Comparing Fractions Worksheet - Free Printable

The task involves comparing fractions and determining whether one fraction is greater than, less than, or equal to another. Below, I will explain the solution for each problem step by step.

General Approach:

1. Find a Common Denominator: If the denominators are different, convert both fractions to have the same denominator.
2. Compare Numerators: Once the denominators are the same, compare the numerators to determine which fraction is larger.
3. Simplify Fractions: If possible, simplify the fractions before comparing to make the process easier.

Detailed Solutions:

#### Column 1:
1. $\frac{1}{2} \quad ? \quad \frac{1}{3}$
- Compare directly: $\frac{1}{2} > \frac{1}{3}$ because the numerator is the same, but the denominator of $\frac{1}{2}$ is smaller.
- Answer: $>$

2. $\frac{1}{5} \quad ? \quad \frac{1}{4}$
- Compare directly: $\frac{1}{5} < \frac{1}{4}$ because the numerator is the same, but the denominator of $\frac{1}{5}$ is larger.
- Answer: $<$

3. $\frac{1}{3} \quad ? \quad \frac{1}{10}$
- Compare directly: $\frac{1}{3} > \frac{1}{10}$ because the numerator is the same, but the denominator of $\frac{1}{3}$ is smaller.
- Answer: $>$

4. $\frac{2}{4} \quad ? \quad \frac{1}{2}$
- Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
- $\frac{1}{2} = \frac{1}{2}$.
- Answer: $=$

5. $\frac{2}{5} \quad ? \quad \frac{1}{5}$
- Compare directly: $\frac{2}{5} > \frac{1}{5}$ because the denominators are the same, but the numerator of $\frac{2}{5}$ is larger.
- Answer: $>$

6. $\frac{2}{9} \quad ? \quad \frac{5}{9}$
- Compare directly: $\frac{2}{9} < \frac{5}{9}$ because the denominators are the same, but the numerator of $\frac{2}{9}$ is smaller.
- Answer: $<$

7. $\frac{3}{10} \quad ? \quad \frac{3}{10}$
- Compare directly: $\frac{3}{10} = \frac{3}{10}$.
- Answer: $=$

8. $\frac{1}{2} \quad ? \quad \frac{1}{5}$
- Compare directly: $\frac{1}{2} > \frac{1}{5}$ because the numerator is the same, but the denominator of $\frac{1}{2}$ is smaller.
- Answer: $>$

9. $\frac{2}{7} \quad ? \quad \frac{2}{5}$
- Compare directly: $\frac{2}{7} < \frac{2}{5}$ because the numerator is the same, but the denominator of $\frac{2}{7}$ is larger.
- Answer: $<$

10. $\frac{5}{10} \quad ? \quad \frac{1}{2}$
- Simplify $\frac{5}{10}$ to $\frac{1}{2}$.
- $\frac{1}{2} = \frac{1}{2}$.
- Answer: $=$

11. $\frac{4}{9} \quad ? \quad \frac{2}{9}$
- Compare directly: $\frac{4}{9} > \frac{2}{9}$ because the denominators are the same, but the numerator of $\frac{4}{9}$ is larger.
- Answer: $>$

12. $\frac{1}{4} \quad ? \quad \frac{3}{4}$
- Compare directly: $\frac{1}{4} < \frac{3}{4}$ because the denominators are the same, but the numerator of $\frac{1}{4}$ is smaller.
- Answer: $<$

#### Column 2:
13. $\frac{1}{9} \quad ? \quad \frac{1}{8}$
- Compare directly: $\frac{1}{9} < \frac{1}{8}$ because the numerator is the same, but the denominator of $\frac{1}{9}$ is larger.
- Answer: $<$

14. $\frac{4}{10} \quad ? \quad \frac{7}{10}$
- Compare directly: $\frac{4}{10} < \frac{7}{10}$ because the denominators are the same, but the numerator of $\frac{4}{10}$ is smaller.
- Answer: $<$

15. $\frac{4}{8} \quad ? \quad \frac{1}{2}$
- Simplify $\frac{4}{8}$ to $\frac{1}{2}$.
- $\frac{1}{2} = \frac{1}{2}$.
- Answer: $=$

16. $\frac{2}{5} \quad ? \quad \frac{2}{9}$
- Compare directly: $\frac{2}{5} > \frac{2}{9}$ because the numerator is the same, but the denominator of $\frac{2}{5}$ is smaller.
- Answer: $>$

17. $\frac{1}{10} \quad ? \quad \frac{1}{4}$
- Compare directly: $\frac{1}{10} < \frac{1}{4}$ because the numerator is the same, but the denominator of $\frac{1}{10}$ is larger.
- Answer: $<$

18. $\frac{3}{8} \quad ? \quad \frac{5}{8}$
- Compare directly: $\frac{3}{8} < \frac{5}{8}$ because the denominators are the same, but the numerator of $\frac{3}{8}$ is smaller.
- Answer: $<$

19. $\frac{2}{4} \quad ? \quad \frac{3}{6}$
- Simplify $\frac{2}{4}$ to $\frac{1}{2}$ and $\frac{3}{6}$ to $\frac{1}{2}$.
- $\frac{1}{2} = \frac{1}{2}$.
- Answer: $=$

20. $\frac{2}{3} \quad ? \quad \frac{2}{5}$
- Compare directly: $\frac{2}{3} > \frac{2}{5}$ because the numerator is the same, but the denominator of $\frac{2}{3}$ is smaller.
- Answer: $>$

21. $\frac{7}{10} \quad ? \quad \frac{9}{10}$
- Compare directly: $\frac{7}{10} < \frac{9}{10}$ because the denominators are the same, but the numerator of $\frac{7}{10}$ is smaller.
- Answer: $<$

22. $\frac{4}{7} \quad ? \quad \frac{4}{5}$
- Compare directly: $\frac{4}{7} < \frac{4}{5}$ because the numerator is the same, but the denominator of $\frac{4}{7}$ is larger.
- Answer: $<$

23. $\frac{8}{9} \quad ? \quad \frac{5}{9}$
- Compare directly: $\frac{8}{9} > \frac{5}{9}$ because the denominators are the same, but the numerator of $\frac{8}{9}$ is larger.
- Answer: $>$

24. $\frac{1}{8} \quad ? \quad \frac{1}{6}$
- Compare directly: $\frac{1}{8} < \frac{1}{6}$ because the numerator is the same, but the denominator of $\frac{1}{8}$ is larger.
- Answer: $<$

Final Answer:

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