Adding and Subtracting Fractions

When we add or subtract fractions, the most important thing to look at is the denominator (the bottom number). The denominator tells us the size of the pieces. If the denominators are the same, it means all the pieces are the identical size! Because the size doesn't change when we put pieces together, the denominator stays the same in our answer. We only add or subtract the numerators (the top numbers), which tell us how many pieces we have. Think of it like counting apples: 2 apples + 3 apples = 5 apples. In fractions: 2 sixths + 3 sixths = 5 sixths.

Subtracting fractions works exactly like addition, but we are separating parts instead of joining them. As long as the denominators match, we simply subtract the second numerator from the first. Imagine you have a juice box that is $\frac{5}{8}$ full. If you drink $\frac{2}{8}$ of the total box, you are just taking 2 of those 8 pieces away. The size of the 'eighths' hasn't changed, only the number of them you have left.

Sometimes you start with a whole object. In fractions, a 'whole' is any fraction where the numerator and denominator are the same, like $\frac{4}{4}$ or $\frac{8}{8}$. If a word problem says you have 'one whole pie' and you eat $\frac{1}{8}$, you should turn that '1' into a fraction like $\frac{8}{8}$ so the denominators match. This makes subtracting easy!