Numbers and operations · Ages 12–13

Dividing 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) ÷ (−4) =
Answer:
2.(+70) ÷ (+7) =
Answer:
3.(−24) ÷ (−6) =
Answer:
4.(−24) ÷ (−4) =
Answer:
5.180 ÷ (+5) ÷ (+3): first 180 ÷ (+5) = ; dividing by (+3) then gives .
Fill in each blank
Answer:
6.144 ÷ (−4) ÷ (+3): first 144 ÷ (−4) = ; dividing by (+3) then gives .
Fill in each blank
Answer:
7.(+17) ÷ (−6) =
Answer in simplest form
Answer:
8.(−15) ÷ (+34) =
Answer:
9.(+27) ÷ (−5) =
Answer in simplest form
Answer:

13.It is 13°C at 2 p.m. and −11°C after 8 hours, changing by the same amount each hour. With a rise as positive, what is the change each hour, in degrees?
Working:
Answer:
14.Against a base of 80, four scores differ by −5, +12, −4, +1. What is their mean?
Working:
Answer:
15.The thermometers show dawn on four days. What is the mean temperature of these days?
Working:
Answer:
16.3 partners share a result equally. With profit positive, the total is +240 dollars. What is each partner's share, in dollars?
Working:
Answer:
17.A water level changes by −75 cm over 5 days, by the same amount each day. What is the change each day, in cm?
Working:
Answer:
18.A tank holds 36 litres and changes by −42 litres every 7 minutes: litres a minute, and litres in it after 3 minutes.
Fill in each blank
Working:
Answer:

Show the answers and working

Dividing directed numbers worksheet: Answers and working

1. 2
Same signs divide to a positive: 8 ÷ 4 = 2. Check: 2 × (−4) = −8.
2. 10
Same signs divide to a positive, different signs to a negative: 70 ÷ 7 = 10, so 10. This is dividing, not subtracting. Check: 10 × (+7) must be +70.
3. 4
Same signs divide to a positive, different signs to a negative: 24 ÷ 6 = 4, so 4. This is dividing, not subtracting. Check: 4 × (−6) must be −24.
4. 6
Same signs divide to a positive: 24 ÷ 4 = 6. Check: 6 × (−4) = −24.
5. 36, 12
Left to right, checking the signs at each step: 180 ÷ (+5) = 36, and 36 ÷ (+3) = 12.
6. −36, −12
Left to right, checking the signs at each step: 144 ÷ (−4) = −36, and −36 ÷ (+3) = −12.
7. −142
Dividing by 6 is multiplying by 16, not by 6; only the divisor turns over, not 17. Same signs give a positive, different signs a negative: −142.
8. −20
Dividing by a fraction is multiplying by its reciprocal: 15 × 43. Same signs give a positive, different signs a negative: −20.
9. −235
Dividing by 5 is multiplying by 15, not by 5; only the divisor turns over, not 27. Same signs give a positive, different signs a negative: −235.

10. True
Division follows the same sign rule as multiplication: same signs positive, different signs negative.
11. True
Division follows the same sign rule as multiplication: same signs positive, different signs negative.
12. D. (−24) ÷ 0
You can't divide by 0: no number times 0 gives −24.

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

13. −3°C
Change = after − before: −11 − (13) = −24; −24 ÷ 8 = −3.
14. 81 points
The mean difference: ((−5) + 12 + (−4) + 1) ÷ 4 = 1, so the mean is 80 + 1 = 81.
15. −1°C
Add the four readings, signs and all, to get −4; then divide by 4, don't multiply: −4 ÷ 4 = −1. Dividing by 4 keeps the sign: a negative total gives a negative mean.
16. 80 dollars
Sharing divides by the number of people; it doesn't multiply: (+240) ÷ 3 = 80. A shared loss is still negative for each.
17. −15 cm
(−75) ÷ 5 = −15: a change of −15 cm a day. Different signs divide to a negative, the same signs to a positive.
18. −6, 18
(−42) ÷ 7 = −6; 36 + 3 × (−6) = 18.

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