Fractions are part of whole. Division is dividing a number into equal parts. In this page, the following for fractions is explained.

• division in first principles -- splitting a quantity into a number of parts and measuring one part

• simplified procedure : Division as multiplication by reciprocal

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Division is the inverse of multiplication. And division of fractions can be easily explained with that.

`3/4 -: 2/3 `

`quad = 3/4 xx 3/2` (multiply by inverse)

`quad = 9/8`.

A learner may stop at this, but I would suggest to read the rest to understand how division works for fractions.

Division `6 -: 3 = 2` is illustrated in the figure.

• `6` is the dividend

• `3` is the divisor

• `2` is the quotient What is the quotient as illustrated in the figure?

- `1`
- `2`
- `2`

The answer is '`2`' Dividend `6` is split into divisor `3` parts and one part of that `2` is the quotient.

One way to understand the integer division:

• Dividend `6` is considered as `3` parts

• in that `3` is the divisor

• In the `3` parts one part is taken. The key in this explanation is " dividend is considered as divisor parts and one part is taken". The same can be extended for fractions.

Division `2 -: 1/3 ` is illustrated in the figure. Dividend `2` is split as divisor `1/3` parts. That is `2` is the fraction `1/3` and the full part for the fraction is found. The `1/3` part is repeated to get the full part. This is shown in the figure.

What is the quotient as illustrated in the figure?

- `2`
- `6`
- `6`

The answer is '`6`'. In this, one part `6` is the quotient. `2-:1/3 = 6`

Division `4 -: 2/3 ` is illustrated in the figure. Dividend `4` is split as divisor `2/3` parts. What is the quotient as illustrated in the figure?

- `6`
- `6`
- `12`

The answer is '`12`'.

In this, one part `6` is the quotient.

`4-:2/3 = 6`

Division `3/4 -: 2/3 ` is considered. The figure shows the dividend `3/4`. The division is illustrated in the next page.

Division `3/4 -: 2/3 ` is illustrated in the figure. Dividend `3/4` is split as divisor `2/3` parts. This is shown in the figure. What is the quotient as illustrated in the figure?

- `3/8`
- `9/8`
- `9/8`

The answer is '`9/8`'. In this, the place value is `1/8` and the count is 9.

The same can be simplified as follows.

`3/4-:2/3 =3/4 xx 3/2 = 9/8`

Division is inverse of multiplication.

**Division of Fractions: **Given two fractions `p/q` and `l/m`, the division is

`p/q -: l/m`

`quad = p/q xx m/l`

`quad = (p xx m)/(q xx l)`

*Solved Exercise Problem: *

Divide `14/18 -: 4/3`.

- `7/12`
- `7/12`
- `13/18`

The answer is '`7/12`'

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