Directed Numbers
Divide integers
Lesson
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?