Comparing Fractions Worksheet - Free Printable

To solve the problem of comparing fractions, we need to determine whether one fraction is greater than (>), less than (<), or equal to (=) another fraction. Here's a step-by-step explanation of how to compare fractions:

Steps to Compare Fractions:

1. Same Denominator: If the denominators are the same, compare the numerators directly.
- Example: $\frac{3}{5} > \frac{2}{5}$ because $3 > 2$.

2. Same Numerator: If the numerators are the same, compare the denominators inversely.
- Example: $\frac{1}{3} > \frac{1}{4}$ because $3 < 4$ (smaller denominator means larger fraction).

3. Different Numerators and Denominators: Find a common denominator or convert the fractions to decimals to compare them.
- Example: To compare $\frac{2}{3}$ and $\frac{3}{4}$, find a common denominator (12):
- $\frac{2}{3} = \frac{8}{12}$
- $\frac{3}{4} = \frac{9}{12}$
- Since $\frac{8}{12} < \frac{9}{12}$, $\frac{2}{3} < \frac{3}{4}$.

Solving Each Problem:

Let's go through each pair of fractions and determine the correct symbol.

#### 1. $\frac{1}{2} \quad ? \quad \frac{1}{3}$
- Same numerator (1), compare denominators: $2 < 3$.
- Therefore, $\frac{1}{2} > \frac{1}{3}$.

#### 2. $\frac{1}{5} \quad ? \quad \frac{1}{4}$
- Same numerator (1), compare denominators: $5 > 4$.
- Therefore, $\frac{1}{5} < \frac{1}{4}$.

#### 3. $\frac{1}{3} \quad ? \quad \frac{1}{10}$
- Same numerator (1), compare denominators: $3 < 10$.
- Therefore, $\frac{1}{3} > \frac{1}{10}$.

#### 4. $\frac{2}{4} \quad ? \quad \frac{1}{2}$
- Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
- Therefore, $\frac{2}{4} = \frac{1}{2}$.

#### 5. $\frac{2}{5} \quad ? \quad \frac{1}{5}$
- Same denominator (5), compare numerators: $2 > 1$.
- Therefore, $\frac{2}{5} > \frac{1}{5}$.

#### 6. $\frac{2}{9} \quad ? \quad \frac{5}{9}$
- Same denominator (9), compare numerators: $2 < 5$.
- Therefore, $\frac{2}{9} < \frac{5}{9}$.

#### 7. $\frac{3}{10} \quad ? \quad \frac{3}{10}$
- Same numerator and denominator.
- Therefore, $\frac{3}{10} = \frac{3}{10}$.

#### 8. $\frac{1}{2} \quad ? \quad \frac{1}{5}$
- Same numerator (1), compare denominators: $2 < 5$.
- Therefore, $\frac{1}{2} > \frac{1}{5}$.

#### 9. $\frac{2}{7} \quad ? \quad \frac{2}{5}$
- Same numerator (2), compare denominators: $7 > 5$.
- Therefore, $\frac{2}{7} < \frac{2}{5}$.

#### 10. $\frac{5}{10} \quad ? \quad \frac{1}{2}$
- Simplify $\frac{5}{10}$ to $\frac{1}{2}$.
- Therefore, $\frac{5}{10} = \frac{1}{2}$.

#### 11. $\frac{4}{9} \quad ? \quad \frac{2}{9}$
- Same denominator (9), compare numerators: $4 > 2$.
- Therefore, $\frac{4}{9} > \frac{2}{9}$.

#### 12. $\frac{1}{4} \quad ? \quad \frac{3}{4}$
- Same denominator (4), compare numerators: $1 < 3$.
- Therefore, $\frac{1}{4} < \frac{3}{4}$.

#### 13. $\frac{1}{9} \quad ? \quad \frac{1}{8}$
- Same numerator (1), compare denominators: $9 > 8$.
- Therefore, $\frac{1}{9} < \frac{1}{8}$.

