Dividing positives and negatives

Take a look at the following four expressions:
(+10) x (+3) = +30 (+10) x (-3) = -30
(-6) x (-3) = +18 (-6) x (+3) = -18

Remember that in past years you learned that if 8 x 7 = 56, then 56 ÷ 7 = 8.

We can use the very same logic on positive and negative numbers. Below each of the four multiplication problems, we can state the related division problem.

The multiplication problems with their related division problem will now look like this:

(+10) x (+3) = +30
+30 ÷ (+3) = (+10)
(+10) x (-3) = -30
-30 ÷ (-3) = +10
(-6) x (-3) = +18
+18 ÷ (-3) = -6
(-6) x (+3) = -18
-18 ÷ (+3) = -6

Just as addition, subtraction, and multiplication all have easy rules that can be used, so does division. Look at the four division problems and try to find a rule or a pattern. If you are having difficulty finding the rule, remove the four multiplication problems, so the problems look as follows:

+30 ÷ (+3) = (+10) -30 ÷ (-3) = +10
+18 ÷ (-3) = -6 -18 ÷ (+3) = -6

 

 

You should now see that the rules for division are the exact same as the rules for multiplication!

When dividing two numbers:

  • If the signs are the same, the quotient is positive
  • If the signs are different, the quotient is negative.

 

 

 

Self-Check


Question 1

$\frac{-20}{-4}=$

 

[show answer]


Question 2

$-6/\overline{+42}$

 

[show answer]


Question 3

$(-32)\div~(+8)=$

 

[show answer]

 

 

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