division of mixed fraction by improper fractions Archives

When a whole number is divided by a fraction, whole number is to be multiplied by the reciprocal of that fraction.
In generalise form, for any whole number ‘a’ and fraction $\cfrac{b}{c}$

a ÷ $\cfrac{b}{c}$ = $\cfrac{a}{1} \times \cfrac{c}{b}$ = $\cfrac{a \times c}{b}$

Reciprocal of a fraction, fraction are said to be reciprocal when we simply reverse the fraction i.e numerator becomes denominator and denominator becomes numerator. Two fractions are said to be reciprocal of each other if their product is 1.
In generalise form, for any fraction $\cfrac{a}{b}$

Reciprocal of $\cfrac{a}{b}$ = $\cfrac{b}{a}$ ; $\cfrac{a}{b} \times \cfrac{b}{a}$ = 1

Example

Divide 40 by $\cfrac{6}{4}$

Solution

We have, 40 ÷ $\cfrac{6}{4}$

In order to divide a whole number by a Fraction, we need to multiply the whole number with the reciprocal of that Fraction.

We have to multiply Whole number by Reciprocal of that Fraction

40 x $\cfrac{4}{6}$ (Since, Reciprocal of $\cfrac{6}{4} \quad is \quad \cfrac{4}{6}$ )

$\cfrac { 40\times 4 }{ 6}$ = $\cfrac{160}{6}$

Simplifying the given Fraction,

HCF of 160 and 6 is 2

= $\cfrac{160 \div 2 }{6 \div 2 }$ = $\cfrac{80}{3}$

When a fraction is divided by a whole number, fraction is to be multiplied by the reciprocal of that whole number.
In generalise form, for any fraction $\cfrac{a}{b}$ and whole number ‘c’

$\cfrac { a }{ b }$ ÷ c = $\cfrac { a }{ b } \times \cfrac { 1 }{ c }$ = $\cfrac { a\times 1 }{ b\times c }$

Example

Divide $\cfrac{3}{7}$ by 6

Solution

We have, $\cfrac{3}{7}$ ÷ 6

In order to divide a Fraction by a whole number

We have to multiply Fraction with Reciprocal of that whole number

$\cfrac{3}{7} \times \cfrac{1}{6}$ (Since, Reciprocal of $\cfrac{6}{1} \quad is \quad \cfrac{1}{6})$

$\cfrac { 3\times 1 }{7\times 6}$ = $\cfrac{3}{42}$

Simplifying the given Fraction,

HCF of 3 and 42 is 3

= $\cfrac{3 \div 3 }{42 \div 3 }$ = $\cfrac{1}{14}$

When a fraction is divided by another fraction, the first fraction is multiplied by the reciprocal of second fraction.
In generalise form, for any two fractions $\cfrac{a}{b}$ and $\cfrac{c}{d}$