Negative Numbers and Rounding

Negative numbers and rounding are two important topics that come up regularly on the CSSE maths paper. Negative numbers appear in temperature problems and number-line questions, while rounding is used in estimation and checking answers. Let us look at both in detail.

Negative Numbers

Negative numbers are numbers less than zero. They are written with a minus sign in front, such as -3, -7, or -15.

The number line

On a number line, negative numbers sit to the left of zero.

... -5 -4 -3 -2 -1 0 1 2 3 4 5 ...

Key facts

-3 is less than -1 (it is further from zero on the left).
The further left a number sits, the smaller it is.
Zero is neither positive nor negative.
-10 is smaller than -2, because -10 is further from zero.

Ordering Negative Numbers

Worked Example

Put these numbers in order from smallest to largest: 3, -5, 0, -1, 7, -3

On the number line: -5, -3, -1, 0, 3, 7

Answer: -5, -3, -1, 0, 3, 7

Adding and Subtracting with Negative Numbers

Adding a positive number: move right on the number line

-4 + 6 = 2 (start at -4, move 6 to the right)

Adding a negative number: move left on the number line

3 + (-5) = 3 - 5 = -2 (start at 3, move 5 to the left)

Subtracting a positive number: move left

2 - 7 = -5 (start at 2, move 7 to the left)

Subtracting a negative number: move right (two negatives make a positive)

4 - (-3) = 4 + 3 = 7

Worked Example

The temperature at midnight was -6°C. By midday it had risen by 14°C. What was the temperature at midday?

-6 + 14 = 8°C

Worked Example

At 6 a.m. the temperature was -3°C. By 9 p.m. it had dropped by 5°C. What was the temperature at 9 p.m.?

-3 - 5 = -8°C

CSSE Tip: Temperature problems are a favourite on the CSSE maths paper. Draw a quick number line if it helps you keep track of the direction of change.

Multiplying and Dividing Negative Numbers

Use these simple rules:

Signs	Result	Example
+ × + = +	Positive	3 × 4 = 12
- × - = +	Positive	(-3) × (-4) = 12
+ × - = -	Negative	3 × (-4) = -12
- × + = -	Negative	(-3) × 4 = -12

The same rules apply to division.

Negative Numbers and Rounding

Negative Numbers and Rounding