GCSE Negative numbers Practice Questions

Free GCSE Negative numbers practice questions with full step-by-step worked solutions. Covers adding directed numbers, number line, adding a negative, adding two negatives. Practise exam-style problems and check your method.

adding directed numbersnumber lineadding a negativeadding two negativesadding to a negativecrossing zero
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Work out −3+5-3 + 5.
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Worked solution

  1. Start on the number line

    begin at −3\text{begin at } -3

    Start at −3. Adding a positive number means moving to the right.

  2. Move 5 to the right

    −3→+52-3\xrightarrow{+5}2

    Count 5 steps right: −3, −2, −1, 0, 1, 2.

  3. State the answer

    −3+5=2-3+5=2

    So the answer is 2.

Answer
22
Question 2
2 markseasy
A bank balance is −£20-\pounds20. A deposit of £30\pounds30 is made. What is the new balance?
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Worked solution

  1. A deposit adds money

    −20+30-20+30

    The balance is −£20 (overdrawn) and a £30 deposit is added.

  2. Work it out

    −20+30=10-20+30=10

    From −20 move 30 right: 20 clears the debt, leaving 10.

  3. State with units

    £10\pounds10

    So the new balance is £10.

Answer
£10\pounds10
Question 3
2 marksintermediate
Find the missing number: −3+□=2-3 + \square = 2.
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Worked solution

  1. Understand the missing number

    −3+□=2-3+\square=2

    We need the number that takes us from −3 up to 2.

  2. Rearrange to find the box

    □=2−(−3)\square=2-(-3)

    The box is the difference between the answer and the start.

  3. Subtracting a negative

    2−(−3)=2+32-(-3)=2+3

    Two minus signs make a plus.

  4. Work it out

    2+3=52+3=5

    So the box is 5.

  5. Check the answer

    −3+5=2 ✓-3+5=2\ \checkmark

    From −3 move 5 right to reach 2, which matches.

  6. State the answer

    □=5\square=5

    So the missing number is 5.

Answer
55
Question 4
3 markshard
Work out −2(3−7)-2(3 - 7).
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Worked solution

  1. Brackets first

    (3−7)(3-7)

    The order of operations says work out the bracket first.

  2. Work out the bracket

    3−73-7

    3 minus 7 goes below zero.

  3. Evaluate

    3−7=−43-7=-4

    From 3 move 7 left to reach −4.

  4. Rewrite the calculation

    −2×(−4)-2\times(-4)

    The −2 outside multiplies the bracket value.

  5. Multiply the numbers

    2×4=82\times4=8

    Ignore the signs first: 2×4=82 \times 4 = 8.

  6. Decide the sign

    (−)×(−)=(+)(-)\times(-)=(+)

    Negative times negative is positive.

  7. So the result

    −2×(−4)=8-2\times(-4)=8

    The answer is +8.

  8. Check by expanding

    −2×3+(−2)×(−7)-2\times3+(-2)\times(-7)

    As a check, multiply out the bracket instead.

  9. Evaluate the expansion

    −6+14=8-6+14=8

    −6 plus 14 is 8, which matches.

  10. State the answer

    −2(3−7)=8-2(3-7)=8

    So the answer is 8.

Answer
88
Question 5
5 markschallenging
Work out ∣−7∣−∣3∣−(−2)|-7| - |3| - (-2), where ∣x∣|x| means the distance of xx from zero.
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Worked solution

  1. Meaning of the modulus

    ∣x∣=distance from 0|x|=\text{distance from }0

    The bars mean the distance of the number from zero, which is never negative.

  2. Work out the first modulus

    ∣−7∣=7|-7|=7

    −7 is 7 away from zero, so ∣−7∣=7|-7| = 7.

  3. Work out the second modulus

    ∣3∣=3|3|=3

    3 is 3 away from zero, so ∣3∣=3|3| = 3.

  4. Rewrite the calculation

    7−3−(−2)7-3-(-2)

    Replace the moduli with their values.

  5. Work left to right: first part

    7−37-3

    Start with 7 − 3.

  6. Evaluate

    7−3=47-3=4

    7−3=47 - 3 = 4.

  7. Now the last part

    4−(−2)4-(-2)

    We still have to subtract −2.

  8. Deal with the double sign

    −(−2)=+2-(-2)=+2

    Subtracting −2 becomes adding 2.

  9. Rewrite

    4+24+2

    So we compute 4 + 2.

  10. Evaluate

    4+2=64+2=6

    4+2=64 + 2 = 6.

  11. Watch the key trap

    ∣−7∣=7, not −7|-7|=7,\ \text{not}\ -7

    The modulus removes the minus sign, so |−7| is +7.

  12. And the double sign

    −(−2)=+2-(-2)=+2

    The final −(−2) turns into +2.

  13. Combine as a check

    7−3+27-3+2

    Written without the moduli or double sign, it is 7 − 3 + 2.

  14. Evaluate the check

    7−3+2=67-3+2=6

    This gives 6, matching.

  15. State the answer

    66

    So the value is 6.

Answer
66

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