}$$ ÷ $$\frac{25}{18}$$

Answers:

(i) $$\frac{3}{16}$$

(ii) $$\frac{64}{225}$$

(iii) 5

(iv) $$\frac{1}{4}$$

(v) $$\frac{7}{4}$$

(vi) $$\frac{1}{24}$$

(vii) $$\frac{4}{9}$$

(viii) $$\frac{3}{8}$$

(ix) $$\frac{9}{5}$$

II. Word Problems on Division in Terms of Reciprocal:

1. 7$$\frac{1}{2}$$ liter of milk has to be packed in bottles of $$\frac{3}{4}$$ liters. How many bottles are required to fill all the milk?

Answer: 10 bottles

2. 12$$\frac{1}{2}$$ m of cloth is required to stitch 1 shirt. How many shirts can be stitched from a cloth of length 75 m?

Answer: 6 shirts

3. A car covers 30$$\frac{5}{6}$$ km in 1 hour. How much time will the car take to cover 360 km?

Answer: 11$$\frac{25}{37}$$ hours

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