Lesson 5: Dividing Integers

Property

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number.
Since division by 5 is the inverse of multiplication by 5, the equation $(-15) \div 5 = x$ tells us that the solution is some number $x$, which when multiplied by 5 gives us $-15$.

Examples

• Calculate $(-48) \div 8$. This problem asks, 'What number multiplied by $8$ equals $-48$?' Since $8 \times (-6) = -48$, the answer is $-6$.
• Calculate $(-63) \div (-9)$. Since a negative divided by a negative results in a positive, the answer is positive. $63 \div 9 = 7$, so $(-63) \div (-9) = 7$.
• A company lost a total of 5,000 dollars over 10 months. To find the average monthly loss, calculate $(-5000) \div 10 = -500$. The average loss was 500 dollars per month.

Explanation

Division asks, 'What number do I multiply the divisor by to get the dividend?' The rules for signs in division are the same as in multiplication. For example, to solve $(-30) \div 6$, you ask $6 \times ? = -30$. The answer is $-5$.

Property

When dividing integers:

• If the signs are the same (both positive or both negative), the quotient is positive
• If the signs are different (one positive, one negative), the quotient is negative
• $\frac{\text{positive}}{\text{positive}} = \text{positive}$ and $\frac{\text{negative}}{\text{negative}} = \text{positive}$
• $\frac{\text{positive}}{\text{negative}} = \text{negative}$ and $\frac{\text{negative}}{\text{positive}} = \text{negative}$

Examples