The Process of Cancellation

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The process of cancellation is used for multiplying and dividing fractions. Two fractions can be cancelled or reduced if a numerator and denominator can be divided by a common factor. This is very similar to reducing two factions.

2		3
---	x	---	=	---
3		4

The first denominator and the second numerator can be divided by 3.

2		3/3
---	x	---	=	---
3/3		4

This gives the following result:

2		1
---	x	---	=	---
1		4

However, don't stop there. The first numerator and the second denominator can also be divided by 2.

2/2		1
---	x	---	=	---
1		4/2

This will give the following result:

1		1		1
---	x	---	=	---
1		2		2

Your answer will be in lowest terms if you cancel out ever numerator with every denominator as much as possible. This saves you the trouble of cancelling or reducing your answer after multiplying or dividing. If you did not cancel the answer would have been:

2		3		6
---	x	---	=	---
3		4		12

6	/	2		3
---		---	=	---
12	/	2		6

3	/	3		1
---		---	=	---
6	/	3		2

You would have to reduce by 2/2 and 3/3 before you get to simplest form. Generally your work is much easier when you cancel out before you multiply the fractions together.

The answer in simplest form is 1/2.

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