Negative numbers Revision Notes for AQA GCSE Maths

Negative numbers

What are negative numbers?

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

On a number line, positive numbers appear to the right of zero, while negative numbers appear to the left of zero. Zero itself is neither positive nor negative.

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Understanding the position of numbers on a number line is fundamental to working with negative numbers. Visualising this relationship will help you with all negative number operations.

Using number lines

Number lines are extremely useful tools when working with negative numbers. They help you visualise calculations and put numbers in order of size.

When using a number line:

Numbers get bigger as you move to the right
Numbers get smaller as you move to the left
Always mark zero clearly on your number line

For addition and subtraction:

To add, move right on the number line
To subtract, move left on the number line

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Worked Example: Using Number Lines

Let's work through these step by step:

Example 1: $-6 + 4 = ?$

Start at -6 on the number line
Move 4 spaces right (because we're adding)
We land on -2
So $-6 + 4 = -2$

Example 2: $4 - 5 = ?$

Start at 4 on the number line
Move 5 spaces left (because we're subtracting)
We land on -1
So $4 - 5 = -1$

Adding and subtracting negative numbers

When adding or subtracting negative numbers, you need to deal with double signs first. Here's how to handle them:

Changing double signs

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Critical Sign Rules:

+ (-) becomes -
- (-) becomes +

These rules are essential for working with negative numbers correctly.

Examples:

$12 + (-3) = 12 - 3 = 9$
$5 - (-9) = 5 + 9 = 14$

Golden rule

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The Golden Rule for Negative Numbers:

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

Remember this rule - it will help you check if your answers make sense!

Multiplying and dividing negative numbers

When multiplying and dividing with negative numbers, use these sign rules to determine whether your answer will be positive or negative:

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Rule 1: Same signs give a positive answer

If both numbers have the same sign (both positive or both negative), the answer is positive.

Example: $-3 \times -7 = 21$

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Rule 2: Different signs give a negative answer

If the numbers have different signs (one positive, one negative), the answer is negative.

Example: $+60 \div -10 = -6$

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A helpful way to remember: "Same stays positive, different goes negative" - like signs attract to give positive results, unlike signs repel to give negative results.

Problem solving strategies

When working with negative numbers in exam questions, these strategies will help you succeed:

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Effective Problem-Solving Approaches:

Try different combinations - especially useful when sorting numbers into groups
Check your work - make sure you've used each number exactly once if required
Use a systematic approach - work through possibilities methodically
Double-check your signs - ensure you've applied the rules correctly

For pairing problems, try adding up totals and see if they work. Remember to check that you've used each number exactly once.

Remember!

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Key Points to Remember:

Negative numbers are smaller than zero and appear to the left of zero on a number line
Use number lines to help visualise addition and subtraction with negative numbers
Change double signs first: + (-) becomes -, and - (-) becomes +
Adding negative makes answers lower, subtracting negative makes answers higher
Same signs = positive answer, different signs = negative answer for multiplication and division
Always check your work and ensure you've applied the rules correctly

Negative numbers (AQA GCSE Maths): Revision Notes