GCSE Maths → Number → Negative Numbers

Negative Numbers GCSE Maths

Negative numbers are numbers below zero. They are used in temperature, bank balances, coordinates, algebra, equations, graphs, and many GCSE maths topics.

Many students struggle with negative numbers because the signs can be confusing, especially when adding, subtracting, multiplying, and dividing.

Video explanation

A short Worthing Maths Tutor video explanation for negative numbers GCSE maths can be embedded here later to improve student engagement and time on page.

What are negative numbers?

Negative numbers are less than zero. On a number line, they are to the left of zero.

..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...

Exam tip: A number line is very useful for adding and subtracting negative numbers.

Adding negative numbers

Adding a negative number moves left on the number line.

Example 1: Calculate 5 + -3

Start at 5 and move 3 places left.

5 + -3 = 2

Example 2: Calculate 4 + -7

Start at 4 and move 7 places left.

4 + -7 = -3

Subtracting negative numbers

Subtracting a negative number becomes addition.

7 - -3 = 7 + 3 = 10

Example 3: Calculate 6 - -4

6 - -4 = 6 + 4 = 10

Example 4: Calculate -2 - -5

-2 - -5 = -2 + 5 = 3

Common mistake: Two minus signs together become a plus when subtracting a negative: 8 - -2 = 10.

Multiplying negative numbers

Use these sign rules:

positive × positive = positive
positive × negative = negative
negative × positive = negative
negative × negative = positive

Example 5: Calculate -4 × 6

-4 × 6 = -24

Example 6: Calculate -5 × -3

-5 × -3 = 15

Dividing negative numbers

Division uses the same sign rules as multiplication.

Example 7: Calculate -20 ÷ 5

-20 ÷ 5 = -4

Example 8: Calculate -24 ÷ -6

-24 ÷ -6 = 4

Exam tip: If the signs are the same, the answer is positive. If the signs are different, the answer is negative.

Negative numbers in algebra

Negative numbers appear often in algebra, especially when solving equations and expanding brackets.

Example 9: Expand -3(x + 4)

-3 × x = -3x

-3 × 4 = -12

-3(x + 4) = -3x - 12

For more algebra examples, see expanding brackets.

Common mistakes with negative numbers

Thinking that 4 + -7 is positive.
Forgetting that subtracting a negative becomes addition.
Thinking negative × negative is negative.
Losing negative signs in algebra questions.
Not using brackets when substituting negative numbers.

Practice questions

Calculate 8 + -5
Calculate 3 + -9
Calculate 7 - -2
Calculate -4 - -10
Calculate -6 × 4
Calculate -7 × -3
Calculate -30 ÷ 5
Calculate -36 ÷ -6

Answers

3
-6
9
6
-24
21
-6
6

Negative numbers FAQ

What is a negative number?

A negative number is a number less than zero, such as -1, -5, or -12.

How do you add negative numbers?

Adding a negative number moves left on the number line. For example, 4 + -6 = -2.

What happens when you subtract a negative number?

Subtracting a negative number becomes addition. For example, 7 - -3 = 10.

What is a negative multiplied by a negative?

A negative multiplied by a negative gives a positive.

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