# Fractions add and subtract

### Concepts

- You can add or subtract fractions as long as both fractions have the same denominator.
- If they do not have the same denominator, you have to make them have the same denominator.

### Theory

1/4 + 2/3 = 3/12 + 8/12 = 11/12.

In steps this is:

- 1x3/4x3 + 2x4/3x4
- => 3/12 + 8/12
- => 11/12

It’s good to reenforce that when numerators and denominators are both multiplied by the same number, the original fraction does not change. It’s easy to explain this using the pizza example again. Slice the pizza in 4 parts or 8 parts, it does not matter - 1/4 is the same as 2/8. You know, pizza satisfaction-wise.

### Common Misconceptions

- Directly adding the numerators, and adding the denominators. So 1/4 + 2/3 = 3/7. Nope!
- Not being able to recognise that 9 is fraction too - 9/1.
- 9 + 35/6

- Adding instead of subtracting, and vice versa. Yes, we’ve all been there.