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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.
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

click on the content to continue..

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.

• 7/12
• 7/12
• 13/18

The answer is '7/12'

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