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

4th Grade Math Activities

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