Numbers and operations · Ages 12–13
Directed numbers worksheet
Covers: Positive and negative numbers, Comparing directed numbers, Adding directed numbers, Subtracting directed numbers, Multiplying directed numbers, Dividing directed numbers, The four operations mixed, Using directed numbers
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Directed numbers worksheet
Numbers and operations · Ages 12–13
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.−3, 0, −3, +1, +6: of these 5 numbers, are negative.
Answer:
2.−(+20) =
Answer:
3.Put these numbers in order, smallest first.
- A. 6
- B. −5
- C. −3
- D. 0
Write the letters in the right order
Answer:
4.33 + (−18) =
Answer:
5.(−6.2) + (−3.8) =
Answer:
6.(+11) − (−25) − (−30) =
Answer:
7.(−11) × (−12) =
Answer:
8.(−12) ÷ (−3) =
Answer:
9.An account holds $350, and $700 is taken out (it may go overdrawn, written as negative). What is the balance, in dollars?
Answer:
Part B: Choose, or true or false (2 marks each)
10.Which of these numbers is the largest?
- A. −0.8
- B. −34
- C. −1
- D. −25
Choose the right answer
Answer:
11.Which of these comes to −9?
- A. (−28) − 19
- B. 28 − (−19)
- C. 28 − 19
- D. (−28) − (−19)
Choose the right answer
Answer:
12.(−9) × (7 − 19) = 110
True or false?
Answer:
Part C: Word problems (4 marks each)
13.The ground floor G is written 0, and basement B3 is written −3. A lift going from B3 to floor 14 rises 16 floors.
True or false?
Working:
Answer:
14.In golf, par is 0 and fewer strokes is better. A is −5, B is −9, C is 0 and D is +6. Who comes first?
- A. D
- B. B
- C. A
- D. C
Choose the right answer
Working:
Answer:
15.East is positive and the start is 0. A cat walks −30, +150, −50 m: m in all, ending at m.
Fill in each blank
Working:
Answer:
16.A temperature goes from −14°C to −2°C. With a rise as positive, what is the change in degrees?
Working:
Answer:
17.A train passes a station at −6 m a second (east is positive). With "12 seconds ago" as −12, how far east was it?
Working:
Answer:
18.A mine's entrance is 190 m above sea level. A miner goes 50 m down from it. With sea level 0 and up positive, where is the miner now, in m?
Working:
Answer:
Show the answers and working
Directed numbers worksheet: Answers and working
Part A: Working out and filling in
1. 2
Only those with a minus sign are negative: 2 of them. 0 is neither positive nor negative.
2. −20
The minus outside the bracket means the opposite: the opposite of 20 is −20, flipped across 0 on the number line.
3. B → C → D → A
Read the number line left to right: −5, −3, 0, 6. Among negatives, further from 0 is smaller.
4. 15
Adding a negative moves left: 33 − 18 = 15. The sign is that of the number further from 0.
5. −10
Decimals work the same way: same signs, add the sizes and keep the sign; different signs, subtract them and take the sign of the one further from 0. The answer is −10.
6. 66
Turn each minus into adding the opposite: (+11) + (+25) + (+30) = 66.
7. 132
Same signs multiply to a positive: 11 × 12 = 132.
8. 4
Same signs divide to a positive: 12 ÷ 3 = 4. Check: 4 × (−3) = −12.
9. −350 dollars
350 + (−700) = −350. Taking money out makes the balance smaller; the $350 it held goes against the withdrawal rather than being added on. If more came out than there was, it is a debt, written as negative.
Part B: Choose, or true or false
10. D. −25
As decimals: 34 = 3 ÷ 4 and 25 = 2 ÷ 5; then see which is nearest 0. Among negatives, nearer 0 is larger.
11. D. (−28) − (−19)
Make each subtraction add the opposite: (−28) − (−19) = (−28) + 19 = −9.
12. False
7 − 19 is negative, and negative times negative is positive. Work it through and compare with 110.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. False
From −3 to 14: 14 − (−3) = 14 + 3. Up 3 floors to G, then 14 more.
14. B. B
Fewer is better, so find the smallest: of −5 and −9, the one further from 0.
15. 230, 70
Distance ignores direction, so add them all: 230 m. Position counts direction: (−30) + 150 + (−50) = 70.
16. 12°C
Change = after − before: (−2) − (−14) = (−2) + 14 = 12. Both are below 0, so the sizes subtract, not add; getting colder is a fall, written as negative.
17. 72 m
(−6) × (−12) = 72. It is heading west, so 12 seconds ago it was 72 m east.
18. 140 m
With sea level as 0: 190 + (−50) = 140.
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