Associative and Commutative Property

Commutative and Associative Properties Practice

For Addition and Multiplication Only!

Multiple Choice

How could you use the Commutative Property to rearrange the problem below to make it easier to solve?

$$25\cdot7\cdot4=$$  

• $$7\cdot4\cdot25$$  

• $$25\cdot4\cdot7$$  

Answer

By using the Commutative Property and rearranging the expression to  $25\cdot4\cdot7$   you can multiply  $25\cdot4$   to get 100 and then multiply  $100\cdot7$  to get 700.  That is much easier than multiplying  $25\cdot7$  and then taking that answer and multipling it by 4.

Multiple Choice

How could you rearrange the problem below to make it easier to solve? 

$$12+7+13+8$$  

• $$8+13+7+12$$  

• $$12+8+13+7$$  

Answer

 $12+8+13+7$   puts the 12+8 together which is a nice number and 13+7 which again is a nice number.

Multiple Choice

Use the associative property to group the expression

$$6\cdot5\cdot2\cdot10$$  to make it easier to solve.

• $$\left(6\cdot2\right)\cdot5\cdot10$$  

• $$6\cdot\left(5\cdot2\cdot10\right)$$  

• $$6\cdot2\cdot\left(5\cdot10\right)$$  

Answer

By grouping  $\left(5\cdot2\cdot10\right)$  you get 100. You can then easily multiply  $6\cdot100$ to get 600.

You can use both properties too!

 $12+7+13+8$   can be rearranged using the Commutative Property to  $12+8+13+7$   but you can also use the Associative Property to group it like  $\left(12+8\right)+\left(13+7\right)$  .