Lesson 8: Divide Integers

Property

Division is the inverse operation of multiplication. The sign of the quotient of two numbers depends on their signs, following the same rules as multiplication.

Examples

• To divide $-45 \div 5$, the signs are different, so the quotient is negative. The result is $-9$.
• To divide $-60 \div (-10)$, the signs are the same, so the quotient is positive. The result is $6$.
• You can check the first example by multiplying back: $-9 \cdot 5 = -45$.

Explanation

The rules for dividing integers are exactly the same as for multiplying!
If the signs match, the answer is positive. If they don't match, the answer is negative. You can always check your answer by multiplying.

Property

For any integers $a$ and $b$ (with $b \neq 0$):

Examples

Property

For any integer $a$, the expression $a \div 0$ is undefined. This is because the related multiplication statement, $0 \times c = a$, has no solution if $a \neq 0$, and has no single, unique solution if $a = 0$.

Examples