Dividing Fractions

We will discuss here about dividing fractions by a whole number, by a fractional number or by another mixed fractional number.

First let us recall how to find reciprocal of a fraction, we interchange the numerator and the denominator.

For example, the reciprocal of ¾ is 4/3.

$Division of Fractions$

Find the reciprocal of 3 ¾

The reciprocal of 3 ¾ is 4/15.

$Division of Fractions Reciprocal$

I. Division of a Fraction by a Whole Number:

4 ÷ 2 = 2 means, there are two 2’s in 4.

6 ÷ 2 = 3 means, there are two 2’s in 6.

Similarly 5 ÷ $\frac{1}{2}$ means, how many halves are there in 5?

We know that $\frac{1}{2}$ + $\frac{1}{2}$ = 1

$\frac{1}{2}$ + $\frac{1}{2}$ +	$\frac{1}{2}$ + $\frac{1}{2}$ +	$\frac{1}{2}$ + $\frac{1}{2}$ +	$\frac{1}{2}$ + $\frac{1}{2}$ +	$\frac{1}{2}$ + $\frac{1}{2}$
1 +	1 +	1 +	1 +	1	= 5

i.e. there are 10 halves in 5.

5 ÷ $\frac{1}{2}$ = 5 × $\frac{2}{1}$ = $\frac{10}{1}$ = 10

For Example:

1. $\frac{7}{10}$ ÷ 5 = $\frac{7}{10}$ ÷ $\frac{5}{1}$

= $\frac{7}{10}$ × $\frac{1}{5}$

= $\frac{7 × 1}{10 × 5}$

= $\frac{7}{50}$

2. What is $\frac{10}{15}$ ÷ 5?

$\frac{10}{15}$ ÷ $\frac{5}{1}$

= $\frac{10}{15}$ × $\frac{1}{5}$

= $\frac{2 × \not 5 × 1}{3 × \not 5 × 5}$

= $\frac{2}{15}$

$Prime Factors of 10, 5 and 3$

10 = 2 × 5

15 = 3 × 5

5 = 1 × 5

To divide a fraction by a number, multiply the fraction with the reciprocal of the number.

For example:

3. Divide 3/5 by 12

Solution:

3/5 ÷ 12

= 3/5 ÷ 12/1

= 3/5 × 1/12

= (3 × 1)/(5 × 12)

= 3/60

= 1/20

Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual.

Step II: Express the product in its lowest terms.

4. Solve: 5/7 ÷ 10

= 5/7 ÷ 10/1

= 5/7 × 1/10

= (5 × 1)/(7 × 10)

= 5/70

Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual.

Step II: Express the product in its lowest terms.

II. Division of a Fractional Number by a Fractional Number:

For example:

1. Divide 7/8 by 1/5

Solution:

7/8 ÷ 1/5

= 7/8 × 5/1

= (7 × 5)/(8 × 1)

= 35/8

= 4 3/8

Step I: Find reciprocal of 1/5.

Step II: Multiply 7/8 by it.

Step III: Express the product in its simplest form.

2. Divide: 5/9 ÷ 10/18

Solution:

5/9 ÷ 10/18

= 5/9 × 18/10

= (5 × 18)/(9 × 10)

= 90/90

= 1

Step I: Find reciprocal of 1/5.

Step II: Multiply 7/8 by it.

Step III: Express the product in its simplest form.

Division of a Fraction by a Fraction:

3. Divide $\frac{3}{4}$ ÷ $\frac{5}{3}$

Step I: Multiply the first fraction with the reciprocal of the second fraction.

Reciprocal of $\frac{5}{3}$ = $\frac{3}{5}$

Therefore, $\frac{3}{4}$ ÷ $\frac{5}{3}$ = $\frac{3}{4}$ × $\frac{3}{5}$

= $\frac{3 × 3}{4 × 5}$

= $\frac{9}{20}$

Step II: Reduce the fraction to the lowest terms. (if necessary)

4. Divide $\frac{16}{27}$ ÷ $\frac{4}{9}$

Therefore, $\frac{16}{27}$ ÷ $\frac{4}{9}$ = $\frac{16}{27}$ × $\frac{9}{4}$ ; [Reciprocal of $\frac{4}{9}$ = $\frac{9}{4}$ ]

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

= $\frac{4}{3}$

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

$Prime Factors of 16, 27, 9 and 4$

16 = 2 × 2 × 2 × 2

9 = 3 × 3

27 = 3 × 3 × 3

4 = 2 × 2

III. Division of a Mixed Number by another Mixed Number:

For example:

1. Divide 2 ¾ by 1 2/3

Solution:

2 ¾ ÷ 1 2/3

= 11/4 ÷ 5/3

= 11/4 × 3/5

= (11 × 3)/(4 × 5)

= 33/20

= 1 13/20

Express the mixed numbers as improper fractions and multiply as usual.

2. Divide: 2 4/17 ÷ 1 4/17

Solution:

2 4/17 ÷ 1 4/17

= 38/17 ÷ 21/17

= 38/17 × 17/21

= (38 × 17)/(17 × 21)

= 646/357

= 38/21

= 1 17/21

Express the mixed numbers as improper fractions and multiply as usual.

Questions and Answers on Dividing Fractions:

I. Divide the following.

(i) $\frac{2}{6}$ ÷ $\frac{1}{3}$

(ii) $\frac{5}{8}$ ÷ $\frac{15}{16}$

(iii) $\frac{5}{6}$ ÷ 15

(iv) $\frac{7}{8}$ ÷ 14

(v) $\frac{2}{3}$ ÷ 6

(vi) 28 ÷ $\frac{7}{4}$

(vii) 2 $\frac{5}{6}$ ÷ 34

(viii) 9 $\frac{1}{2}$ ÷ $\frac{38}{2}$

(ix) 3 $\frac{1}{4}$ ÷ $\frac{26}{28}$

(x) 7 $\frac{1}{3}$ ÷ 1 $\frac{5}{6}$

(xi) 2 $\frac{3}{5}$ ÷ 1 $\frac{11}{15}$

(xii) 1 $\frac{1}{2}$ ÷ $\frac{4}{7}$

Related Concept

● Fraction of a Whole Numbers

● Representation of a Fraction

● Equivalent Fractions

● Properties of Equivalent Fractions

● Like and Unlike Fractions

● Comparison of Like Fractions

● Comparison of Fractions having the same Numerator

● Types of Fractions

● Changing Fractions

● Conversion of Fractions into Fractions having Same Denominator

● Conversion of a Fraction into its Smallest and Simplest Form

● Addition of Fractions having the Same Denominator

● Subtraction of Fractions having the Same Denominator

● Addition and Subtraction of Fractions on the Fraction Number Line

4th Grade Math Activities

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Dividing Fractions

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