Now the numerators match and the denominators differ, like $\frac{2}{3}$ and $\frac{2}{5}$. You have the same number of pieces, so the question is: whose pieces are bigger? Remember more parts means smaller parts.
Why it works
Both fractions take 2 pieces of the same whole. A whole cut into 3 parts has bigger parts than a whole cut into 5. Two big pieces are more than two small pieces. So $\frac{2}{3} > \frac{2}{5}$, even though 5 is bigger than 3.
Key idea
Same numerator: the fraction with the smaller denominator is greater, because its pieces are bigger.
Worked example: Use a symbol
Compare $\frac{2}{3}$ and $\frac{2}{5}$.
- 2 pieces each.
- Thirds are bigger than fifths.
Answer: $\frac{2}{3} > \frac{2}{5}$
Worked example: A story
Two pans of cornbread are the same size. Leo ate $\frac{3}{4}$ of one pan and Mia ate $\frac{3}{8}$ of the other. Who ate more?
- Both ate 3 pieces.
- Fourths are bigger pieces than eighths.
Answer: Leo
Common mistake
Picking the bigger denominator as larger. With whole numbers, 5 is more than 3. But in $\frac{2}{5}$ the 5 means fifths, small pieces. Check with circles or bars of the same size: two fifths covers less than two thirds.