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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsFractionsArithmetics with Fractions

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 quotientfraction division 6/3 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. fraction division 6/3 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.fraction division 2 by 1/3 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.fraction division 4 by 2/3 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.fraction division 3/4 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.fraction division 3/4 by 2/3 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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