# Brackets (Parentheses)

*Brackets are symbols used in pairs to group things together.*

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 |

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.