Brackets (Parentheses)
Brackets are symbols used in pairs to group things together.
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Types of brackets include:
(Note: Angle brackets can be confusing as they |
When we see things inside brackets we do them first (as explained in Order of Operations).
Example: (3 + 2) × (6 − 4)
The parentheses group 3 and 2 together, and 6 and 4 together, so they get done first:
| (3 + 2) × (6 − 4) |
| = (5) × (2) |
| = 5×2 |
| = 10 |
Without the parentheses the multiplication is done first:
3 + 2 × 6 − 4
= 3 + 12 − 4
= 11 (not 10)
With more complicated grouping we can use different types of brackets:
Example: [(3 + 2) × (6 − 4) + 2] × 4
The parentheses group 3 and 2 together, and 6 and 4 together, and the square brackets tell us to do all the calculations inside them before multiplying by 4:
| [(3 + 2) × (6 − 4) + 2] × 4 |
| = [(5) × (2) + 2] × 4 |
| = [10 + 2] × 4 |
| = 12 × 4 |
| = 48 |
Curly Brackets
Curly brackets {} are used in Sets:
Example: {2, 4, 6, 8}
Is the set of even numbers from 2 to 8
Angle Brackets
Angle brackets 〈 〉 are used in Bra-Ket Notation.