Working with numbers · Ages 12–13
Brackets inside brackets
Inside out: ( ) → [ ] → ｛ ｝.
How to do it
Method
Inside out: ( ) → [ ] → ｛ ｝
2 × [10 − (3 + 1)] = 2 × [10 − 4] = 2 × 6 = 12
Another way
Opening the brackets
20 − (5 + 3) = 20 − 5 − 3 = 12
In full
Inside out: the innermost round brackets ( ) first, then the square brackets [ ], then the braces ｛ ｝. Inside each, it is still times and divide before plus and minus, left to right at the same rank. 2 × [10 − (3 + 1)] = 2 × [10 − 4] = 2 × 6 = 12. Undo one layer a line and copy the rest, and nothing gets lost. Taking away a bracket takes away everything in it: 20 − (5 + 3) = 20 − 5 − 3 = 12.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
[22 − (13 − 8)] × 5 =
Show the answer and working
Answer: 85
Inside out: (13 − 8) = 5, [22 − 5] = 17, 17 × 5 = 85.
Example 2
64 − (7 + 8) = 49
True or false?
Show the answer and working
Answer: True
Taking away a bracket takes away everything in it: 64 − (7 + 8) = 64 − 7 − 8 = 49.
Example 3
Work out ｛8 + [3 × (13 − 2) − 15] ÷ 2｝ × 4: the round brackets come to , the square brackets to , the braces to , and the whole to .
Fill in each blank
Show the answer and working
Answer: 11, 18, 17, 68
Inside out, and inside each layer times and divide before plus and minus: (13 − 2) = 11; [3 × 11 − 15] = 18; ｛8 + 18 ÷ 2｝ = 17; 17 × 4 = 68.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.81 − [20 + (11 − 4) × 5] = 81 − [20 + × 5] = 81 − [20 + ] = 81 − =
Fill in each blank
Answer:
2.6 + 9 × (19 − 3) ÷ 2 = ?
- A. 150
- B. 120
- C. 78
- D. 294
Choose the right answer
Answer:
3.Work out 81 − [15 + (7 − 4) × 6]. Put the steps in order.
- A. 15 + 18 = 33
- B. 3 × 6 = 18
- C. 81 − 33 = 48
- D. 7 − 4 = 3
Write the letters in the right order
Answer:
4.3 × ｛56 − [4 + (12 − 3)]｝ ÷ 3 =
Answer:
5.Work out ｛9 + [5 × (11 − 4) − 1] ÷ 2｝ × 4: the round brackets come to , the square brackets to , the braces to , and the whole to .
Fill in each blank
Answer:
All the answers
- 1. 7, 35, 55, 26
- 2. C. 78
- 3. D → B → A → C
- 4. 43
- 5. 7, 34, 26, 104
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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