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Class 8Algebra13:53Published 29 May 2024

Operations on Positive and Negative Numbers (Part 1)

A clear, step-by-step introduction to adding and subtracting positive and negative numbers, with the sign rules and plenty of worked examples.

This lesson builds up the rules for working with signed numbers from the ground up. It starts with what positive and negative numbers mean, then covers the three cases of addition and the change-the-sign rule for subtraction. Each rule is followed by worked examples and extra practice questions so the method becomes second nature.

What you'll learn

What positive and negative numbers really mean as amounts above and below zero
How to add two numbers using the three sign cases, including when the signs differ
How to subtract by changing it into an addition and flipping the sign of the second number
Why writing the sign first matters so a negative answer never turns positive by mistake

Lesson chapters

0:00What positive and negative numbers mean

1:53The three rules for addition

4:33More addition practice

6:20The rule for subtraction

11:24More subtraction practice

Lesson notes

This lesson introduces the operations of addition and subtraction on positive and negative numbers, building from what the signs mean up to a reliable method with worked examples.

What the signs mean

A positive number is greater than $0$ and is written with a plus sign, for example $+2$ , which means $2$ more than $0$ . A negative number is less than $0$ and is written with a minus sign, for example $-5$ , which means $5$ less than $0$ . So every positive number sits above zero and every negative number sits below it.

The three rules for addition

There are three cases when you add two signed numbers.

Positive plus positive gives a positive result.
Negative plus negative gives a negative result.
One positive and one negative: find the difference (subtract the smaller from the larger) and keep the sign of the larger number.

Worked examples

$+8 + (+2) = +10$

$-8 + (-2) = -10$

For $-8 + (+2)$ the signs differ, so take the difference $8 - 2 = 6$ and keep the sign of the larger number, $8$ , which is negative:

$-8 + (+2) = -6$

For $+8 + (-2)$ the difference is again $8 - 2 = 6$ , and the larger number $8$ is positive:

$+8 + (-2) = +6$

More practice

$+100 + (-100) = 0$

$-1 + (+8) = +7$

$-10 + (-10) = -20$

With two negatives, write the negative sign first, then add $10 + 10 = 20$ . If you forget the sign, the answer wrongly becomes positive.

$+8 + (+18) = +26$

$0 + (-1) = -1 \qquad +5 + 0 = +5$

The rule for subtraction

To subtract one number from another, change the subtraction into an addition and change the sign of the second number (the one being subtracted). Then use the addition rules above.

Worked examples

$+100 - (-12) = +100 + (+12) = +112$

$-20 - (-1) = -20 + (+1) = -19$

$0 - (+5) = 0 + (-5) = -5$

$+5 - (-5) = +5 + (+5) = +10$

More practice

$+15 - (-2) = +15 + (+2) = +17$

$-8 - (+1) = -8 + (-1) = -9$

$+5 - (+5) = +5 + (-5) = 0$

$0 - (-5) = 0 + (+5) = +5$

$+5 - 0 = +5$

Since $0$ has no sign, subtracting $0$ leaves the number unchanged.

Key takeaways

Same signs add and keep the sign; different signs subtract and keep the sign of the larger number.
To subtract, change it to an addition and flip the sign of the second number, then apply the addition rules.
Always write the sign first so a negative result is never lost.