Multiplication and Division of Integers

When We Multiply:

			Example
(+) ×  (+)	Two Positives make a Positive:	(+)	3 × 2 = 6
(-)  ×  (-)	Two Negatives make a Positive:	(+)	(−3) × (−2) = 6
(-) ×  (+)	A Negative and a Positive make a Negative:	(-)	(−3) × 2 = −6
(+)  ×  (-)	A Positive and a Negative make a Negative:	(-)	3 × (−2) = −6

Yes indeed, two negatives make a positive, and we will explain why, with examples! (source: https://www.mathsisfun.com/multiplying-negatives.html)

 

Division of Integers

Dividing integers is the opposite of multiplying integers. It is the process by which one is trying to know how many times a number is contained into another.

Example: 36÷12 =

You are trying to determine how many times 12 is contained into 36

Since 12 x 3 = 36, so 12 is contained into 36 three times.

Thus: 36 ÷ 12 = 3

Bear in mind that:

quotient × divisor = dividend

dividend ÷ divisor = quotient

dividend ÷ quotient = divisor

In other words, the product of 45 × 2 = 90

Then, dividing the product, which is 90 by 2 gives you back 45

However, dividing the product (90) by 45 gives you back 2

We can use this fact to find the rule for dividing integers

 

12 × 5 = 60

60 ÷ 5 = 12

12, 5, and 60 are positive, so: Positive ÷ Positive = Positive

For:

12 × -5 = -60

-60 ÷ -5 = 12

60 and 5 are negative, but 12 is positive, so Negative ÷ Negative = Positive

In the previous example, notice that -60 ÷ 5 = -12

60 is negative, 5 is positive, but 12 is negative, so: Negative ÷ Positive = Negative

Finally, consider:

-2 × – 6 = 12

12 ÷ -2 = -6

12 is positive, 2 is negative, and 6 is negative, so: Positive ÷ Negative = Negative

 

Take Note:

The rule for division of integers is the same for multiplying integers. Therefore, if you remember the rule for multiplying integers, you already know it for division.

The division of two integers with the same signs is positive

The division of two integers with different signs is Negative

Practice:

1. https://www.ixl.com/math/grade-7/integer-multiplication-and-division-rules

 

2. https://www.ixl.com/math/grade-7/complete-multiplication-and-division-equations-with-integers