Real Numbers

Recall the following property of negative numbers:

It follows that:

Recall that the Commutative Propery of Addition states:

It follows that:

To help you tell the difference between commutative, associative, and distributive just remember what the words themselves mean.

When you commute you go from one place to another. With commutative properties, numbers are moving from one position to another.

When you associate with someone you are connected or grouped with them. The associative properties involve moving parentheses so that different numbers are grouped together, but they are not changing positions.

When you distribute things you are handing them out. With the distributive property, the number outside the parentheses is being handed out to the numbers inside the parentheses.

Recall the following property of negative numbers:

It follows that:

Recall the following property of negative numbers:

It follows that:

Recall that the Distributive Property states:

It follows that:

To help you tell the difference between commutative, associative, and distributive just remember what the words themselves mean.

When you commute you go from one place to another. With commutative properties, numbers are moving from one position to another.

When you associate with someone you are connected or grouped with them. The associative properties involve moving parentheses so that different numbers are grouped together, but they are not changing positions.

When you distribute things you are handing them out. With the distributive property, the number outside the parentheses is being handed out to the numbers inside the parentheses.

Recall that the Distributive Property states:

The number outside the parentheses can be on the left or right side of the parentheses, so the following is also true:

It follows that:

To help you tell the difference between commutative, associative, and distributive just remember what the words themselves mean.

When you commute you go from one place to another. With commutative properties, numbers are moving from one position to another.

When you associate with someone you are connected or grouped with them. The associative properties involve moving parentheses so that different numbers are grouped together, but they are not changing positions.

When you distribute things you are handing them out. With the distributive property, the number outside the parentheses is being handed out to the numbers inside the parentheses.

Every answer choice is equivalent to this, so they are all correct.

When dividing fractions, remember to multiply the first fraction by the reciprocal of the second, as illustrated by the following identity:

Recall that the Commutative Property of Multiplication states:

It follows that :

To help you tell the difference between commutative, associative, and distributive just remember what the words themselves mean.

When you commute you go from one place to another. With commutative properties, numbers are moving from one position to another.

When you associate with someone you are connected or grouped with them. The associative properties involve moving parentheses so that different numbers are grouped together, but they are not changing positions.

When you distribute things you are handing them out. With the distributive property, the number outside the parentheses is being handed out to the numbers inside the parentheses.