# Cancel

Pronunciation: /ˈkæn.səl/ Explain

To cancel is to simplify an expression using sums totaling 0 and common factors. Cancellation is the process of canceling.

Example 1: Simplify x + 3 = 5
StepExpressionExplanation
1 In order to get x by itself on the left side of the equation, the 3 will be canceled.
2 The 3 will be canceled. Create a zero sum by subtracting 3 from both sides of the equation. This uses the subtractive property of equality.
3 Group the numeric expressions. 3 - 3 is the zero sum on the left, and 5 - 3 = 2 on the right. The associative property of addition allows one to change the order of the terms, if necessary.
4 Simplify the numeric expressions using the substitution property of equality. Use the additive property of zero to change x+0 to x.
5 The solution to the equation is x = 2.
Table 1

Example 2: Simplify x + y = 3y
StepExpressionExplanation
1 In order to get x by itself on the left side of the equation, the y on the left side of the equation will be canceled.
2 The y will be canceled. Create a zero sum by subtracting y from both sides. This uses the subtractive property of equality.
3 Group the numeric expressions. y - y is the zero sum on the left, and 3y - y = 2y on the right. The associative property of addition allows one to change the order of the terms, if necessary.
4 Simplify the numeric expressions using the substitution property of equality. Use the Additive property of zero to change x + 0 to x.
5 The solution set of the equation is x = 2y.
Table 2

Example 3: Simplify
StepExpressionExplanation
1 The fraction will be simplified using cancellation.
2 Factor the numerator and denominator of the fraction. 4x = 2·2·x and 6 = 2·3.
3 Find the common factors of the numerator and denominator. The common factor is 2. Use the associative property of multiplication to group the common factors together.
4 Since anything divided by itself is 1, use the substitution property of equality to substitute 1 for 2 / 2.
5 Use the multiplicative property of 1 to eliminate the 1 from the expression.
6 The fraction 4x / 6 can be simplified to 2x / 3.
Table 3

Example 4: Simplify
StepExpressionExplanation
1 The fraction will be simplified using cancellation.
2 Factor the numerator and denominator of the fraction. 6xy = 2·3·x·y and 10x=2·5·x.
3 Find the common factors of the numerator and denominator. The common factor is 2x. Use the associative property of multiplication to group the common factors together.
4 Since anything divided by itself is 1, use the substitution property of equality to substitute 1 for 2x / 2x.
5 Use the multiplicative property of 1 to eliminate the 1 from the expression.
6 The fraction 6xy / 10x can be simplified to 3y / 5, assuming x is not 0.
Table 3

### References

1. McAdams, David E.. All Math Words Dictionary, cancel. 2nd Classroom edition 20150108-4799968. pg 29. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Cancel. 4/14/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/cancel.html.

### Revision History

4/14/2019: Updated equations and expressions to new format. (McAdams, David E.)
3/1/2019: Corrected formatting. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)