Numbers and operations · Ages 12–13

Multiplying 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.

13.For 10 months in a row, a small shop's result is −2000 dollars a month (profit positive). What is its total over that time, in dollars?
Working:
Answer:
14.A star is +3, a bomb −3. 11 stars score , 14 bombs −, in all .
Fill in each blank
Working:
Answer:
15.A water level is 50 cm below the warning line, so it is at −50 cm. Then it changes by −14 cm an hour. Where is it after 2 hours, in cm?
Working:
Answer:
16.A train passes a station at −2 m a second (east is positive). With "7 seconds ago" as −7, how far east was it?
Working:
Answer:
17.15 negative numbers are written on a board. Multiplying them all gives a positive product.
True or false?
Working:
Answer:
18.Starting from 19°C, the temperature falls 2°C an hour. What is it after 7 hours?
Working:
Answer:

Show the answers and working

Multiplying directed numbers worksheet: Answers and working

1. 20
Same signs multiply to a positive: 2 × 10 = 20.
2. −88
This is multiplying, not adding or subtracting: 11 × 8. Same signs give a positive, different signs a negative: −88.
3. 18
Same signs multiply to a positive: 6 × 3 = 18.
4. 60
Count the minus signs: an even number makes the product positive, an odd number negative. The size is 2 × 6 × 5: 60.
5. −315
Count the minus signs: an even number makes the product positive, an odd number negative. The size is 5 × 9 × 7: −315.
6. −310
Same signs give a positive, different signs a negative; tops times tops, bottoms times bottoms, in lowest terms: −310.
7. 15
The power comes before the minus: −10² = −(10 × 10) = −100; adding 115 gives 15. With a bracket, (−10)² is 100.
8. −66
The power comes before the minus: −9² = −(9 × 9) = −81; adding 15 gives −66. With a bracket, (−9)² is 81.
9. −340
Same signs give a positive, different signs a negative; tops times tops, bottoms times bottoms, in lowest terms: −340.

10. D. 225
(−15)² = (−15) × (−15) = 225.
11. False
No need to work it out, just count the minus signs: an odd number makes a negative product, an even number a positive one.
12. True
No need to work it out, just count the minus signs: an odd number makes a negative product, an even number a positive one.

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

13. −20000 dollars
It is the same every month, so multiply rather than count one month: 10 × (−2000) = −20000. A loss is negative.
14. 33, 42, −9
11 × 3 = 33; 14 × (−3) = −42; 33 + (−42) = −9.
15. −78 cm
(−50) + 2 × (−14) = (−50) + (−28) = −78.
16. 14 m
(−2) × (−7) = 14. It is heading west, so 7 seconds ago it was 14 m east.
17. False
Count the minus signs: an even number of negatives gives a positive, an odd number a negative. Here there are 15.
18. 5°C
A fall is negative, and it falls every hour, so multiply: 7 × (−2) = −14; then 19 + (−14) = 5.

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