Algebraic Properties Examples

Which property is illustrated below?

xy + ac = ac + xy

We first need to figure out how the expression on the left is different from the expression on the right. Notice the terms have switched places like a couple of mischievous toddlers.

This illustrates the commutative property of addition.

Fill in the blanks to illustrate the associative property of multiplication.

(3x)y = 3( )

The associative property of multiplication says we can shift parentheses around different numbers as long as everything is being multiplied.

Moving the parentheses from the 3x to the xy shows the associative property.

(3x)y = 3(xy)

Find the additive inverse of -4 and prove that it's the inverse by adding to get the identity.

It's Opposite Day up in here. The additive inverse of a number is the same number with the opposite sign, so the additive inverse of -4 is 4.

If we add a number and its inverse, we should get 0, the additive identity. Since -4 + 4 = 0, we know that 4 is in fact the additive inverse of -4.

Find the multiplicative inverse of and prove that it's the inverse by multiplying to get the identity.

The multiplicative inverse of any number is its reciprocal. In other words, flip the numerator and denominator but keep the sign the same.

So the multiplicative inverse of is .

Multiply 'em together.

Nice—since 1 is the multiplicative identity, we know these numbers are inverses.