# Arithmetic and mathematics¶

## Definition and syntax¶

The following symbols are used to do mathematics in Python. The symbols are known as operators because they perform operations on the numbers.

Symbol Meaning Example Result
`+` Addition `5 + 5` `10`
`-` Subtraction `10 - 3` `7`
`*` Multiplication `20 * 3` `60`
`/` Division `5 / 2` `2.5`
`//` Integer division (divides and rounds down) `15 % 6` `2`
`%` Modulus (gives the remainder after division) `15 % 6` `3`
`**` Exponent / Power of `5**2` `25`

Note

Notice in the examples how spaces can be used around mathematical operators to make code clearer.

## Easy example¶

```result = 15 + 5
```
Show/Hide Output
```No output is given from this code
```

Python does the calculation `15 + 5` and stores the result `20` in the variable `result`.

## Orders of precedence¶

Certain operations will be performed before others in Python. This is similar to how operations such as addition, multipication are carried out in mathematics. This is known as orders of precedence. You may know the term BIDMAS or BODMAS to remember the order.

The following table shows the orders of precedence. Operators at the top will be carried out before those underneath.

Operators Description
`(`, `)` Brackets / Parentheses
`**` Exponentiation / Power
`*`, `/`, `%`, `//` Multiplication, division, modulus, floor division
`+`, `-` Addition, subtraction
`<`, `<=`, `>`, `>=`, `!=`, `==` Comparison operators
`!=`, `==` Equality operators
`not`, `and`, `or` Boolean operators

## Examples¶

### Example 1 - Subtraction¶

```answer = 15 - 5
```
Show/Hide Output
```10
```

### Example 2 - Division¶

```answer = 15 / 6
```
Show/Hide Output
```2.5
```

### Example 3 - Brackets¶

```answer = 15 * (3 - 1)
answer2 = 15 * 3 - 1
```
Show/Hide Output
```30
44
```

### Example 4 - Integer division¶

```answer1 = 20 // 7
```
Show/Hide Output
```2
2
```

For `answer1 = 20 % 7`, `7` goes into `20` twice. Therefore `2` is stored in `answer1` then printed. This is integer division, so we do not store any fractions or decimal places. For `answer2 = 20 % 10`, `10` goes into `20` twice exactly. Therefore `2` is stored in `answer2` then printed.

### Example 5 - Modulus¶

```answer1 = 20 % 7
```
Show/Hide Output
```6
0
```

For `answer1 = 20 % 7`, `7` goes into `20` twice making `14`. The remainder from `20` is `6` which is stored in `answer1` then printed. For `answer2 = 20 % 10`, `10` goes into `20` twice exactly. The remainder is therefore `0` which is stored in `answer2` then printed.

### Example 6 - Exponent / Power¶

```answer = 3**2
```
Show/Hide Output
```9
```

3 to the power 2 = 9

### Example 7 - Orders of precedence - without brackets¶

```tempC = 37
tempF = tempC*9/5 + 32

print(tempF)
```
Show/Hide Output
```98.6
```

### Example 8 - Orders of precedence - with and without brackets¶

```answerA = 103 - 3 * 5 + 5
answerB = (103 - 3) * (5 + 5)

```93
The `*` symbol is produced by pressing `SHIFT-8`.