Numbers and operations · Ages 12–13

Using directed numbers worksheet

Part of: Directed numbers

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Numbers and operations · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.It was −11°C at dawn and 15°C at noon. By how much did the temperature rise?
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2.It is −13°C now. What is the temperature after it rises 16°C?
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3.It is −12°C now. What is the temperature after it rises 8°C?
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4.A shop's record over three days is +$750, −$500, −$150. With profit positive, what is its total over the three days, in dollars?
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5.An account holds $400, and $700 is taken out (it may go overdrawn, written as negative). What is the balance, in dollars?
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6.A shop's record over three days is +$300, −$350, −$150. With profit positive, what is its total over the three days, in dollars?
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7.With London as 0, city A is −3 hours and city B +3 hours. How many hours is B's clock ahead of A's?
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8.A quiz has 22 questions: +1 for right, −1 for wrong. All are answered, 17 wrong. What is the total score?
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9.A quiz has 29 questions: +1 for right, −1 for wrong. All are answered, 6 wrong. What is the total score?
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10.With London as 0, city A is −1 hours and city B +4 hours. How many hours is B's clock ahead of A's?
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13.A mine's entrance is 120 m above sea level. A miner goes 290 m down from it. With sea level 0 and up positive, where is the miner now, in m?
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14.Ice at −26°C warms 2°C a minute. It must rise °C to reach 0°C, taking minutes.
Fill in each blank
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15.A balance is −600 dollars. Each month $400 goes in and $150 is spent. How many months until it is no longer negative?
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16.A gull is 80 m above the sea and a fish 90 m below it. After the fish dives 15 m more, how far above the fish is the gull, in m?
- A. 155
- B. 170
- C. 185
- D. 10
Choose the right answer
Working:
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17.City A is −7 hours, city B +1. It is 10:00 in A (24-hour clock). What hour is it in B?
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18.A balloon is 600 m up. Down 100 m: m up. Down 100 m more: m up.
Fill in each blank
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Show the answers and working

Using directed numbers worksheet: Answers and working

1. 26°C
15 − (−11) = 15 + 11 = 26. Up to 0°C first, then on to 15°C.
2. 3°C
(−13) + 16 = 3, so 3°C. Rising goes up, not colder, and with different signs the sizes subtract. Until it reaches 0°C, it is still below zero.
3. −4°C
(−12) + 8 = −4, so −4°C. Rising goes up, not colder, and with different signs the sizes subtract. Until it reaches 0°C, it is still below zero.
4. 100 dollars
Profit is positive, loss negative: 750 + (−500) + (−150) = 100.
5. −300 dollars
400 + (−700) = −300. Taking money out makes the balance smaller; the $400 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.
6. −200 dollars
Profit is positive, loss negative: 300 + (−350) + (−150) = −200.
7. 6 hours
3 − (−3) = 3 + 3 = 6. They are on either side of 0, so add.
8. −12 points
5 right: 5 × 1 + 17 × (−1) = −12.
9. 17 points
23 right: 23 × 1 + 6 × (−1) = 17.
10. 5 hours
4 − (−1) = 4 + 1 = 5. They are on either side of 0, so add.

11. A. (−80) + (−50)
With sea level 0 and up positive: start at −80, then change by −50: (−80) + (−50).
12. B. (−50) + (−70)
With sea level 0 and up positive: start at −50, then change by −70: (−50) + (−70).

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. −170 m
With sea level as 0: 120 + (−290) = −170.
14. 26, 13
From −26°C to 0°C is a rise of 26°C, and 26 ÷ 2 = 13 minutes.
15. 3 months
The net change is 400 − 150 = +250 a month. 600 ÷ 250 isn't whole, so round up: 3 months.
16. C. 185
The fish is at (−90) + (−15). 80 − [(−90) + (−15)] = 185.
17. 18:00
City B is 1 − (−7) = 8 hours ahead of city A: 10 + 8 = 18.
18. 500, 400
600 + (−100) = 500; 500 + (−100) = 400.

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