Skip to main content
Academy11+

11+ Maths · Topic explained

Negative numbers

It's 3 °C and the temperature falls by 5 degrees. What is it now?

The big idea

Negative numbers are numbers below zero, like temperatures colder than freezing.

Picture it

A number line is a thermometer on its side: left of zero, the numbers are negative.

Key words

negative number
A number less than zero, written with a minus sign: −4.
positive number
A number greater than zero.
difference
How far apart two numbers are on the number line.

Worked examples

  1. 1Warm-up

    Which is colder: −4 °C or −1 °C?

    • −4 is further below zero than −1
    • So −4 °C is colder
  2. 211+ standard

    The temperature rises from −7 °C to 5 °C. By how many degrees?

    • −7 up to 0 is 7 degrees
    • 0 up to 5 is 5 more
    • 7 + 5 = 12 degrees
  3. 311+ standard

    Work out −3 − 6

    • Start at −3
    • Taking away 6 moves 6 further left
    • −3 − 6 = −9
  4. 411+ standard

    Put in order, smallest first: 2, −5, 0, −1, −10

    • The further below zero, the smaller
    • −10, −5, −1, 0, 2

The common mistake

The mistake

−7 is bigger than −2, because 7 is bigger than 2.

Instead

−2 is bigger: it is nearer zero, higher up the thermometer.

Why: Below zero, the bigger the digit, the colder (smaller) the number.

Where it comes up in the 11+

Temperature changes, number lines, the difference across zero and ordering negative numbers.

The video

Video coming soon

We're making a short video that explains negative numbers step by step. Until then, everything it covers is on this page.

Free printable

Negative numbers worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

Free account needed: it takes a minute.

Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Work out −8 + 11.

    • −19
    • −3
    • 3
    • 19
    Show the answer

    3

    8 steps up gets to 0, then 3 more: 3.

  2. 2. At midnight it was −6 °C. At noon it was 4 °C. How many degrees warmer was noon?

    • 2
    • 6
    • 10
    • −10
    Show the answer

    10

    6 degrees up to 0, then 4 more: 6 + 4 = 10.

  3. 3. Which is the smallest: −12, −3, 0 or −8?

    • −12
    • −3
    • 0
    • −8
    Show the answer

    −12

    −12 is the furthest below zero.