# Division of Fractions

## Notes

### Division of the Whole Number by a Fraction:

Let us find 3 ÷ 1/4.

Number of 1/4 parts obtained when each of the 3 whole, are divided into 1/4 equal parts = 12

Observe That, 3 xx 4/1 = 3 xx 4 = 12.

Thus, 3 ÷ 1/4 = 3 xx 4/1 = 12.

#### 1. Divide a whole number by any fraction:

While dividing a whole number by a fraction, we multiply the whole number with the reciprocal of that fraction.

For example,
2 ÷ 3/5 = 2 xx 5/3 = 10/3.

7 ÷ 2/5 = 7 xx 5/2 = 35/2.

6 ÷ 4/7 = 6 xx 7/4 = 42/4 = 21/2

#### 2. Divide a whole number by a mixed fraction:

While dividing a whole number by a mixed fraction, first convert the mixed fraction into an improper fraction and then solve it.

Thus,
4 ÷ 2 2/5 = 4 ÷ 12/5 = 4 xx 5/12 = 20/12 = 5/3.

5 ÷ 3 1/3 = 5 ÷ 10/3 = 5 xx 3/10 = 15/10 = 3/2.

#### 3. Division of a Fraction by a Whole Number:

While dividing a fraction by a whole number we multiply the fraction by the reciprocal of the whole number.

For example, 2/3 ÷ 7 = 2/3 xx 1/7 = 2/21.

#### 4. Division of a Fraction by Another Fraction:

While dividing one fraction by another fraction, we multiply the first fraction by the reciprocal of the other.

So, 2/3 ÷ 5/7 = 2/3 xx 7/5 = 14/15.

## Example

There are 6 blocks of jaggery, each of one kilogram. If one family requires one and a half kg jaggery every month, for how many families will these blocks suffice?

One and a half is 1 + 1/2 = 3/2.

Let us divide to see how many families can share the jaggery.

6 ÷ 3/2 = 6/1 ÷ 3/2 = 6/1 xx 2/3 = 4.

Therefore, 6 blocks will suffice for 4 families.

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Division of Fractions- Why Do We Invert & Multiply? [00:57:25]
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