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.

Find the reciprocal of 3 ¾

The reciprocal of 3 ¾ is 4/15.

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

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? \(\frac{10}{15}\) ÷ \(\frac{5}{1}\) = \(\frac{10}{15}\) × \(\frac{1}{5}\) = \(\frac{2 × \not 5 × 1}{3 × \not 5 × 5}\) = \(\frac{2}{15}\)

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

4. Solve: 5/7 ÷ 10

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

For example:

1. Divide 7/8 by 1/5

2. Divide: 5/9 ÷ 10/18

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\(\frac{1}{3}\)

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

2. Divide: 2  4/17 ÷ 1  4/17

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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