Numbers and operations · Ages 12–13

Brackets inside brackets worksheet

Part of: Working with 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.[24 − (12 − 8)] × 2 =
Answer:
2.131 − [9 + (9 − 3) × 2] = 131 − [9 + × 2] = 131 − [9 + ] = 131 − =
Fill in each blank
Answer:
3.Work out 142 − [7 + (6 − 1) × 2]. Put the steps in order.
- A. 7 + 10 = 17
- B. 6 − 1 = 5
- C. 5 × 2 = 10
- D. 142 − 17 = 125
Write the letters in the right order
Answer:
4.5 × ｛29 − [9 + (8 − 1)]｝ ÷ 5 =
Answer:
5.Work out ｛7 + [3 × (14 − 4) − 16] ÷ 2｝ × 6: the round brackets come to , the square brackets to , the braces to , and the whole to .
Fill in each blank
Answer:
6.Work out ｛12 + [3 × (15 − 3) − 20] ÷ 4｝ × 2: the round brackets come to , the square brackets to , the braces to , and the whole to .
Fill in each blank
Answer:
7.5 × ｛26 − [2 + (10 − 4)]｝ ÷ 5 =
Answer:

8.72 − (11 + 8) = 53
True or false?
Answer:
9.13 + 4 × (17 − 1) ÷ 2 = ?
- A. 77
- B. 141
- C. 45
- D. 136
Choose the right answer
Answer:
10.92 − (15 + 8) = 85
True or false?
Answer:
11.45 − [17 − (12 − 4)] = ?
- A. 44
- B. 36
- C. 20
- D. 12
Choose the right answer
Answer:
12.59 − [26 − (11 − 2)] = ?
- A. 24
- B. 20
- C. 46
- D. 42
Choose the right answer
Answer:

13.Ballpoint pens come 12 to a box for $45, or $7 each loose. Ka-lok buys 4 boxes and 4 loose pens. What is the average cost of a pen?
Working:
Answer:
14.Chi-keung has 75 sweets, gives 19 to a little brother, splits the rest into 2 equal shares and keeps one; then Mum gives him 3 more. In (75 − 19) ÷ 2 + 3: the brackets make , ÷ 2 gives , and Chi-keung ends with sweets.
Fill in each blank
Working:
Answer:
15.Ka-yan has $100, buys 3 notebooks at $12 each and a pencil case for $36, then shares the money left equally among 4 younger brothers and sisters. How many dollars does each get?
Working:
Answer:
16.A bookshop shares 210 books equally over 5 bookcases, each with 3 shelves holding the same number. Then 6 more books go on each shelf. How many are on each shelf now?
Working:
Answer:
17.Cinema tickets cost $60 for an adult and $34 for a child. Tsz-ching's family buys 3 adult and 3 child tickets and pays $1,000. How much change should they get?
Working:
Answer:
18.Tsz-ching gets $120 pocket money a week, spends $12 a day and saves the rest. How much is saved after 3 weeks?
Working:
Answer:

Show the answers and working

Brackets inside brackets worksheet: Answers and working

1. 40
Inside out: (12 − 8) = 4, [24 − 4] = 20, 20 × 2 = 40.
2. 6, 12, 21, 110
Round brackets first, 9 − 3 = 6; times 2 is 12; then the square brackets, 9 + 12 = 21; last, 131 − 21 = 110.
3. B → C → A → D
Inside out: the round brackets, then inside the square ones (times before plus), and the subtraction outside last.
4. 13
Inside out: (8 − 1) = 7, [9 + 7] = 16, ｛29 − 16｝ = 13, and 5 × 13 ÷ 5 = 13.
5. 10, 14, 14, 84
Inside out, and inside each layer times and divide before plus and minus: (14 − 4) = 10; [3 × 10 − 16] = 14; ｛7 + 14 ÷ 2｝ = 14; 14 × 6 = 84.
6. 12, 16, 16, 32
Inside out, and inside each layer times and divide before plus and minus: (15 − 3) = 12; [3 × 12 − 20] = 16; ｛12 + 16 ÷ 4｝ = 16; 16 × 2 = 32.
7. 18
Inside out: (10 − 4) = 6, [2 + 6] = 8, ｛26 − 8｝ = 18, and 5 × 18 ÷ 5 = 18.

8. True
Taking away a bracket takes away everything in it: 72 − (11 + 8) = 72 − 11 − 8 = 53.
9. C. 45
Brackets first, 17 − 1; then times and divide from left to right, 4 × (17 − 1) ÷ 2; add 13 last: 45.
10. False
Taking away a bracket takes away everything in it: 92 − (15 + 8) = 92 − 15 − 8 = 69.
11. B. 36
Inside out: (12 − 4) = 8, [17 − 8] = 9, and 45 − 9 = 36.
12. D. 42
Inside out: (11 − 2) = 9, [26 − 9] = 17, and 59 − 17 = 42.

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

13. 4 dollars
As one calculation: (4 × 45 + 4 × 7) ÷ (4 × 12 + 4) = 4. Total cost over total pens, both brackets first.
14. 56, 28, 31
(75 − 19) = 56, 56 ÷ 2 = 28, 28 + 3 = 31.
15. 7 dollars
As one calculation: [100 − (3 × 12 + 36)] ÷ 4 = 7.
16. 20 books
As one calculation: 210 ÷ (5 × 3) + 6 = 20. There are 5 × 3 shelves, so the brackets come first.
17. 718 dollars
As one calculation: 1000 − (3 × 60 + 3 × 34) = 718. Work out the total in the brackets first.
18. 108 dollars
A week's spending is 7 × $12, so (120 − 7 × 12) × 3 = 108.

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