#### 14. $\frac{4}{10} \quad ? \quad \frac{7}{10}$
- Same denominator (10), compare numerators: $4 < 7$.
- Therefore, $\frac{4}{10} < \frac{7}{10}$.

#### 15. $\frac{4}{8} \quad ? \quad \frac{1}{2}$
- Simplify $\frac{4}{8}$ to $\frac{1}{2}$.
- Therefore, $\frac{4}{8} = \frac{1}{2}$.

#### 16. $\frac{2}{5} \quad ? \quad \frac{2}{9}$
- Same numerator (2), compare denominators: $5 < 9$.
- Therefore, $\frac{2}{5} > \frac{2}{9}$.

#### 17. $\frac{1}{10} \quad ? \quad \frac{1}{4}$
- Same numerator (1), compare denominators: $10 > 4$.
- Therefore, $\frac{1}{10} < \frac{1}{4}$.

#### 18. $\frac{3}{8} \quad ? \quad \frac{5}{8}$
- Same denominator (8), compare numerators: $3 < 5$.
- Therefore, $\frac{3}{8} < \frac{5}{8}$.

#### 19. $\frac{2}{4} \quad ? \quad \frac{3}{6}$
- Simplify $\frac{2}{4}$ to $\frac{1}{2}$ and $\frac{3}{6}$ to $\frac{1}{2}$.
- Therefore, $\frac{2}{4} = \frac{3}{6}$.

#### 20. $\frac{2}{3} \quad ? \quad \frac{2}{5}$
- Same numerator (2), compare denominators: $3 < 5$.
- Therefore, $\frac{2}{3} > \frac{2}{5}$.

#### 21. $\frac{7}{10} \quad ? \quad \frac{9}{10}$
- Same denominator (10), compare numerators: $7 < 9$.
- Therefore, $\frac{7}{10} < \frac{9}{10}$.

#### 22. $\frac{4}{7} \quad ? \quad \frac{4}{5}$
- Same numerator (4), compare denominators: $7 > 5$.
- Therefore, $\frac{4}{7} < \frac{4}{5}$.

#### 23. $\frac{8}{9} \quad ? \quad \frac{5}{9}$
- Same denominator (9), compare numerators: $8 > 5$.
- Therefore, $\frac{8}{9} > \frac{5}{9}$.

#### 24. $\frac{1}{8} \quad ? \quad \frac{1}{6}$
- Same numerator (1), compare denominators: $8 > 6$.
- Therefore, $\frac{1}{8} < \frac{1}{6}$.

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & \frac{1}{2} > \frac{1}{3} \\
2) & \frac{1}{5} < \frac{1}{4} \\
3) & \frac{1}{3} > \frac{1}{10} \\
4) & \frac{2}{4} = \frac{1}{2} \\
5) & \frac{2}{5} > \frac{1}{5} \\
6) & \frac{2}{9} < \frac{5}{9} \\
7) & \frac{3}{10} = \frac{3}{10} \\
8) & \frac{1}{2} > \frac{1}{5} \\
9) & \frac{2}{7} < \frac{2}{5} \\
10) & \frac{5}{10} = \frac{1}{2} \\
11) & \frac{4}{9} > \frac{2}{9} \\
12) & \frac{1}{4} < \frac{3}{4} \\
13) & \frac{1}{9} < \frac{1}{8} \\
14) & \frac{4}{10} < \frac{7}{10} \\
15) & \frac{4}{8} = \frac{1}{2} \\
16) & \frac{2}{5} > \frac{2}{9} \\
17) & \frac{1}{10} < \frac{1}{4} \\
18) & \frac{3}{8} < \frac{5}{8} \\
19) & \frac{2}{4} = \frac{3}{6} \\
20) & \frac{2}{3} > \frac{2}{5} \\
21) & \frac{7}{10} < \frac{9}{10} \\
22) & \frac{4}{7} < \frac{4}{5} \\
23) & \frac{8}{9} > \frac{5}{9} \\
24) & \frac{1}{8} < \frac{1}{6} \\
\end{array}
}
\]