When two fractions have the same denominator, the pieces are the same size. Comparing them is like comparing 3 apples with 5 apples.
Why it works
Eighths are all the same size. So $\frac{3}{8}$ is 3 of them and $\frac{5}{8}$ is 5 of them. Five pieces of the same size are more than three. On the number line, $\frac{5}{8}$ is two jumps farther from 0.
Key idea
Same denominator: compare the numerators. More pieces of the same size is more. ($>$ means "is greater than," $<$ means "is less than.")
Worked example: Use a symbol
Compare $\frac{3}{8}$ and $\frac{5}{8}$.
- Both are eighths, so the pieces match.
- 3 pieces is fewer than 5 pieces.
Answer: $\frac{3}{8} < \frac{5}{8}$
Worked example: A story
Ana ran $\frac{3}{4}$ of a mile. Ben ran $\frac{2}{4}$ of a mile. Who ran farther?
- Both distances are in fourths of a mile.
- 3 fourths is more than 2 fourths.
Answer: Ana
Worked example: Order three
Put $\frac{4}{6}$, $\frac{1}{6}$ and $\frac{5}{6}$ in order from least to greatest.
- All are sixths, so compare the numerators: 1, 4, 5.
- On a number line they sit 1, 4 and 5 jumps from 0.
Answer: $\frac{1}{6}, \frac{4}{6}, \frac{5}{6}$
Common mistake
Comparing parts of different wholes. $\frac{1}{2}$ of a small pizza can be less than $\frac{1}{4}$ of a giant one. Comparing fractions only makes sense when they are parts of the same-size whole.