Comparing Fractions Worksheet - Free Printable

To compare fractions, we look at the numerators (top numbers) and denominators (bottom numbers).

Rule 1: Same Denominator
If the bottom numbers are the same, look at the top numbers. The fraction with the bigger top number is larger.
* Example: $\frac{3}{5}$ vs $\frac{1}{5}$. Since $3 > 1$, then $\frac{3}{5} > \frac{1}{5}$.

Rule 2: Same Numerator
If the top numbers are the same, look at the bottom numbers. The fraction with the *smaller* bottom number is actually larger (because the pieces are bigger).
* Example: $\frac{1}{2}$ vs $\frac{1}{4}$. Half of a pizza is bigger than a quarter of a pizza. So, $\frac{1}{2} > \frac{1}{4}$.

Rule 3: Different Numerators and Denominators
Sometimes it helps to simplify the fraction first or find a common denominator.
* Example: $\frac{2}{4}$ is the same as $\frac{1}{2}$.

Let's solve each problem step-by-step:

1) $\frac{1}{2}$ vs $\frac{1}{3}$: Same top number. 2 is smaller than 3, so halves are bigger than thirds. >
2) $\frac{1}{5}$ vs $\frac{1}{4}$: Same top number. 5 is bigger than 4, so fifths are smaller than fourths. <
3) $\frac{1}{3}$ vs $\frac{1}{10}$: Same top number. 3 is smaller than 10, so thirds are bigger. >
4) $\frac{2}{4}$ vs $\frac{1}{2}$: Simplify $\frac{2}{4}$ by dividing top and bottom by 2. It becomes $\frac{1}{2}$. They are equal. =
5) $\frac{2}{5}$ vs $\frac{1}{5}$: Same bottom number. 2 is bigger than 1. >
6) $\frac{2}{9}$ vs $\frac{5}{9}$: Same bottom number. 2 is smaller than 5. <
7) $\frac{3}{10}$ vs $\frac{3}{10}$: They are exactly the same. =
8) $\frac{1}{2}$ vs $\frac{1}{5}$: Same top number. 2 is smaller than 5, so halves are bigger. >
9) $\frac{2}{7}$ vs $\frac{2}{5}$: Same top number. 7 is bigger than 5, so sevenths are smaller pieces. <
10) $\frac{5}{10}$ vs $\frac{1}{2}$: Simplify $\frac{5}{10}$ by dividing by 5. It becomes $\frac{1}{2}$. They are equal. =
11) $\frac{4}{9}$ vs $\frac{2}{9}$: Same bottom number. 4 is bigger than 2. >
12) $\frac{1}{4}$ vs $\frac{3}{4}$: Same bottom number. 1 is smaller than 3. <
13) $\frac{1}{9}$ vs $\frac{1}{8}$: Same top number. 9 is bigger than 8, so ninths are smaller pieces. <
14) $\frac{4}{10}$ vs $\frac{7}{10}$: Same bottom number. 4 is smaller than 7. <
15) $\frac{4}{8}$ vs $\frac{1}{2}$: Simplify $\frac{4}{8}$ by dividing by 4. It becomes $\frac{1}{2}$. They are equal. =
16) $\frac{2}{5}$ vs $\frac{2}{9}$: Same top number. 5 is smaller than 9, so fifths are bigger pieces. >
17) $\frac{1}{10}$ vs $\frac{1}{4}$: Same top number. 10 is bigger than 4, so tenths are smaller pieces. <
18) $\frac{3}{8}$ vs $\frac{5}{8}$: Same bottom number. 3 is smaller than 5. <
19) $\frac{2}{4}$ vs $\frac{3}{6}$: Simplify both. $\frac{2}{4} = \frac{1}{2}$ and $\frac{3}{6} = \frac{1}{2}$. They are equal. =
20) $\frac{2}{3}$ vs $\frac{2}{5}$: Same top number. 3 is smaller than 5, so thirds are bigger. >
21) $\frac{7}{10}$ vs $\frac{9}{10}$: Same bottom number. 7 is smaller than 9. <
22) $\frac{4}{7}$ vs $\frac{4}{5}$: Same top number. 7 is bigger than 5, so sevenths are smaller pieces. <
23) $\frac{8}{9}$ vs $\frac{5}{9}$: Same bottom number. 8 is bigger than 5. >
24) $\frac{1}{8}$ vs $\frac{1}{6}$: Same top number. 8 is bigger than 6, so eighths are smaller pieces. <

Final Answer:
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3) >
4) =
5) >
6) <
7) =
8) >
9) <
10) =
11) >
12) <
13) <
14) <
15) =
16) >
17) <
18) <
19) =
20) >
21) <
22) <
23) >
24) <