Multiplicati on Zero property Associative property Commutative property Identity property Distributive property

0 x 4 =0 0 x 8 =0 0 x 12 =0 0 x 6 =0 0 x 144 =0 1,250 x 0 =0

1 x 5 = 5 1 x 7=7 1 x 9= 9 1 x 29= x 1=451 1 x 12 = 12

multiplication In multiplication, if you change the factors, product order of the factors, the product remains the same. 6 x 8 = 48 8 x 6 = 48 5 x 2 = 10 2 x 5 = 10 9 x 7= 63 7 x 9 = 63

6 x 2 x 4 = 48 (6 x 2) x 4 = 48 6 x (2 x 4) = 48 (6 x 4) x 2 = 48 3 x 5 x 4 = 60 (3 x 5) x 4 = 60 3 x (5 x 4) = 60 (3 x 4) x 5 = 60 *always do what’s in the parenthesis' ( ) first

You can multiply 3 x 4 first.3 x 4 = 12 Then multiply that product by x 2 = 24 You can group the factors differently and get the same product! You can multiply 4 x 2 first. 4 x 2 = 8 Then multiply that product by 3. 8 x 3 = 24 This is the associative property! (3 x 4) x 2 3 x (4 x 2)

(4 x 5) x 1 = 4 x 5 = x 1 =20

4 x (5 x 1) = 5 x 1 =5 4 x 5 =20 The answer is 20 either way you group the numbers.

(2 x 6) x 2 = 2 x 6 =12 12 x 2 =24 2 x (6 x 2) = 6 x 2 = x 12 = The answer is the same either way we group the numbers. This is the Associative Property Let’s do it again.

(5 x 2) x 2 = 10 x 2 =20 5 x (2 x 2)= 4 x 5 = OR same 20 Associative Property One more time!

3 x 3 x 4 = Compare your work to a partner’s. Does your work look like this? (3 x 3) x 4 = 9 x 4 = 36 3 x (3 x 4) = 12x 3 = 36 Now you try it by yourself on your notes. Show it both ways!

2 x 5 x 8 = Compare your work to a partner’s Does your work look like this? (2 x 5) x 8 = 10 x 8 = 80 2 x (5 x 8) = 40 x 2 =80 Now you try it by yourself on your white board. Show it both ways!

3 x 3 x 3 = Compare your work to a partner’s Does your work look like this? (3 x 3) x 3 = 9 x 3 = 27 3 x (3 x 3) = 9 x3 = Now you try it by yourself on your white board. Show it both ways!

3 X ( 2 + 3) = 3 x x 3 = = 15 3 X 5 = 15 This problem can be broken down to an addition problem. The five is equal to Then both addends can be multiplied by 3 and the product will remain the same.

Break the 7 into an addition problem (3 + 4) Now, bring down the 5 and the sign. 5 x Distribute the 5 across the problem. 5 x 35 x 4 Don’t forget to bring down the sign! + Now multiply the 5 and 3 15 Now multiply the 5 and Finally add the two product together 35 The answer is the same!

3 X 13 = 39 Break the 13 into an addition problem (3 + 10) Now, bring down the 3 and the sign. 3 X Distribute the 3 across the problem. 3 X 3 3 X 10 Don’t forget to bring down the sign! + Now multiply the 3 and 3. 9 Now multiply the 3 and Finally add the two product together 39 The answer is the same!

6 X 18 = ? 4 X 15 = ? 9 X 14 = ? 3 X 22 = ? 8 X 13 = ?

8 x 13 = ? Break the 13 into an addition problem ( ) Now, bring down the 8 and the sign. 8 X Distribute the 3 across the problem. 8 X 10 8 X 3 + Now multiply the 8 and Finally add the two products together 104 Now multiply the 8 and x 13 = 104

4 X 15 = ? Break the 15 into an addition problem (6 + 9)4 x Distribute the 4 across the problem. 4 X 6 4 X 9 + Do the multiplication X 15 = 60

3 X 27 = ? Break the 2 7 into an addition problem with three addends! ( ) 3 X Distribute the 3 across the problem. 3 X 10 3 X X 27 = 81

4 x 6 x 5 = 4 x (6x5) = (4 x 6) x 5 = A.ZERO PROPERTY B.DISTRIBUTIVE PROPERTY C.ASSOCIATIVE PROPERTY D.COMMUTATIVE PROPERTY CORRECT ANSWER IS: C – ASSOCIATIVE

4,589 x 0= A.ZERO PROPERTY B.DISTRIBUTIVE PROPERTY C.ASSOCIATIVE PROPERTY D.COMMUTATIVE PROPERTY CORRECT ANSWER IS: A. ZERO PROPERTY 9 X 6 = 6 X 9 A.ZERO PROPERTY B.DISTRIBUTIVE PROPERTY C.IDENTITY PROPERTY D.COMMUTATIVE PROPERTY 56 X 5 X 7 = (56 X 5) X 7 = 56 X (5 X 7) A.ZERO PROPERTY B.DISTRIBUTIVE PROPERTY C.ASSOCIATIVE PROPERTY D.COMMUTATIVE PROPERTY CORRECT ANSWER IS: D. COMMUTATIVE PROPERTY CORRECT ANSWER IS: C. ASSOCIATIVE PROPERTY 14,855 X 1 =14, 855 A.ZERO PROPERTY B.DISTRIBUTIVE PROPERTY C.IDENTITY PROPERTY D.COMMUTATIVE PROPERTY CORRECT ANSWER IS: C. ASSOCIATIVE PROPERTY

4 x 26= 4 X X X 6 A.ZERO PROPERTY B.DISTRIBUTIVE PROPERTY C.ASSOCIATIVE PROPERTY D.COMMUTATIVE PROPERTY CORRECT ANSWER IS: B. DISTRIBUTIVE PROPERTY CORRECT ANSWER IS: D. IDENTITY PROPERTY 4 x 1= A.ZERO PROPERTY B.DISTRIBUTIVE PROPERTY C.ASSOCIATIVE PROPERTY D.IDENTITY PROPERTY

IdentityCommutativeAssociative Your task is to complete the tree map by writing one example of each multiplication property. Distributive

IdentityCommutativeAssociativeDistributive Name:__________________________