Subjects
Grades
Multiplying and Dividing Positive and Negative Numbers
Concept sheet | Mathematics
Secondary
1
Table of contents
Multiplication and division can be performed with positive numbers, but also with negative numbers. It's important to make sure you're comfortable with the set of integers. There is a close link between the multiplication and division of positive and negative numbers, since they are inverse operations. Both operations follow the sign rule.
The sign rule is used to determine the sign of the result of a multiplication or division.
-
If the 2 numbers being multiplied or divided have the same sign, the answer is positive.
-
If the 2 numbers being multiplied or divided have opposite signs, the answer is negative.
Note: The sign rule also applies when the 2 signs are placed together in a chain of operations.
To multiply or divide positive and negative numbers, first perform the operation without taking the signs into account, then determine the sign of the answer using the sign rule. This technique applies equally to multiplying decimal numbers and fractions and to dividing decimal numbers and fractions.
Find the result of the multiplication |-15 \times 3.|
We start by finding the product, ignoring the signs.
||15 \times 3 = 45||
Since the 2 factors have opposite signs, the result is negative, according to the sign rule.
Answer: The result of the multiplication |-15 \times 3| is |-45.|
The sign rule also applies to fractions, since fractions represent divisions. By convention, we put the "-" sign in front of the fraction or in the numerator, but not in the denominator. ||\begin{align}\dfrac{-15}{-4}\ &\Rightarrow\ \dfrac{15}{4}\\[3pt] \dfrac{2}{-3}\ &\Rightarrow\ -\dfrac{2}{3}\end{align}||
If there is a chain of operations with several multiplications or divisions, and you want to determine the sign of the final result, count the number of "-" signs. If there is an even number, the result is positive. If there is an odd number, the result is negative.
Find the result of the chain of operations |-452 \div -16 \times 12 \times 2 \div -15.|
First, we perform the calculations, ignoring the signs.||\begin{align}&452 \div 16 \times 12 \times 2 \div 15\\=\ &28.25 \times 12 \times 2 \div 15\\=\ &339 \times 2 \div 15\\=\ &678 \div 15\\=\ &45.2 \end{align}||
Since there are 3 negative numbers in the chain of operations |(-452,| |-16| and |-15),| the result is negative.
Answer: The result of the chain of operations |-452 \div -16 \times 12 \times 2 \div -15| is |-45.2.|