Numbers and operations · Ages 12–13

Subtracting directed numbers worksheet

Part of: Directed numbers

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Numbers and operations · Ages 12–13

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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.

1.−8 − 40 =
Answer:
2.(−3) − (−55) =
Answer:
3.−50 − (−46) =
Answer:
4.(−19) − (−26) =
Answer:
5.20 − 38 =
Answer:
6.Turn the subtraction into an addition: (−22) − (−26) = (−22) + =
Fill in each blank
Answer:
7.The two dots on the number line are −3 and 4. The distance between them is 4 − (−3). What is it?
Answer:
8.(+43) − (+21) =
Answer:
9.(−10) − (−5) − (−10) =
Answer:
10.(−58) − (−38) =
Answer in simplest form
Answer:

13.An account's balance was −600 dollars and is now −650 dollars. With a rise as positive, what is the change in dollars?
Working:
Answer:
14.Of these four pairs of temperatures, which pair differs the most (in degrees)?
- A. −6°C and −7°C
- B. 9°C and 2°C
- C. −9°C and 2°C
- D. 6°C and −7°C
Choose the right answer
Working:
Answer:
15.A temperature goes from −15°C to −3°C. With a rise as positive, what is the change in degrees?
Working:
Answer:
16.1 BC is followed by AD 1, with no year 0. How many years are there from 210 BC to AD 620?
Working:
Answer:
17.A peak is at 1700 m, a trench at −700 m. The gap: 1700 − (−700) = 1700 + = m.
Fill in each blank
Working:
Answer:
18.City A is +7 hours, city B −10. It is 20:00 in A (24-hour clock). What hour is it in B?
Working:
Answer:

Show the answers and working

Subtracting directed numbers worksheet: Answers and working

1. −48
Taking away 40 is adding −40: −8 + (−40) = −48. Same signs add the sizes; only different signs subtract them.
2. 52
(−3) − (−55) = (−3) + 55 = 52. The sign is that of the number further from 0.
3. −4
Taking away a negative is adding its opposite: −50 + 46 = −4.
4. 7
(−19) − (−26) = (−19) + 26 = 7. The sign is that of the number further from 0.
5. −18
Taking away 38 is adding −38: 20 + (−38) = −18. Same signs add the sizes; only different signs subtract them.
6. 26, 4
The opposite of −26 is 26, so it is (−22) + 26 = 4.
7. 7
From −3 to 0 is 3 steps, from 0 to 4 is 4 steps: 7 in all. The sum 4 − (−3) = 4 + 3 = 7 agrees.
8. 22
Taking a number away is adding its opposite, not taking more away: (+43) + (−21) = 22.
9. 5
Turn each minus into adding the opposite: (−10) + (+5) + (+10) = 5.
10. −14
Taking away −38 is adding 38: 3 − 58 = −14, in lowest terms.

11. C. (−3) − (−27)
Make each subtraction add the opposite: (−3) − (−27) = (−3) + 27 = 24.
12. D. (−18) − (−2)
Make each subtraction add the opposite: (−18) − (−2) = (−18) + 2 = −16.

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

13. −50 dollars
Change = after − before: (−650) − (−600) = (−650) + 600 = −50. Less owing means the balance went up; more owing means it went down.
14. D. 6°C and −7°C
On a number line, opposite signs have 0 between them, so the sizes add; same signs, the sizes subtract.
15. 12°C
Change = after − before: (−3) − (−15) = (−3) + 15 = 12. Both are below 0, so the sizes subtract, not add; getting colder is a fall, written as negative.
16. 829 years
With a year 0 it would be 620 − (−210) = 620 + 210. There is none, so take off 1: 829.
17. 700, 2400
Taking away −700 is adding 700: 1700 + 700 = 2400 m.
18. 3:00
They differ by 7 − (−10) = 17 hours, and city B is behind: 20 − 17 = 3.

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