2
Parentheses and brackets change the answer
Discover Mathematics P5: Term 1, Unit 6, Lessons 1–4
GoalUse parentheses ( ) and brackets [ ] to change the order, and place them to make a target value.
New words
parentheses · the curved signs ( ) that tell us to work out what is inside firstbrackets · the square signs [ ] used outside parenthesesgrouping symbols · parentheses and brackets, which group part of an expression
Explanation
Grouping symbols say “do this first”. In (8 + 6) × 3 we add inside the parentheses first: 14 × 3 = 42. Without them, 8 + 6 × 3 = 26, so the symbols change the answer. When there are parentheses inside brackets, work from the inside out: parentheses first, then brackets, then the rest by the usual order. To place symbols for a target, try grouping different pairs of numbers and work out each result until you hit the target.
| Expression | Value |
|---|---|
| 8 + 6 × 3 | 26 |
| (8 + 6) × 3 | 42 |
Worked examples
| Expression | First step | Value |
|---|---|---|
| 8 + 6 × 3 | 6 × 3 = 18 | 26 |
| (8 + 6) × 3 | 8 + 6 = 14 | 42 |
| Step | Work | Result |
|---|---|---|
| 1 | 15 − 3 | 12 |
| 2 | 12 ÷ 4 | 3 |
| 3 | 3 + 5 | 8 |
| 4 | 2 × 8 | 16 |
Place parentheses in 7 + 3 × 4 − 2 to make 38. Try (7 + 3) × 4 − 2: 10 × 4 = 40 and 40 − 2 = 38. It works.
Class activity
Parentheses puzzle. Write 3 + 4 × 5 − 2 on paper and find as many different values as you can by putting ( ) in different places (for example (3 + 4) × 5 − 2 = 33 and 3 + 4 × (5 − 2) = 15). Write each version and its value in a list.
Practice
1
Work out (12 − 4) × 5.
8 × 5 = 40.
2
Work out 60 ÷ (2 + 3).
60 ÷ 5 = 12.
3
Work out [20 − (3 + 2)] × 2.
3 + 2 = 5; 20 − 5 = 15; 15 × 2 = 30.
4
Place parentheses in 2 + 3 × 5 + 1 to make 26.
(2 + 3) × 5 + 1 = 5 × 5 + 1 = 26.
5
Work out 3 × (2.5 + 1.5).
2.5 + 1.5 = 4 and 3 × 4 = 12.