Algebraic Properties

Front

What is the Commutative Property?

Back

The Commutative Property states that the order of addition or multiplication does not change the result. For example, a + b = b + a and ab = ba.

Front

What is the Identity Property?

Back

The Identity Property states that adding zero to a number does not change the number (a + 0 = a) and multiplying a number by one does not change the number (a • 1 = a).

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

What is the Inverse Property?

Back

The Inverse Property states that for every number a, there is an additive inverse (-a) such that a + (-a) = 0, and a multiplicative inverse (1/a) such that a • (1/a) = 1.

Front

What is the Associative Property?

Back

The Associative Property states that the way numbers are grouped in addition or multiplication does not change the result. For example, (a + b) + c = a + (b + c) and (ab)c = a(bc).

Front

Example of Commutative Property: 7 + 3 = ?

Back

7 + 3 = 3 + 7 = 10.

Front

Example of Identity Property: 15 • 1 = ?

Back

15 • 1 = 15.

Front

Example of Distributive Property: 3(4 + 5) = ?

Back

3(4 + 5) = 3•4 + 3•5 = 12 + 15 = 27.

Front

Example of Inverse Property: 8 + ? = 0

Back

8 + (-8) = 0.

Front

Example of Associative Property: (2 + 3) + 4 = ?

Back

(2 + 3) + 4 = 2 + (3 + 4) = 9.