Negative Numbers and Rounding

Negative numbers and rounding are two topics that appear regularly on the SET 11+ maths papers. You need to understand how negative numbers work in real-life contexts (such as temperature) and how to round numbers to a given degree of accuracy. This lesson covers both topics in detail.

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Understanding Negative Numbers

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

You can picture them on a number line:

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

The further left a number is on the number line, the smaller it is.

Key Facts

• -7 is less than -3 (because -7 is further left on the number line).
• 0 is greater than any negative number.
• -1 is the largest negative integer.

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Ordering Negative Numbers

Worked Example

Put these numbers in order from smallest to largest: 3, -5, -1, 0, -8, 4

Think of the number line. The further left, the smaller the number.

Answer: -8, -5, -1, 0, 3, 4

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Adding and Subtracting with Negative Numbers

Adding a positive number

Move right on the number line.

• -4 + 7 = 3 (start at -4, move 7 to the right)

Adding a negative number

Move left on the number line.

• 5 + (-3) = 2 (start at 5, move 3 to the left)
• This is the same as 5 - 3 = 2.

Subtracting a positive number

Move left on the number line.

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

Subtracting a negative number

Subtracting a negative is the same as adding.

• 3 - (-4) = 3 + 4 = 7
• -2 - (-6) = -2 + 6 = 4

Memory aid: Two minuses together make a plus. Think of it as "the opposite of going backwards is going forwards."

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Temperature Problems

Temperature is the most common real-life context for negative numbers on the SET.

Worked Example

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

-6 + 14 = 8°C

Worked Example

The temperature in Moscow is -12°C. The temperature in London is 5°C. What is the difference in temperature?

Count from -12 up to 5: that is 12 + 5 = 17°C difference.

SET Tip: On Stage 1, draw a quick number line in your head (or on scrap paper) to avoid sign errors. On Stage 2, show your working clearly.

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