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

Step	Expression	Explanation
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

Step	Expression	Explanation
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

Step	Expression	Explanation
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

Step	Expression	Explanation
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

Cite this article as:

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

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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.)
6/22/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/4/2010: Added "References". (McAdams, David E.)
12/24/2008: Expanded examples and used images for equations. (McAdams, David E.)
4/22/2008: Initial version. (McAdams, David E.)