# 3. Arithmetic order errors

#### Not using arithmetic order properly

In maths, you should be familiar with the *order *of operations when working out a calculation (BODMAS)

```
20 + (1+5)/2 - 3*4
```

First work out the brackets, then multiply and divide, then add or subtract.

Let's look at some broken code (below). This code is to work out miles per gallon. It takes the starting and end mileage of the car and the amount of petrol used.

```
Line 30: startMiles = 20
Line 31: endMiles = 26
Line 32: petrolUsed = 2
Line 33: milesPerGallon = EndMiles - StartMiles/petrolUsed
```

In line 33, by slotting in the value of each variable, the miles per gallon value is going to be worked out as

milesPerGallon = 26 - 20/2

The answer produced by this code is 16, which is clearly wrong. This is because the order rules of maths say always divide before subtracting. The correct code in line 33 is

```
Line 33: milesPerGallon = (EndMiles - StartMiles)/petrolUsed
```

The brackets have been added to force it to work as intended.

**Challenge** see if you can find out one extra fact on this topic that we haven't
already told you

Click on this link: What are some examples of logic errors in programming?