Brackets (Parentheses)

Brackets are symbols used in pairs to group things together.

brackets

Types of brackets include:

  • parentheses or "round brackets" ( )
  • "square brackets" or "box brackets" [ ]
  • braces or "curly brackets" { }
  • "angle brackets" < >
(Note: Angle brackets can be confusing as they
look like the "less than" and "greater than" signs)

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 it is good to 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