# Multiplying and Dividing with Negatives

## Multiplying with Negatives

There's a simple rule here:

• (positive) $×$ (positive) = (positive)
• (positive) $×$ (negative) = (negative)
• (negative) $×$ (positive) = (negative)
• (negative) $×$ (negative) = (positive)

Example :

• $\left(3\right)\left(7\right)=21$
• $\left(3\right)\left(-7\right)=-21$
• $\left(-3\right)\left(7\right)=-21$
• $\left(-3\right)\left(-7\right)=21$

Important Thing To Notice:

Since a positive times a positive is positive, and a negative times a negative is also positive, it follows that any number times itself is either zero or positive.

• $\left(12\right)\left(12\right)=144$
• $\left(-12\right)\left(-12\right)=144$

## Dividing with Negatives

The same rule works with division:

• (positive) $÷$ (positive) = (positive)
• (positive) $÷$ (negative) = (negative)
• (negative) $÷$ (positive) = (negative)
• (negative) $÷$ (negative) = (positive)

Example :

• $56÷7=8$
• $56÷\left(-7\right)=-8$
• $-56÷7=-8$
• $-56÷\left(-7\right)=8$