Comparing fractions with the same numerator worksheet for math practice.

Problem: Comparing Fractions with the Same Numerator

The task is to compare fractions where the numerators are the same and determine whether one fraction is greater than (>) or less than (<) the other. When comparing fractions with the same numerator, the fraction with the smaller denominator is larger because it represents a larger portion of the whole.

Solution:

#### Step-by-Step Explanation:

1. General Rule: When the numerators are the same, the fraction with the smaller denominator is larger.
- For example, $\frac{2}{3} > \frac{2}{4}$ because 3 is smaller than 4, making $\frac{2}{3}$ a larger portion.

2. Apply the Rule to Each Pair:
- Compare the denominators of each pair of fractions.
- If the first fraction has a smaller denominator, use the ">" symbol.
- If the second fraction has a smaller denominator, use the "<" symbol.

#### Detailed Comparisons:

1. $\frac{2}{9} \quad \square \quad \frac{2}{4}$
- Denominators: 9 and 4
- Since 9 > 4, $\frac{2}{9} < \frac{2}{4}$
- Answer: $<$

2. $\frac{2}{11} \quad \square \quad \frac{2}{8}$
- Denominators: 11 and 8
- Since 11 > 8, $\frac{2}{11} < \frac{2}{8}$
- Answer: $<$

3. $\frac{2}{9} \quad \square \quad \frac{2}{3}$
- Denominators: 9 and 3
- Since 9 > 3, $\frac{2}{9} < \frac{2}{3}$
- Answer: $<$

4. $\frac{5}{11} \quad \square \quad \frac{5}{9}$
- Denominators: 11 and 9
- Since 11 > 9, $\frac{5}{11} < \frac{5}{9}$
- Answer: $<$

5. $\frac{1}{8} \quad \square \quad \frac{1}{5}$
- Denominators: 8 and 5
- Since 8 > 5, $\frac{1}{8} < \frac{1}{5}$
- Answer: $<$

6. $\frac{1}{3} \quad \square \quad \frac{1}{8}$
- Denominators: 3 and 8
- Since 3 < 8, $\frac{1}{3} > \frac{1}{8}$
- Answer: $>$

7. $\frac{4}{7} \quad \square \quad \frac{4}{8}$
- Denominators: 7 and 8
- Since 7 < 8, $\frac{4}{7} > \frac{4}{8}$
- Answer: $>$

8. $\frac{1}{4} \quad \square \quad \frac{1}{3}$
- Denominators: 4 and 3
- Since 4 > 3, $\frac{1}{4} < \frac{1}{3}$
- Answer: $<$

9. $\frac{1}{12} \quad \square \quad \frac{1}{9}$
- Denominators: 12 and 9
- Since 12 > 9, $\frac{1}{12} < \frac{1}{9}$
- Answer: $<$

10. $\frac{2}{8} \quad \square \quad \frac{2}{3}$
- Denominators: 8 and 3
- Since 8 > 3, $\frac{2}{8} < \frac{2}{3}$
- Answer: $<$

11. $\frac{1}{5} \quad \square \quad \frac{1}{8}$
- Denominators: 5 and 8
- Since 5 < 8, $\frac{1}{5} > \frac{1}{8}$
- Answer: $>$

12. $\frac{4}{11} \quad \square \quad \frac{4}{10}$
- Denominators: 11 and 10
- Since 11 > 10, $\frac{4}{11} < \frac{4}{10}$
- Answer: $<$

13. $\frac{3}{11} \quad \square \quad \frac{3}{10}$
- Denominators: 11 and 10
- Since 11 > 10, $\frac{3}{11} < \frac{3}{10}$
- Answer: $<$

14. $\frac{9}{10} \quad \square \quad \frac{9}{12}$
- Denominators: 10 and 12
- Since 10 < 12, $\frac{9}{10} > \frac{9}{12}$
- Answer: $>$

15. $\frac{1}{7} \quad \square \quad \frac{1}{3}$
- Denominators: 7 and 3
- Since 7 > 3, $\frac{1}{7} < \frac{1}{3}$
- Answer: $<$

16. $\frac{6}{12} \quad \square \quad \frac{6}{9}$
- Denominators: 12 and 9
- Since 12 > 9, $\frac{6}{12} < \frac{6}{9}$
- Answer: $<$

Final Answers:

1. $<$
2. $<$
3. $<$
4. $<$
5. $<$
6. $>$
7. $>$
8. $<$
9. $<$
10. $<$
11. $>$
12. $<$
13. $<$
14. $>$
15. $<$
16. $<$

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & < \\
2. & < \\
3. & < \\
4. & < \\
5. & < \\
6. & > \\
7. & > \\
8. & < \\
9. & < \\
10. & < \\
11. & > \\
12. & < \\
13. & < \\
14. & > \\
15. & < \\
16. & <
\end{array}
}
\]