Properties of Numbers Examples

Which property of addition is illustrated by the equation below?

(3 + 4) + 5 = 3 + (4 + 5)

When the order of the numbers doesn't change but the grouping of the numbers does change, we're talkin' the associative property.

Which property of multiplication is illustrated by the equation below?

3 × 4 × 5 = 3 × 5 × 4

Our equation shows the product of the numbers 3, 4, and 5 is the same no matter what order they're in. The commutative property states that we can multiply factors of a product in any order. Coincidence? We think not.

This equation illustrates the commutative property.

Name the additive identity and the additive inverse for the number 73.

The additive identity is 0 for any number. If we add 0 to 73, we get 73 right back again.

73 + 0 = 73

The additive inverse is a number that gives us 0 when added to 73. And only one number does that:

73 + (-73) = 0

There we go. The additive inverse is -73, or the opposite of 73.

Fill in the blanks on the right side of the equation to illustrate the distributive property:

5(71 + 14) = (__)(__) + (__)(__)

To distribute means to multiply the number outside the parentheses to each number inside the parentheses, like a tired mom giving both her kids the same toy so they don't fight over who got the better one. And to illustrate the distributive property, we won't actually multiply them; we'll write them as a multiplication problem. We first multiply 5 by 71.

5(71 + 14) = (5)(71) + (__)(__)

We finish by multiplying 5 by 14. Fair is fair.

5(71 + 14) = (5)(71) + (5)(14)