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Positive & negative numbers

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Addition and subtraction

Positive & negative numbers

Below zero, the rules feel upside down: āˆ’8 is colder than āˆ’3, even though 8 is bigger than 3. A number line keeps it straight.

Subtract ā†’ count back-6-5-4-3-2-10123= āˆ’5Add ā†’ count forward-6-5-4-3-2-10123= āˆ’2

Numbers below zero

NEGATIVE numbers are less than zero. They are written with a minus sign in front: āˆ’3, āˆ’8, āˆ’20. On a number line they sit to the LEFT of zero. Numbers get bigger as you move right and smaller as you move left. So āˆ’8 is LESS than āˆ’3, because it is further left. The further a negative number is from zero, the smaller it is.

Rises and falls

A RISE means move right. A FALL means move left. Start at 2 Ā°C and fall 5 degrees: move 5 left from 2, landing on āˆ’3 Ā°C. Start at āˆ’3 Ā°C and rise 8 degrees: move 8 right, landing on 5 Ā°C. The number line does the thinking for you ā€” you never have to remember a rule.

Counting the gap between two temperatures

To find how much colder one place is than another, count the steps along the line. London is 4 Ā°C and Montreal is 16 degrees colder. Count 16 left from 4: first 4 steps to reach zero, then 12 more. So Montreal is āˆ’12 Ā°C. Splitting the journey at zero makes it much easier than trying to do it in one jump.

Calculating without a picture

Once you trust the line you can work without drawing it. 0 āˆ’ 78 = āˆ’78 (start at zero, go 78 left) 45 āˆ’ 150 = āˆ’105 (go 150 left from 45 ā€” that is 45 to reach zero, then 105 more) āˆ’13 + 79 = 66 (go 79 right from āˆ’13 ā€” that is 13 to reach zero, then 66 more) Always split the journey at zero.

Worked examples

A fall below zero

  1. Start at 2 Ā°C.
  2. A fall of 5 degrees means move 5 places left.
  3. 2 ā†’ 1 ā†’ 0 ā†’ āˆ’1 ā†’ āˆ’2 ā†’ āˆ’3.

Answer: The new temperature is āˆ’3 Ā°C

A rise from below zero

  1. Start at āˆ’3 Ā°C.
  2. A rise of 8 degrees means move 8 places right.
  3. 3 steps get you to zero, and 5 more make 8.

Answer: The new temperature is 5 Ā°C

Which is colder?

  1. Compare āˆ’8 Ā°C and āˆ’3 Ā°C.
  2. On a number line, āˆ’8 is further left than āˆ’3.
  3. Further left means smaller.

Answer: āˆ’8 Ā°C is colder

Finding a temperature 16 degrees colder

  1. London is 4 Ā°C.
  2. Count 4 left to reach zero.
  3. 12 more steps left from zero.

Answer: Montreal is āˆ’12 Ā°C

45 āˆ’ 150

  1. Start at 45 and move 150 left.
  2. 45 steps take you to zero.
  3. There are 105 steps still to go, all below zero.

Answer: 45 āˆ’ 150 = āˆ’105

Where you see this in real life

  • Winter temperatures in Montreal drop well below zero, so āˆ’12 Ā°C is an ordinary reading.
  • A bank balance of āˆ’Ā£20 means you owe Ā£20.
  • Floors below ground in a lift are numbered āˆ’1 and āˆ’2.

Key words

Negative number
A number less than zero.
Positive number
A number greater than zero.
Zero
The number between the positives and the negatives.
Number line
A line showing numbers in order, smaller to the left.
Rise
An increase ā€” move right on the number line.
Fall
A decrease ā€” move left on the number line.
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