PROPERTIES OF MULTIPLICATIONBy: Mr. Reed

PROPERTIES OF MULTIPLICATION

•Commutative Property

•Associative Property

•Distributive Property

COMMUTATIVE PROPERTY

COMMUTATIVE PROPERTY:

•This property basically states that each part on either side of the multiplication sign can be switched around.

CORRECT EXAMPLES

5 X 4 = 4 X 5

2 X 3 = 3 X 2

0 X 5 = 5 X 0

NOT EXAMPLES

5 X 1 = 5 ←Identity Property

  3 X 0 = 0 ←Zero Property

1 X (10 X 3) = (1 X 10) X 3 ←Associative Property

PRACTICE A

•1.  Which of the following is an example of the commutative property? a.  3 X (5 X 2) = (3 X 5) X 2   →b.  6 X 7 = 7 X 6 c.  4 X 0 = 0 d.  1 X 9 = 9

The correct answer is b, because there are same 2 numbers on each side of the X sign.  They are just switched around.  All of the other answer choices are showing different properties.

PRACTICE B

2.  Which of the following is correct? a.  3 X 2 X 5 = 325 b.  1 X 9 = 10    →c.  8 X 4 = 4 X 8 d.  0 X 5 = 5The correct answer is c, because there are same 2 numbers on each side of the X sign.  They are just switched around.  All of the other answer choices are incorrect (wrong).•

ASSOCIATIVE PROPERTY

ASSOCIATIVE PROPERTY

This property basically keeps all 3 numbers the same.  It just switches the numbers around or moves the ( ).

CORRECT EXAMPLES

10 X (5 X 3) = (10 X 5) X 3 or (10 X 5) X 3 = 10 X (5 X 3)

10 X (5 X 3) = 10 X 15 or (10 X 5 ) X 3 = 50 X 3

10 X (5 X 3) = 150 or (10 X 5) X 3 = 150

OTHER CORRECT EXAMPLES

10 X 5 X 3 = 5 X 10 X 3

10 X 5 X 3 = 3 X 5 X 10

10 X 5 X 3 = 10 X 3 X 5

PRACTICE

1.  Which of these are not equal to 5 X (4 X 3)? a.  (5 X 4) X 3 b.  5 X 12 c.  60     →d.  20 x 6

The correct answer is d, because the other 3 choices are all equal to 5 X (4 X 3).  20 X 6 is not equal, it should have been 20 X 3.

MORE PRACTICE

2.  Which of the following are not equal to 6 X 4 X 9?      →a.  30 X 9 b.  6 X 36 c.  9 X 6 X 4 d.  6 X (4 X 9)

The correct answer is a, because the other 3 choices are all equal to 6 X 4 X 9.   30 X 9 is not equal, it should have been 24 X 9.

DISTRIBUTIVE PROPERTY

DISTRIBUTIVE PROPERTY

This property allows you to break up the larger number into 2 smaller numbers. This way you are multiplying 2 sets of familiar numbers and then adding them together.

DETAILED EXAMPLE PART A: SETTING UP THE EQUATION

8 X 16 = (8 X 6) + (8 X 10)

*The 8 is put in each of the ( ). (8 X ) + (8 X )

*The 16 is broken down into 6 and 10, because 6 + 10 = 16, so now we have each of these numbers in each ( ). (8 X 6) + (8 X 10)

DETAILED EXAMPLE PART B: STEP TO SOLVING #1

DETAILED EXAMPLE PART B: STEP TO SOLVING #2

DETAILED EXAMPLE PART B: STEP TO SOLVING #3

DETAILED EXAMPLE PART B: STEP TO SOLVING #4

DETAILED EXAMPLE PART B: STEP TO SOLVING #5

DETAILED EXAMPLE PART B: STEP TO SOLVING #6

6. Put the number of chocolate chips above each of these cookies below each of the ( ).

(8 X 6) + (8 X 10) 48 + 80

DETAILED EXAMPLE PART B: STEP TO SOLVING #7

7. Find the sum (add +).

80 + 48 128

DISTRIBUTIVE PROPERTY-AREA

DISTRIBUTIVE PROPERTY-AREA

DISTRIBUTIVE PROPERTY-AREA