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Class 8Algebra9:53Published 28 Jul 2025

Multiplication and Division of Positive and Negative Numbers

Learn the sign rules for multiplying and dividing positive and negative numbers, then apply them to worked examples including brackets and zero.

This lesson explains how the signs work when you multiply or divide positive and negative numbers: like signs give a positive result and unlike signs give a negative result. After laying out the rules, the teacher works through a series of examples, multiplying and dividing the numbers and combining the answers, including problems with brackets, zero, and several operations in one expression.

What you'll learn

The sign rules for multiplying and dividing: like signs give positive, unlike signs give negative
How to handle expressions with brackets and several operations by working one part at a time
Why multiplying or dividing involving zero gives the result you expect, and how to combine the final signs

Lesson chapters

0:04Introduction

0:41The sign rules for multiplication and division

2:09Worked multiplication examples

4:51Worked division examples

6:27Examples with brackets and zero

Lesson notes

This lesson covers how to multiply and divide positive and negative numbers. It starts with the sign rules and then works through examples that combine multiplication, division, brackets, and zero.

The sign rules

The sign of a product or quotient depends only on the signs of the two numbers.

Like signs give a positive result: $(+)\times(+)=(+)$ and $(-)\times(-)=(+)$ .
Unlike signs give a negative result: $(+)\times(-)=(-)$ and $(-)\times(+)=(-)$ .

The same pattern holds for division: $(+)\div(+)=(+)$ , $(-)\div(-)=(+)$ , $(+)\div(-)=(-)$ , and $(-)\div(+)=(-)$ .

The method is always: first decide the sign, then multiply or divide the numbers.

Multiplication examples

$(+8)\times(+3)=+24$ $(-3)\times(-8)=+24$ $(+10)\times(-5)=-50$ $(-2)\times(+15)=-30$

A product of several factors

Work left to right, one factor at a time, keeping track of the sign each step.

$(+2)\times(-8)\times(-2)\times(-2)$

Step 1. $(+2)\times(-8)=-16$ .

Step 2. $(-16)\times(-2)=+32$ .

Step 3. $(+32)\times(-2)=-64$ .

Brackets, zero, and adding the results

$(-12)\times(-2)+(+2)\times 0$

First term. $(-12)\times(-2)=+24$ .

Second term. $(+2)\times 0=0$ , since anything multiplied by zero is zero.

Adding: $+24+0=+24$ .

Adding two positives stays positive:

$(+16)+(+6)=+22$

Division examples

$(+10)\div(+5)=+2$ $(-20)\div(-10)=+2$ $(+7)\div(+7)=+1$ $(-8)\div(-1)=+8$

Combining division and multiplication

$(-12)\div(-3)=+4,\qquad (+8)\div(-2)=-4$

Then multiply the two results:

$(+4)\times(-4)=-16$

Dividing one quotient by another

$\big[(+20)\div(-10)\big]\div\big[(-2)\div(-2)\big]$

First bracket. $(+20)\div(-10)=-2$ .

Second bracket. $(-2)\div(-2)=+1$ .

Then: $(-2)\div(+1)=-2$ .

A larger combination

$\big[(-100)\div(-2)\big]\times\big[(-50)\div(-1)\big]$

First bracket. $(-100)\div(-2)=+50$ .

Second bracket. $(-50)\div(-1)=+50$ .

Then: $(+50)\times(+50)=+2500$ .

Mixing division, multiplication, and addition

$(-25)\div(-1)+(+8)\times(-2)$

First term. $(-25)\div(-1)=+25$ .

Second term. $(+8)\times(-2)=-16$ .

Adding a positive and a negative, subtract and keep the sign of the larger: $+25+(-16)=+9$ .

Zero and subtraction together

$0\times(+8)-\big[(-2)\div(-2)\big]$

First term. $0\times(+8)=0$ .

Bracket. $(-2)\div(-2)=+1$ .

Then: $0-(+1)=-1$ .

Subtracting a negative

$(-2)\times(-2)+8-(-2)$

First term. $(-2)\times(-2)=+4$ .

Subtracting a negative is the same as adding: $+4+8+2=+14$ .

Key takeaways

Multiplying or dividing two numbers with the same sign gives a positive result; with different signs it gives a negative result.
Always decide the sign first, then multiply or divide the numbers.
Work brackets and one operation at a time, and remember that any number times zero is zero and that subtracting a negative is the same as adding.