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Negative Numbers: What They Are and How to Use Them

In one line: A negative number is a number less than zero, written with a minus sign in front (like −3), and it sits to the left of zero on a number line.

Why it works

Negative numbers describe real things that go below a starting point: temperatures below freezing, money owed, floors below ground, and depths below sea level. They also let us always subtract, even when we take away more than we have (for example, 3 − 5 = −2). Later topics such as algebra, graphs with four quadrants (sections) and equations rely on being confident with them.

Think of it like: Think of a lift in a tall building with car park levels underground. Ground floor is 0, the floors above are 1, 2, 3 and the basement levels are −1, −2, −3. Going up means adding, going down means subtracting. If you start on level −2 and go up 5 floors, you reach level 3. Level −3 is lower than level −1, just as −3 is smaller than −1. (Where this breaks: The lift works well for ordering numbers and for adding or subtracting positive numbers, but it does not explain what it means to subtract a negative number (like 4 − (−2)) or to multiply two negatives. For those, it is better to use rules and patterns on the number line.)

Worked example

At 6 am the temperature is −4 °C. By midday it rises by 9 degrees. By night it falls by 7 degrees from the midday temperature. What is the temperature at night?

  1. Start at −4 on the number line (4 steps to the left of zero).
  2. Rising by 9 means adding 9, so move 9 steps to the right: 4 steps take you to 0, then 5 more steps take you to 5. Midday is 5 °C.
  3. Falling by 7 means subtracting 7, so move 7 steps to the left from 5.
  4. 5 steps left takes you to 0, then 2 more steps takes you to −2.
  5. Check: −4 + 9 − 7 = −2.

Answer: The temperature at night is −2 °C.

Common mistakes

  • Thinking −8 is bigger than −3 because 8 is bigger than 3; fix this by remembering that the further left a number is on the number line, the smaller it is, so −8 < −3.
  • Treating 2 − (−5) as if it were 2 − 5; fix this by remembering that subtracting a negative number is the same as adding the positive, so 2 − (−5) = 2 + 5 = 7.
  • Joining the numbers together and keeping the minus sign, such as writing −3 + 8 = −11; fix this by starting at −3 on a number line and moving 8 steps right, which lands on 5.
  • Finding the gap between −4 and 5 by doing 5 − 4 = 1; fix this by counting the steps to zero and then past it, which is 4 + 5 = 9.

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Which number is smaller: −7 or −2?

Questions parents ask

What year do kids learn negative numbers?

In the UK, children meet negative numbers in context in Year 5 and calculate across zero in Year 6, with all four operations in Years 7–8. In Australia they are introduced on number lines around Year 6 and calculated with in Years 7–8. In the US they are introduced in Grade 6, with adding, subtracting, multiplying and dividing them in Grade 7.

How can I help my child with negative numbers at home?

Use everyday examples such as weather forecasts below zero, lift buttons for basement levels, or a bank balance going into the red. Drawing a quick number line and moving left or right for each step helps children see the answer rather than guess a rule.

Why does subtracting a negative number give a bigger answer?

Taking away a debt leaves you better off, so removing a negative amount increases the total. A simple pattern also shows it: 3 − 2 = 1, 3 − 1 = 2, 3 − 0 = 3, so continuing gives 3 − (−1) = 4.

What is the difference between a negative number and an integer?

An integer is any whole number, which can be positive, negative or zero, such as −3, 0 or 7. Negative numbers do not have to be whole, so −2.5 is a negative number but not an integer.