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GCSE Maths · Number
Negative numbers GCSE Questions and Worked Answers
Negative numbers are below zero. A number line shows their order; adding a signed number follows its direction, while subtracting it reverses that change.
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Start with the meaning
What you need to know about negative numbers
A temperature of −3°C is three degrees below zero. A temperature of +1°C is one degree above zero. Put them on a line with equally spaced numbers: moving right means a greater value. So −3 is less than +1 even though the digit 3 is larger than 1. The minus sign belongs to the value; zero itself is neither positive nor negative.
See the idea first
Crossing zero is an ordinary change
The temperature rises by 4 degrees from −3°C: three degrees reach zero and the fourth reaches +1°C. We write −3 + 4 = 1. Here −3 is the starting value and +4 is the change.
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Order signed numbers
What the problem asks: Put −0.8, −2, 0 and 0.3 in increasing order.
How to solve it: Read from left to right: −2, −0.8, 0, 0.3. A negative number closer to zero is greater.
Undo a negative change
What the problem asks: Calculate 5 − (−3).
How to solve it: Subtracting means undoing the addition of that number. Adding −3 moves left three; undoing it moves right three. The result is 8.
Multiply or divide signed numbers
What the problem asks: Calculate (−4) × (−6).
How to solve it: Four lots of −6 total −24. Four lots and minus four lots together make zero lots, so their products must add to zero too. The number that adds to −24 to make zero is +24. Therefore (−4) × (−6) = +24.
A reliable routine
Track signed additions and subtractions
Use the number line for sums and differences. Adding a negative moves left; subtracting a negative undoes that leftward change.
- Mark the starting value.
- For addition, move right for a positive change and left for a negative change.
- For subtraction, reverse the direction of the number being subtracted.
- For products and quotients, calculate magnitudes then use positive for matching signs and negative for differing signs.
Check: The sign rule for multiplying two numbers is not a rule for adding them: −4 + (−6) = −10, not +10. For a product with several negative factors, each pair contributes a positive sign.
Fully worked
Negative numbers GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Order decimals
Question
Write −1.4, −1.04, 0.2, −2 in increasing order.
Align the decimals mentally: −1.40 is further below zero than −1.04.
Example 2
Add across zero
Question
Work out −8 + 13.
Eight of the thirteen rightward steps reach zero; five remain.
Example 3
Subtract a positive
Question
Work out −4 − 7.
Start at −4 and move seven left.
Example 4
Subtract a negative
Question
Work out −6 − (−9).
Undo a nine-unit leftward change by moving nine right.
Example 5
Multiply and divide
Question
Work out (−7) × (−3), then 21 ÷ (−3).
Matching signs give a positive product.
To get positive 21 by multiplying by −3, the other factor must be −7.
Example 6
Temperature difference
Question
A freezer is at −18°C and a room is at 22°C. How much warmer is the room?
From −18 to zero is 18 degrees; from zero to 22 is another 22.
The room is 40°C warmer.
10 original questions · total 20 marks
Negative numbers GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 25 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Compare
Insert < or >: −9 ___ −4.
Show worked answer
−9 is further left.
Order
Order −0.5, −0.05, −5 from smallest to largest.
Show worked answer
The smallest is furthest below zero.
Add a negative
Calculate 7 + (−12).
Show worked answer
Move twelve left from seven.
Two negative addends
Calculate −6 + (−8).
Show worked answer
Move eight left from −6.
Undo subtraction
Calculate 3 − (−5).
Show worked answer
Decimal change
Calculate −2.4 + 0.9.
Show worked answer
Move 0.9 right, but remain below zero.
Different signs
Calculate (−9) × 4.
Show worked answer
Nine times four is 36. Different signs give
Matching signs
Calculate (−42) ÷ (−7).
Show worked answer
The quotient is positive because multiplying it by −7 must give −42.
Three factors
Calculate (−2) × (−3) × (−4).
Show worked answer
Three negative factors give a negative product.
Explain a sign error
A pupil says −5 − 2 = −3. Explain and correct it.
Show worked answer
Subtracting positive 2 moves left, not towards zero.
−3 would be the result of adding 2.
Examiner-style feedback
Common negative numbers mistakes
Compare complete signed values, not just their digits.
Two negative addends make a more negative sum.
Brackets decide whether the negative sign is squared; revise BIDMAS for powers.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Right means greater.
- Adding a negative moves left.
- Subtracting reverses the change.
- Use sign rules only for their stated operation.
Quick answers
Negative numbers FAQ
Is zero a positive number?
No. Zero is neither positive nor negative.
Can decimals be negative?
Yes. −0.4 is four tenths below zero.
Content standards
Curriculum and rights review
N1–N3 ordering and operations with signed integers and decimals, across tiers. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references