# Division of a Fractional Number

This topic would discuss about division of a fractional number with another fractional number. In this case if any one or both of the fractional number are in mixed fraction then we will have to change that mixed fraction into improper fraction.

The rule of division of fractional number is that:

Fraction ÷ Another Fraction = Fraction × Multiplicative Inverse or, Reciprocal of the Another Fraction

Here are few examples to show division of a fraction by another fraction:

1. (i) 14 2/5 ÷ 1 11/25

⟹ 72/5 ÷ 36/25; [Changing into improper fraction]

⟹ 72/5 × 25/36; [Multiplicative inverse of the second fraction]

⟹ (72 × 25)/(5 × 36); [Product of numerator and denominator]

⟹ 1800/180

⟹ (1800 ÷ 180)/(180 ÷ 180) [Changing into lowest term]

⟹ 10

Explanation:

The fractions are in mixed form so, in the first step it is changed into improper fraction. Then the first fraction is multiplied with the reciprocal of the second fraction. The next step is both the numerators and denominators are multiplied to get the result. Then the result is reduced into lowest terms to obtain the final answer.

2. (i) 11 1/15 ÷ 1 11/45

⟹ 166/15 ÷ 56/45 [Changing into improper fraction]

⟹ 166/15 × 45/56 [Multiplicative inverse of the second fraction]

⟹ (166 × 45)/(15 × 56)                                   [Product of numerator and denominator]

⟹ 7470/840

⟹ (7470 ÷ 30)/(840 ÷ 30) [Changing into lowest term]

⟹ 249/28

⟹ 8 25/28

Explanation:

The fractions are in mixed form so, in the first step it is changed into improper fraction. Then the first fraction is multiplied with the reciprocal of the second fraction. The next step is both the numerators and denominators are multiplied to get the result. Then the result is reduced into lowest terms and finally into mixed fraction to obtain the final result.

3. (i) 1 1/5 ÷ 12/45

⟹ 6/5 ÷ 12/45; [Changing mixed fraction into improper fraction]

⟹ 6/5 × 45/12; [Multiplicative inverse of the second fraction]

⟹ (6 × 45)/(5 × 12); [Product of numerator and denominator]

⟹ 270/60

⟹ (270 ÷ 30)/(60 ÷ 30); [Changing into lowest term]

⟹ 9/2

⟹ 4 1/2

Explanation:

The first fraction is in mixed form so, in the first step it is changed into improper fraction. Then the first fraction is multiplied with the reciprocal of the second fraction. The next step is both the numerators and denominators are multiplied to get the result. Then the result is reduced into lowest terms and finally into mixed fraction to obtain the final result.

The above examples show the division of fraction by another fraction where the first fraction is multiplied by the reciprocal of the second fraction to obtain the result. After this step the division of fraction is same as multiplication of fractions where numerator and numerator is multiplied and denominator and denominator is multiplied $$\frac{Product of the Numerator}{Product of the Denominator}$$ to get the answer. The final answer is expressed in lowest terms and then in proper fraction or mixed fraction (if after changing into lowest terms it is an improper fraction).

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