Commutative
True or false?
When subtracting two numbers, the difference will be the same if you switch the order that they are in.
False
True or False?
When multiplying three numbers together you can switch the location of the parentheses and the product of the three numbers will always be the same.
True
Use the commutative property
17 x 2 = ______________
2 x 17
Use the distributive property to create an equivalent expression. 7(m + 3)
7m + 21
Factor out the GCF to make an equivalent expression.
15c - 25d
5(3c - 5d)
Use the commutative property of addition to fill in the blank.
47 + 92 = ___________
92 + 47
Use the associative property of addition to add the parentheses where they belong in the second expression.
3 + (83 + 6) = 3 + 83 + 6
(3 + 83) + 6
Use the associative property:
5 + (a + 6) = ____________
(5 + a) + 6
Use the distributive property to create an equivalent expression. 10(4d - 2)
40s - 20
Factor out the GCF to make an equivalent expression.
56y + 64
8(7y + 8)
Use the commutative property of multiplication to fill in the blank.
(3a)(7)(4b) = _________
any other order
Use the associative property of multiplication to add parentheses where they belong in the second expression.
(1 x 5) x 7 = 1 x 5 x 7
1 x (5 x 7)
Which property is being used?
5(x + 7) = 5x +35
Distributive property
Use the distributive property to create an equivalent expression. 4(6x + 2y + 3z)
24x + 8y + 12z
Factor out the GCF to make an equivalent expression.
17m + 34
17(m + 2)
Use the commutative property of addition to fill in the blank.
2a + 3b + 4c= _________
any other order
Use the associative property of addition to fill in the blanks.
(3 + _) + _ = _ (8 + 10)
(3 + 8) + 10 = 3 + (8 +10)
Which of the following are equivalent to the expression 7(3y + 6)? Select ALL that apply.
A. 21y + 42 B. 10y + 11y + 42
C. 21y + 6 D. 10y + 13
A and B
Use the distributive property to create an equivalent expression. 1.1(2w - 1.2y)
2.2w - 1.32y
Factor out the GCF to make an equivalent expression.
22a + 11b + 77c
11(2a + b + 7c)
Prove the commutative property of multiplication to be true by solving each expression in the order shown. SHOW ALL WORK!
10.7 + 2.35 + 0.75 = 0.75 + 10.7 + 2.35
13.05 + 0.75 = 11.45 + 2.35
13.8 = 13.8
Prove the associative property of multiplication to be true by solving each expression. SHOW ALL WORK!
(10.1 x 1.5) x 2 = 10.1 x (1.5 x 2)
15.15 x 2 = 10.1 x 3
30.3 = 30.3
Name and explain the 2 properties being used in the example:
8n + (9 + 12m) = (8n + 12m) + 9
Commutative (order changed) and Associative (groups changed)
Use the distributive property to create an equivalent expression.
1/3 (15g + 27h)
5g + 9h
Factor out the GCF to make an equivalent expression.
39a - 52b - 65c
13(3a - 4b - 5c)