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commutative property
associative property
Find the sum for each pair of expressions. Add the terms in parentheses first.
Here are some of the properties you will study in this course:
Commutative Property
Associative Property
Identity Property
Distributive Property
Equality Properties (there are several of these!)
Is subtraction commutative?
Is 50 - 10 the same as 10 - 50?
Subtraction is NOT commutative. For example:
50 - 10 = 40 but 10 - 50 = - 40
However, if you change the subtraction to an addition problem (remember, subtraction is like adding the opposite), you can use the commutative property:
50 - 10 = 50 + (-10) = (-10) + 50 = 40
Is division commutative?
Is 1/2 the same as 2/1?
1/2 is not the same as 2/1, which means that division is not commutative. You cannot swap the numerator and denominator and get the same answer.
The associative property of multiplication says: (a • b) • c = a • (b • c).
The associative property of addition says: (a + b) + c = a + (b + c).
multiplication is also commutative, which means the numbers can be swapped and order does not matter. This property works with addition and multiplication
1/2 is not the same as 2/1, which means that division is not commutative. You cannot swap the numerator and denominator and get the same answer.
Problem Answer
4 + 6 + 15 6 + 4 + 15 = 25
15 + 6 + 4 = 25
9 + 8 + 1
9 + 1 + 8 = 18
8 + 9 + 1 = 18
12 + 8 + 5
12 + 5 + 8 = 25
8 + 5 + 12 = 25
14 + 16 + 7
16 + 7 + 14 = 37
14 + 7 + 16 = 37
5 x 20 x 3 = 300
5 x 3 x 20 = 300
4 x 6 x 10 4 x 10 x 6 = 240
6 x 4 x 10 = 240
5 x 4 x 13 5 x 13 x 4 = 260
4 x 5 x 13 = 260
8 x 2 x 5 8 x 5 x 2 = 80
2 x 8 x 5 = 80
Like the commutative property, the associative property works with addition and multiplication, but not with subtraction and division.
(4 + 6) + 15 = 25
4 + (6 + 15) = 25
9 + (8 + 1)
(9 + 8) + 1 9 + (8 + 1) = 18
(9 + 8) + 1 = 18
(12 + 8) + 5
12 + (8 + 5) (12 + 8) + 5 = 25
12 + (8 + 5) = 25
14 + (16 + 7)
(14 + 16) + 7 14 + (16 + 7) = 37
(14 + 16) + 7 = 37
(3 x 5) x 20 = 300
3 x (5 x 20) = 300
4 x (6 x 10)
(4 x 6) x 10 4 x (6 x 10) = 240
(4 x 6) x 10 = 240
5 x (4 x 13)
(5 x 4) x 13 5 x (4 x 13) = 260
(5 x 4) x 13 = 260
8 x (2 x 5)
(8 x 2) x 5 8 x (2 x 5) = 80
(8 x 2) x 5 = 80
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