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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
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