Comparing Fractions (J) Worksheet for 5th Grade | Lesson Planet - Free Printable

To solve the problem of comparing fractions, we need to determine whether each pair of fractions is equal or which one is greater. Here's how we can approach each comparison step by step:

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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. Use Inequality or Equal Sign: Based on the comparison, use `<`, `>`, or `=` to indicate the relationship.

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Solutions:

#### A. \( \frac{4}{9} \) vs. \( \frac{5}{6} \)
- Find the least common denominator (LCD) of 9 and 6, which is 18.
- Convert each fraction:
\[
\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}
\]
\[
\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}
\]
- Compare the numerators: \( 8 < 15 \).
- Therefore, \( \frac{4}{9} < \frac{5}{6} \).

#### B. \( \frac{2}{5} \) vs. \( \frac{3}{6} \)
- Simplify \( \frac{3}{6} \):
\[
\frac{3}{6} = \frac{1}{2}
\]
- Find the LCD of 5 and 2, which is 10.
- Convert each fraction:
\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\]
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
- Compare the numerators: \( 4 < 5 \).
- Therefore, \( \frac{2}{5} < \frac{3}{6} \).

#### C. \( \frac{3}{7} \) vs. \( \frac{4}{8} \)
- Simplify \( \frac{4}{8} \):
\[
\frac{4}{8} = \frac{1}{2}
\]
- Find the LCD of 7 and 2, which is 14.
- Convert each fraction:
\[
\frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14}
\]
\[
\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
\]
- Compare the numerators: \( 6 < 7 \).
- Therefore, \( \frac{3}{7} < \frac{4}{8} \).

#### D. \( \frac{5}{8} \) vs. \( \frac{3}{4} \)
- Find the LCD of 8 and 4, which is 8.
- Convert each fraction:
\[
\frac{5}{8} = \frac{5}{8}
\]
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]
- Compare the numerators: \( 5 < 6 \).
- Therefore, \( \frac{5}{8} < \frac{3}{4} \).

#### E. \( \frac{3}{6} \) vs. \( \frac{2}{4} \)
- Simplify both fractions:
\[
\frac{3}{6} = \frac{1}{2}, \quad \frac{2}{4} = \frac{1}{2}
\]
- Both fractions are equal.
- Therefore, \( \frac{3}{6} = \frac{2}{4} \).

#### F. \( \frac{3}{9} \) vs. \( \frac{2}{6} \)
- Simplify both fractions:
\[
\frac{3}{9} = \frac{1}{3}, \quad \frac{2}{6} = \frac{1}{3}
\]
- Both fractions are equal.
- Therefore, \( \frac{3}{9} = \frac{2}{6} \).

#### G. \( \frac{2}{5} \) vs. \( \frac{1}{2} \)
- Find the LCD of 5 and 2, which is 10.
- Convert each fraction:
\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\]
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
- Compare the numerators: \( 4 < 5 \).
- Therefore, \( \frac{2}{5} < \frac{1}{2} \).

#### H. \( \frac{1}{2} \) vs. \( \frac{2}{3} \)
- Find the LCD of 2 and 3, which is 6.
- Convert each fraction:
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
- Compare the numerators: \( 3 < 4 \).
- Therefore, \( \frac{1}{2} < \frac{2}{3} \).

#### I. \( \frac{1}{3} \) vs. \( \frac{1}{2} \)
- Find the LCD of 3 and 2, which is 6.
- Convert each fraction:
\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\]
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
- Compare the numerators: \( 2 < 3 \).
- Therefore, \( \frac{1}{3} < \frac{1}{2} \).

#### J. \( \frac{1}{3} \) vs. \( \frac{2}{6} \)
- Simplify \( \frac{2}{6} \):
\[
\frac{2}{6} = \frac{1}{3}
\]
- Both fractions are equal.
- Therefore, \( \frac{1}{3} = \frac{2}{6} \).

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Final Answers:

\[
\boxed{
\begin{aligned}
&\text{A. } \frac{4}{9} < \frac{5}{6} \\
&\text{B. } \frac{2}{5} < \frac{3}{6} \\
&\text{C. } \frac{3}{7} < \frac{4}{8} \\
&\text{D. } \frac{5}{8} < \frac{3}{4} \\
&\text{E. } \frac{3}{6} = \frac{2}{4} \\
&\text{F. } \frac{3}{9} = \frac{2}{6} \\
&\text{G. } \frac{2}{5} < \frac{1}{2} \\
&\text{H. } \frac{1}{2} < \frac{2}{3} \\
&\text{I. } \frac{1}{3} < \frac{1}{2} \\
&\text{J. } \frac{1}{3} = \frac{2}{6}
\end{aligned}
}
\]