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Maths: Negative Numbers

▶  Watch: how to answer a negative numbers question4 min

Four steps in about four minutes — one real question, worked step by step, then the traps to watch out for.

In a negative numbers question, you read a temperature below zero, then work out what it becomes when it changes. There are five answers to choose from.

There's no calculator, and only one of the five answers is right.

In GL's papers this comes as a thermometer with marks between the labels, and every wrong answer is a way to misread it. So two of the four steps are about reading the scale. The video above and the worked example below work through the same question, with the options in the same order.

The method

Four steps: find what each mark is worth, read where it stops, decide up or down, count to zero, then on.

  1. Step 1 of 4

    Find what each mark is worth

    Count the spaces between two labelled numbers, and share the gap between them.
  2. Step 2 of 4

    Read where it stops

    Find the nearest label, then count the marks from it.
  3. Step 3 of 4

    Decide up or down

    Warmer or higher: up. Colder or lower: down.
  4. Step 4 of 4

    Count to zero, then on

    Zero is a stop on the way.

Worked example

James reads this thermometer early in the morning. By noon the temperature is 12 degrees higher. What is the temperature at noon?

The thermometer: marked from −30 °C to 30 °C, labelled every 10 degrees, with four small marks between each pair of labels. The liquid stops one small mark above −10 °C.

A. 4°C B. 2°C C. 3°C D. 0°C E. −20°C

  1. Find what each mark is worth. From −10 up to 0 there are five spaces, and 10 shared into 5 is 2. So each mark is worth 2 degrees. Count each mark as 1, and you'd read −9, which leads to 3 degrees. That's C, so C is out.
  2. Read where it stops. The liquid stops one mark above −10. One mark is 2 degrees, and above means nearer to zero, so it shows −8. B starts from −10 itself, the labelled number, so B is out. D starts one mark below, at −12, so D is out too.
  3. Decide up or down. Higher, or warmer, means up the scale. Lower, or colder, means down. Here it's 12 degrees higher, so we go up. E went down to −20, so E is out.
  4. Count to zero, then on. From −8, 8 degrees takes you up to zero. That leaves 4 of the 12, so keep going: 4 degrees. So the answer is A.

Answer: A — 4°C (−8 °C, up 8 to zero, then 4 more)

Things to watch out for

  1. Zero is a step too. Stop at zero, then go on. What is 15 less than 9? Count back 9 to reach zero, then 6 more: −6. Jump straight from 1 to −1, and you land on −7, which is B. Count the 9 itself as a step, and you get −5, which is D.
  2. Across zero, add the two parts. Up to zero, then up the other side. One night it was −12 °C, and another night it was 3 °C. How many degrees warmer was the second night? 12 degrees up to zero, then 3 more: 15. 12 take away 3 gives 9. That's C, and it's a trap.
  3. Colder means further below zero. −11 °C is colder than −2 °C. Which is the coldest: −11 °C, 3 °C, −10 °C, 14 °C or −2 °C? −11 is furthest below zero, so it's the coldest. −2 has the smallest number, but it's only just below zero.

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