Numbers and operations · Ages 12–13

The four operations mixed 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.(−20) + 6 × (+2) =
Answer:
2.60 + (−3) × 2 =
Answer:
3.(−15) + 9 × (−6) =
Answer:
4.38 + (−5) × 6 =
Answer:
5.(−11 + 10)² =
Answer:
6.−32 + 29 − 20 + 23: the positives add to , the negatives to −, so the answer is .
Fill in each blank
Answer:
7.Work out (−6) × [9 − (−4)] + 23. Put the steps in order.
- A. 9 − (−4) = 13
- B. (−78) + 23 = −55
- C. (−6) × 13 = −78
Write the letters in the right order
Answer:
8.−12 + 30 − 23 + 35: the positives add to , the negatives to −, so the answer is .
Fill in each blank
Answer:
9.Work out (−3) × [6 − (−8)] + 28. Put the steps in order.
- A. 6 − (−8) = 14
- B. (−42) + 28 = −14
- C. (−3) × 14 = −42
Write the letters in the right order
Answer:
10.(−0.9) × (−3) + 0.95 =
Answer:
11.(−0.8) × (−2) + 0.33 =
Answer:

13.A lake changes by −9 cm a day for 2 days, then +5 cm a day for 5 days. What is the total change in cm?
Working:
Answer:
14.A kiosk sells 25 items at $6 profit each; 9 more expire at a $4 loss each. With profit positive, what is the overall result, in dollars?
Working:
Answer:
15.Right +4, wrong −1, blank 0. 10 right, 11 wrong, 5 blank: gained, lost, in all.
Fill in each blank
Working:
Answer:
16.In a game, the energy is x² − xy. If x = −6 and y = −6, what is the energy?
Working:
Answer:
17.Against a standard of 130 g, five apples differ by −7, +2, −10, +30, 0 (in g). What is their mean weight in g?
Working:
Answer:
18.Fahrenheit to Celsius: C = (F − 32) × 59. What is +41°F in °C?
Working:
Answer:

Show the answers and working

The four operations mixed worksheet: Answers and working

1. −8
Multiply before adding; don't add first, left to right: 6 × (+2) = 12; adding −20 then gives −8.
2. 54
Multiply before adding: (−3) × 2 = −6, and 60 + (−6) = 54.
3. −69
Multiply before adding; don't add first, left to right: 9 × (−6) = −54; adding −15 then gives −69.
4. 8
Multiply before adding: (−5) × 6 = −30, and 38 + (−30) = 8.
5. 1
The bracket first: −11 + 10 = −1. Then square: (−1)² = 1.
6. 52, 52, 0
Split the positives and negatives, then combine: 29 + 23 = 52, 32 + 20 = 52, 52 + (−52) = 0.
7. A → C → B
The bracket first, then multiply, then add: −55.
8. 65, 35, 30
Split the positives and negatives, then combine: 30 + 35 = 65, 12 + 23 = 35, 65 + (−35) = 30.
9. A → C → B
The bracket first, then multiply, then add: −14.
10. 3.65
Multiply first: same signs give a positive, different signs a negative, and the size is 0.9 × 3. Then add 0.95: 3.65.
11. 1.93
Multiply first: same signs give a positive, different signs a negative, and the size is 0.8 × 2. Then add 0.33: 1.93.

12. True
3 − 18 is negative, and negative times negative is positive. Work it through and compare with 105.

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

13. 7 cm
2 × (−9) + 5 × 5 = (−18) + 25 = 7. A rise is positive and the sizes subtract; how far it moved in all isn't the total change.
14. 114 dollars
25 × 6 + 9 × (−4) = 114.
15. 40, 11, 29
10 × 4 + 11 × (−1) + 5 × 0 = 40 − 11 = 29. The blanks score nothing either way.
16. 0
(−6)² − (−6) × (−6) = 6² + 6 × (−6) = 0. Bracket a negative when you put it in.
17. 133 g
The differences add to 15; ÷ 5 gives 3: 130 + 3 = 133 g. The 0 is still an apple, so divide by 5.
18. 5°C
F − 32, in the bracket, comes first: 9; then times 59, without taking off 32 again: 9 × 59 = 5.

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