Negative numbers Revision Notes for Edexcel GCSE Maths

Negative numbers

What are negative numbers?

Negative numbers are numbers that are less than zero. They appear to the left of zero on a number line and are written with a minus sign (-) in front of them.

Key points about negative numbers:

They are smaller than zero
Zero itself is neither positive nor negative
As you move left on a number line, numbers get smaller
As you move right on a number line, numbers get bigger

Using number lines

A number line is a visual tool that helps you understand the order and size of numbers. It's particularly useful when working with negative numbers.

On a number line:

Negative numbers appear to the left of zero
Positive numbers appear to the right of zero
Numbers get larger as you move to the right
Always mark zero clearly on your number line

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Number lines are especially helpful when adding and subtracting negative numbers, as you can visualise moving left (subtracting) or right (adding) along the line.

Adding and subtracting negative numbers

When working with negative numbers, you need to be careful with the signs. A useful approach is to change double signs first before calculating.

The golden rule

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This is the most important rule to remember:

When you add a negative number, the answer is lower
When you subtract a negative number, the answer is higher

Examples of sign changes

When you see double signs, change them:

$+ -$ becomes $-$
$- -$ becomes $+$

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Worked Example: Sign Changes

Step 1: $12 + (-3) = 12 - 3 = 9$ Step 2: $5 - (-9) = 5 + 9 = 14$

Multiplying and dividing negative numbers

There are two simple rules for multiplication and division with negative numbers:

Rule 1: Same signs

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If both numbers have the same sign, the answer is positive

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Examples: Same Signs

$(-3) \times (-7) = 21$ (both negative, so answer is positive)
$8 \times 4 = 32$ (both positive, so answer is positive)

Rule 2: Different signs

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If the numbers have different signs, the answer is negative

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Examples: Different Signs

$(+6) \times (-10) = -60$ (one positive, one negative, so answer is negative)
$(-15) \div 3 = -5$ (one negative, one positive, so answer is negative)

Problem solving strategies

When solving problems with negative numbers:

Try working with a few pairs at a time
Add up totals step by step
Always check your work by ensuring you've used each number correctly
Use a number line to visualise the problem if needed

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For card-sorting problems, look for pairs that give the same total when combined. This helps organise your work and makes checking easier.

Exam tips

Always show your working clearly
Mark zero on any number lines you draw
Double-check your signs before calculating
Remember the golden rule for addition and subtraction
Use the same/different sign rules for multiplication and division

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Key Points to Remember:

Negative numbers are less than zero and appear to the left of zero on a number line
Adding a negative makes the answer smaller; subtracting a negative makes the answer bigger
For multiplication and division: same signs give positive answers, different signs give negative answers
Number lines are your friend - use them to visualise problems
Always check your signs before calculating

Negative numbers (Edexcel GCSE Maths): Revision Notes