## Rules for Multiplying Integers

## Formative Assessment

# Summary of the Math: Rules for Multiplying Integers

**Read and Discuss**

- A positive number multiplied by a positive number results in a positive number.
- A negative number multiplied by a negative number results in a positive number.
- A positive number multiplied by a negative number results in a negative number.
- A negative number multiplied by a positive number results in a negative number.
- Multiplying by a negative number is the same as taking the opposite.
*a*⋅*b*is the opposite of −(*a*⋅*b*), or −1(*a*⋅*b*). - When multiplying a negative number by a negative number, the opposite of an opposite is the number itself.

−*a*⋅ −*b*is the opposite of −1(*a*⋅*b*), and −1(*a*⋅*b*) is the opposite of*a*⋅*b*. Since a negative number times a negative number results in a positive number, we can conclude that the opposite of an opposite is the number itself, or −*a*⋅ −*b*=*a*⋅*b*.

## Hint:

Can you:

- Describe how to represent the product of a positive integer and a negative integer on a number line?
- Explain how you can use patterns to show that the product of two negative integers is positive?
- Explain how you know what the sign of the product of any two integers will be?