Commutative Property

This property states that you can add or multiply numbers in any order.  

  • For example, 3 + 5 = 5 + 3.
  • Similarly, 4 x 7 = 7 x 4.

Associative Property

When you are only adding or multiplying, you can group any of the numbers together.  

  • For example, (2 + 4) + 6 = 2 + (4 + 6).
  • Similarly, (3 x 6) x 9 = 3 x (6 x 9).
  • When adding, look for ways to regroup to get sums that are multiples of 10.
  • When multiplying, look for ways to regroup to get products that are multiples of 10.

Distributive Property

When you’re multiplying a number times a sum, there are 2 ways you can simplify.

  1. You can find the sum first, then multiply.   For example, 5 x (4 + 2) = 5 x 6 = 30
  2. You can multiply each number in the sum, then add.   For example, 5 x (4 + 2) = (5 x 4) + (5 x 2) = 20 + 10 = 30

Evaluate the Expressions

Use the properties above to make your work simpler!

1) 14 + 7 + 16 + 23

2)  6 + 21 + 14 + 9

3)  2 x 32 x 10

4) 5 x 12 x 2

5) 8 x 32

6) 4 x 57

7) 4(2 + 3)  This is four times two plus three.

8) 5(8+9)

 

Answers

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