Properties of Real Numbers

Commutative and Associative Properties

Example of Commutative and Associative Properties

Example 1

$3 + 4 = 4 + 3$ $7=7$

This is commutative property because if you add two real numbers in any order, the sum will always be the same or equal.

Example 2

$(1 + 2) + 3 = 1 + (2 + 3)$

$6=6$

This is associative property because if you are adding three real numbers, the sum is always the same regardless of their grouping.

Identity Properties of Addition and Multiplication

Example of Identity Properties of Addition and Multiplication

Example 1

$12,753+0=12,753$
This is Identity Property of Addition because if you add a real number to zero, the sum will be the original number itself.

Example 2

$62,385 \times 1 =62,385$
This is Identity Property of Multiplication because if you multiply a real number to one (1), you will get the original number itself.

Zero Property of Multiplication

Example of Zero Property of Multiplication

Example 1

$1,845 \times 0=0$

If you multiply any real number to zero, the answer will be always zero.

Example 2

$5,825 \times 0=0$

If you multiply any real number to zero, the answer will be always zero.

Multiplication Property of -1

Example of Multiplication Property of -1

Example 1

$548,756 \times -1=-548,756$

Example 2

$1,653 \times -1=-1,653$

After you finish this lesson, view all of our Algebra 1 lessons and practice problems.