Comparing and Ordering Fractions - Worksheet | Math 2nd Grade - Free Printable

Problem: Comparing Fractions Worksheet

The task is to compare the given fractions using the symbols > (greater than) and < (less than). Additionally, shading diagrams can be used to help visualize the comparisons.

Solution:

#### 1. Compare \( \frac{1}{4} \) and \( \frac{3}{4} \)

- Fractions: \( \frac{1}{4} \) and \( \frac{3}{4} \)
- Comparison: Both fractions have the same denominator (4). When the denominators are the same, the fraction with the larger numerator is greater.
- Here, \( 3 > 1 \), so \( \frac{3}{4} > \frac{1}{4} \).
- Answer: \( \frac{1}{4} < \frac{3}{4} \)

#### 2. Compare \( \frac{4}{5} \) and \( \frac{2}{5} \)

- Fractions: \( \frac{4}{5} \) and \( \frac{2}{5} \)
- Comparison: Both fractions have the same denominator (5). The fraction with the larger numerator is greater.
- Here, \( 4 > 2 \), so \( \frac{4}{5} > \frac{2}{5} \).
- Answer: \( \frac{4}{5} > \frac{2}{5} \)

#### 3. Compare \( \frac{7}{8} \) and \( \frac{5}{8} \)

- Fractions: \( \frac{7}{8} \) and \( \frac{5}{8} \)
- Comparison: Both fractions have the same denominator (8). The fraction with the larger numerator is greater.
- Here, \( 7 > 5 \), so \( \frac{7}{8} > \frac{5}{8} \).
- Answer: \( \frac{7}{8} > \frac{5}{8} \)

#### 4. Compare \( \frac{1}{6} \) and \( \frac{3}{6} \)

- Fractions: \( \frac{1}{6} \) and \( \frac{3}{6} \)
- Comparison: Both fractions have the same denominator (6). The fraction with the larger numerator is greater.
- Here, \( 3 > 1 \), so \( \frac{3}{6} > \frac{1}{6} \).
- Answer: \( \frac{1}{6} < \frac{3}{6} \)

#### 5. Compare \( \frac{5}{10} \) and \( \frac{8}{10} \)

- Fractions: \( \frac{5}{10} \) and \( \frac{8}{10} \)
- Comparison: Both fractions have the same denominator (10). The fraction with the larger numerator is greater.
- Here, \( 8 > 5 \), so \( \frac{8}{10} > \frac{5}{10} \).
- Answer: \( \frac{5}{10} < \frac{8}{10} \)

#### 6. Compare \( \frac{9}{12} \) and \( \frac{3}{12} \)

- Fractions: \( \frac{9}{12} \) and \( \frac{3}{12} \)
- Comparison: Both fractions have the same denominator (12). The fraction with the larger numerator is greater.
- Here, \( 9 > 3 \), so \( \frac{9}{12} > \frac{3}{12} \).
- Answer: \( \frac{9}{12} > \frac{3}{12} \)

Final Answers:

1. \( \frac{1}{4} < \frac{3}{4} \)
2. \( \frac{4}{5} > \frac{2}{5} \)
3. \( \frac{7}{8} > \frac{5}{8} \)
4. \( \frac{1}{6} < \frac{3}{6} \)
5. \( \frac{5}{10} < \frac{8}{10} \)
6. \( \frac{9}{12} > \frac{3}{12} \)

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
1. & \quad \frac{1}{4} < \frac{3}{4} \\
2. & \quad \frac{4}{5} > \frac{2}{5} \\
3. & \quad \frac{7}{8} > \frac{5}{8} \\
4. & \quad \frac{1}{6} < \frac{3}{6} \\
5. & \quad \frac{5}{10} < \frac{8}{10} \\
6. & \quad \frac{9}{12} > \frac{3}{12}
\end{aligned}
}
\]