Associative Property of Addition / Multiplication
Associative Property of Addition (APA)
This property allows you to use grouping symbols to group two of the three things you are adding together; the first and second, or the second and the third. The sum will be the same either way you group them. When you apply the associative property of addition you change the locations of the grouping symbols, not the locations of what is being added.

THIS DOES NOT WORK FOR SUBTRACTION !!!
(12 - 7) - 5 = 0, this is not the same as 12 - (7 - 5) which is 10.

The table below on the left shows some examples of APA. The table on the right can be used to practice APA problems. Press the 'Try one' button to get started.

Associative Property of Addition
(change locations of parentheses)
(a + b) + c = a + (b + c)
8 + (7 + 6) = (8 + 7) + 6
(a + b) + c = a + (b + c)
(x + y) + z = x + (y + z)
z + (3 + y) = (z + 3) + y
(x + -4) + 7 = x + (-4 + 7)

Associatative Property of Multiplication (APM)
This property allows you to use grouping symbols to group two of the things you are multiplying together; the first and second, or the second and the third. The product will be the same either way you group them. When you apply the associative property of multiplication you change the locations of the grouping symbols, not the locations of what is being multiplied.

THIS DOES NOT WORK FOR DIVISION !!!
(16 ÷ 4) ÷ 4 = 1 this is not the same as 16 ÷ (4 ÷ 4) which is 16.

The table below on the left shows some examples of APM. The table on the right can be used to practice APM problems. Press the 'Try one' button to get started.

Associative Property of Multiplication
(change locations of parentheses)
(a • b) • c = a • (b • c)
8 • (7 • 6) = (8 • 7) • 6
(a • b) • c = a • (b • c)
(x • y) • z = x • (y • z)
z • (3 • y) = (z • 3) • y
(-4 • x) • 7 = -4 • (x • 7)