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Division of Fractions

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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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Shaalaa.com | Division of Fractions- Why Do We Invert & Multiply?

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