## Dividing Fractions

### Dividing Whole numbers by Fractions:

- 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

a ÷ = =

- 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

Reciprocal of = ; = 1

**Example **

Divide 40 by

**Solution**

We have, 40 ÷

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 (Since, Reciprocal of )

=

Simplifying the given Fraction,

HCF of 160 and 6 is 2

= =

__Dividing Fraction by Whole Number:__

- 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 and whole number ‘c’

÷ c ==

**Example**

Divide by 6

**Solution**

We have, ÷ 6

In order to divide a Fraction by a whole number

We have to multiply Fraction with Reciprocal of that whole number

(Since, Reciprocal of

=

Simplifying the given Fraction,

HCF of 3 and 42 is 3

= =

__Dividing Fraction by Fractions__

- 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 and

÷==

**Example**

Divide ÷

**Solution**

We have, ÷

In order to divide a Fraction by another Fraction

We have to multiply First Fraction with Reciprocal of the second Fraction

We have ÷

= (Since, Reciprocal of )

=

Simplifying the given Fraction,

HCF of 20 and 180 is 20

= =

### Division of Mixed Fraction by Improper or Proper Fractions

- When a mixed fraction is divide by a proper or improper fraction, convert mixed fraction into improper fraction and then divide them.

**Example**

Divide ÷

**Solution**

We have, ÷

Simplifying, the above equation, we get ÷

In order to divide a Fraction by another Fraction

We have to multiply First Fraction with Reciprocal of the second Fraction

(Since, Reciprocal of )

=

Simplifying the given Fraction,

HCF of 45 and 60 is 15

= =

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