## Divide and conquer

As division is just the opposite of multiplication, the rules for dividing by integers are the same as the rules for multiplying integers. Let's recap them:

**You already know the quotient of two positive integers is a positive integer.**

#### Examples

$20\div5=4$20÷5=4

$200\div20=10$200÷20=10

**The quotient of a negative and a positive integer is a negative integer.**

#### Examples

$20\div\left(-5\right)=-4$20÷(−5)=−4

$\left(-49\right)\div7=-7$(−49)÷7=−7

**The quotient of two negative integers is a positive integer.**

#### Examples

$\left(-20\right)\div\left(-5\right)=4$(−20)÷(−5)=4

$\left(-60\right)\div\left(-3\right)=20$(−60)÷(−3)=20

## Word problems using division

Some division questions are written as word problems, which we can write as algebraic expressions.

##### question 3

**Evaluate:** A number $n$`n` is divided by $-6$−6 to give $4$4. What is the value of $n$`n`?

**Think: **That expression means $n\div\left(-6\right)=4$`n`÷(−6)=4

**Do:** $n=-24$`n`=−24

##### question 4

**Evaluate: **A number, $n$`n`, is divided by $-5$−5 to give $-4$−4. What is the value of $n$`n`?