GCSE Mathematics (9-1)

Work through these on your own. Keep your working neat: the method matters as much as the answer. Questions marked H are for Higher tier.

1.3 Negative numbers — Practise

Work through these on your own. Keep your working neat: the method matters as much as the answer. Questions marked H are for Higher tier.

  1. Write these in order, smallest first: 4, −2, 0, −7, 14,\ -2,\ 0,\ -7,\ 1.
  2. Work out −8+3-8 + 3.
  3. Work out 5−125 - 12.
  4. Work out −6−4-6 - 4.
  5. Work out 2−(−9)2 - (-9).
  6. Work out (−7)×3(-7) \times 3.
  7. Work out (−6)×(−6)(-6) \times (-6).
  8. Work out (−36)÷4(-36) \div 4.
  9. The temperature falls from 2 ∘C2\, ^\circ\text{C} to −5 ∘C-5\, ^\circ\text{C}. By how many degrees did it fall?
  10. A submarine is at −40-40 m and rises 1515 m. What is its new depth?
  11. A shop's takings are £210 and its costs are £235. Work out the profit as a negative number and describe the result.
  12. In a quiz, teams score +3+3 for a correct answer and −1-1 for a wrong answer. A team gets 7 correct and 4 wrong. What is its total score?
  13. H Work out −4+6−3+2−5-4 + 6 - 3 + 2 - 5.
  14. H The product of two negative numbers is +36+36. Give two possible pairs.
Answers and concise solutions

1. Order the numbers

Answer: −7<−2<0<1<4-7 < -2 < 0 < 1 < 4.

2. −8+3-8 + 3

Answer: −5-5

3. 5−125 - 12

Answer: −7-7

4. −6−4-6 - 4

Answer: −10-10

5. 2−(−9)2 - (-9)

Answer: 1111

6. (−7)×3(-7) \times 3

Answer: −21-21

7. (−6)×(−6)(-6) \times (-6)

Answer: 3636

8. (−36)÷4(-36) \div 4

Answer: −9-9

9. Temperature change

Answer: 77 degrees.

10. New submarine depth

Answer: −25-25 m.

11. Profit or loss

Answer: 210−235=−25210 - 235 = -25, a loss of £25.

12. Total quiz score

Answer: 7×3+4×(−1)=21−4=177 \times 3 + 4 \times (-1) = 21 - 4 = 17.

13. Mixed calculation

Answer: −4+6=2-4 + 6 = 2, 2−3=−12 - 3 = -1, −1+2=1-1 + 2 = 1, 1−5=−41 - 5 = -4.

14. Two possible pairs

Answer: (−6)×(−6)(-6) \times (-6) and (−4)×(−9)(-4) \times (-9), for example.

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