Division of Fractions
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
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.
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.
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.
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`.
The answer is '`7/12`'