Negative Numbers
A negative number is a number less than zero, used to represent values below a starting point, such as temperatures below freezing, depths below sea level, or an overdrawn bank balance. Negative numbers are ordered on a number line running from smallest to largest from left to right, so a number further to the left is always smaller even if it looks bigger without its minus sign, for example -20 is smaller than -3, and the four operations work with them using consistent rules.
Before you start
Make sure you're comfortable with these topics first:
Method
- Picture a number line running from negative values on the left, through zero, to positive values on the right.
- To add a positive number, move right along the number line; to subtract a positive number, move left.
- Adding a negative number has the same effect as subtracting, so move left; subtracting a negative number has the same effect as adding, so move right.
- For multiplying or dividing two directed numbers, work out the sign first: the same signs (both positive or both negative) give a positive answer, and different signs give a negative answer.
- Once the sign is decided, calculate the size of the answer using the numbers without their signs, then attach the correct sign.
- To order a list of negative numbers, compare their distance below zero: the number furthest below zero is the smallest value, not the largest.
- In a real-life context, decide what zero represents (freezing point, sea level, a zero balance) before turning the words into a calculation.
- Check an answer makes sense in context: a temperature that has fallen should be a smaller number than before, and a balance after a payment out should be more negative, not less.
Worked example
The temperature in Aviemore at 6am was -8 degrees C. By 2pm it had risen by 11 degrees C. By 9pm it had then fallen by 6 degrees C from the 2pm value. Work out the temperature at 9pm.
- Start with the 6am temperature: -8 degrees C.
- A rise of 11 degrees C means adding 11: -8 + 11 = 3, so the temperature at 2pm is 3 degrees C.
- A fall of 6 degrees C from the 2pm value means subtracting 6: 3 - 6 = -3.
- The temperature at 9pm is -3 degrees C.
Practice questions
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Q1Work out -12 + 5.Show answer
Answer: -7
Q2Work out -9 - 6.Show answer
Answer: -15
Q3Work out -8 x 3.Show answer
Answer: -24
Q4Work out -30 / -5.Show answer
Answer: 6
Q5Order these temperatures from coldest to warmest: -3 degrees C, 4 degrees C, -11 degrees C, 0 degrees C.Show answer
Answer: -11 degrees C, -3 degrees C, 0 degrees C, 4 degrees C
Q6A submarine is at a depth of -240 m (240 m below sea level). It rises by 95 m. Work out its new depth.Show answer
Answer: -145 m (-240 + 95 = -145)
Q7Explain why -2 is greater than -9, even though 9 is greater than 2.Show answer
Answer: On a number line, -2 is further to the right (closer to zero) than -9, and numbers further right are greater; being 'more negative' (further below zero) makes a number smaller, not larger.
Q8A bank account balance is -45 pounds (it is overdrawn by 45 pounds). A payment of 120 pounds is paid in. Work out the new balance.Show answer
Answer: 75 pounds (-45 + 120 = 75)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
The temperature at the summit of a mountain is -14 degrees C. The temperature at the base of the mountain is 9 degrees C higher than at the summit. Work out the temperature at the base of the mountain.
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Work out -6 x (-4 + 9), showing your working.
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On Monday, a company's profit was -2400 pounds (a loss of 2400 pounds). On Tuesday, the profit was 3150 pounds higher than Monday's. On Wednesday, the profit fell by 900 pounds from Tuesday's value. (a) Work out the profit on Tuesday. (b) Work out the profit on Wednesday.
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Free printable worksheet
Want more practice on paper? Download the negative numbers worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 7 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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