OpenStax-CNX module: m35927
1
Solve problems using the
commutative property
∗
Mackenzie Karkheck
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0
†
Abstract
Solve problems involving the addition, subtraction, and multiplication of integers, using a variety of
mental strategies (e.g., use the commutative property.
Solve problems involving the addition, subtraction, and multiplication of integers, using a variety of
mental strategies.
Ex. Use the commutative property: 5 x 18 x 2 = 5 x 2 x 18,which gives 10 x 18 = 180
Example Problem:
Use the commutative property to following multi-step multiplication problem in the most simple and
fastest manner. Hint: You may not want to multiply the numbers in the order they are written, instead
multiply the smaller numbers together so that the entire process can be done in your head.
a) 2 x 7 x 2 =
b) 2 x 5 x 12 =
c) 3 x 3 x 3 x
d) 2 x 3 x 4 x 5
Answers:
a) 2 x 7 x 2 = 2 x 2 x 7
=4 x 7
= 28
If you multiply 2 x 7 rst you get 14, which is outside of the times tables most students have memorized.
b) 2 x 5 x 12 = 10 x 12
= 120
Whenever you see two numbers that multiply to 10, using these will make the rest of the problem simple
to solve. After all we know our 10s times tables very well.
c) 3 x 3 x 3 x 3 = 9 x 3 x 3
=9x9
= 81
This problem is signicant because it has 4 numbers and there are more ways we can multiply them
together. If we try 3 x 9 we get 27 which is outside of the times tables most students have memorized.
However, there are still 2 3s left that need to be accounted for.
d) 2 x 3 x 4 x 5 = 2 x 5 x 3 x 4
= 10 x 12
∗ Version
1.1: Nov 4, 2010 1:33 pm -0500
† http://creativecommons.org/licenses/by/3.0/
http://cnx.org/content/m35927/1.1/
OpenStax-CNX module: m35927
2
= 120
First of all, the 2 x 5 = 10, and this is something we are instructed to always look for when using the
commutative property. Second, if we multiply 3 x 5 or 4 x 5 we realize that we begin to deal with numbers
that are outside of the times tables we have memorized.
http://cnx.org/content/m35927/1.1/