Comparing Fractions 3rd Grade Worksheet | Educational Resource - Free Printable

Problem: Comparing Fractions

The task involves comparing fractions and coloring them. Let's solve each part step by step.

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#### Part 1: Comparing Fractions

We need to compare the given fractions using `<`, `>`, or `=`. To do this, we can either:
1. Find a common denominator.
2. Convert the fractions to decimals.
3. Use cross-multiplication.

Let's solve each comparison:

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1. $\frac{2}{5} \_\_\_ \frac{2}{3}$

- Both fractions have the same numerator (2), so the fraction with the smaller denominator is larger.
- Since $5 > 3$, $\frac{2}{5} < \frac{2}{3}$.

Answer: $\frac{2}{5} < \frac{2}{3}$

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2. $\frac{3}{4} \_\_\_ \frac{1}{6}$

- Find a common denominator: The least common multiple (LCM) of 4 and 6 is 12.
- Convert the fractions:
- $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$
- $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
- Compare: $\frac{9}{12} > \frac{2}{12}$.

Answer: $\frac{3}{4} > \frac{1}{6}$

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3. $\frac{7}{8} \_\_\_ \frac{2}{6}$

- Simplify $\frac{2}{6}$: $\frac{2}{6} = \frac{1}{3}$.
- Find a common denominator: The LCM of 8 and 3 is 24.
- Convert the fractions:
- $\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}$
- $\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}$
- Compare: $\frac{21}{24} > \frac{8}{24}$.

Answer: $\frac{7}{8} > \frac{2}{6}$

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4. $\frac{2}{3} \_\_\_ \frac{1}{4}$

- Find a common denominator: The LCM of 3 and 4 is 12.
- Convert the fractions:
- $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
- Compare: $\frac{8}{12} > \frac{3}{12}$.

Answer: $\frac{2}{3} > \frac{1}{4}$

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5. $\frac{1}{5} \_\_\_ \frac{2}{8}$

- Simplify $\frac{2}{8}$: $\frac{2}{8} = \frac{1}{4}$.
- Find a common denominator: The LCM of 5 and 4 is 20.
- Convert the fractions:
- $\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$
- $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$
- Compare: $\frac{4}{20} < \frac{5}{20}$.

Answer: $\frac{1}{5} < \frac{2}{8}$

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6. $\frac{1}{4} \_\_\_ \frac{4}{6}$

- Simplify $\frac{4}{6}$: $\frac{4}{6} = \frac{2}{3}$.
- Find a common denominator: The LCM of 4 and 3 is 12.
- Convert the fractions:
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
- $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
- Compare: $\frac{3}{12} < \frac{8}{12}$.

Answer: $\frac{1}{4} < \frac{4}{6}$

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7. $\frac{1}{3} \_\_\_ \frac{3}{5}$

- Find a common denominator: The LCM of 3 and 5 is 15.
- Convert the fractions:
- $\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$
- $\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$
- Compare: $\frac{5}{15} < \frac{9}{15}$.

Answer: $\frac{1}{3} < \frac{3}{5}$

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8. $\frac{1}{8} \_\_\_ \frac{1}{4}$

- Both fractions have the same numerator (1), so the fraction with the smaller denominator is larger.
- Since $8 > 4$, $\frac{1}{8} < \frac{1}{4}$.

Answer: $\frac{1}{8} < \frac{1}{4}$

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9. $\frac{2}{3} \_\_\_ \frac{1}{8}$

- Find a common denominator: The LCM of 3 and 8 is 24.
- Convert the fractions:
- $\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}$
- $\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$
- Compare: $\frac{16}{24} > \frac{3}{24}$.

Answer: $\frac{2}{3} > \frac{1}{8}$

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#### Part 2: Coloring the Fractions

We need to color the given fractions in the provided boxes.

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10. $\frac{1}{6}$

- The box has 6 squares.
- Color 1 square out of 6.

Answer: Color 1 square.

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11. $\frac{1}{2}$

- The box has 6 squares.
- Color 3 squares out of 6 (since $\frac{1}{2} = \frac{3}{6}$).

Answer: Color 3 squares.

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12. $\frac{3}{4}$

- The box has 4 squares.
- Color 3 squares out of 4.

Answer: Color 3 squares.

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13. $\frac{1}{2}$

- The box has 2 squares.
- Color 1 square out of 2.

Answer: Color 1 square.

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Final Answers:

1. $\frac{2}{5} < \frac{2}{3}$
2. $\frac{3}{4} > \frac{1}{6}$
3. $\frac{7}{8} > \frac{2}{6}$
4. $\frac{2}{3} > \frac{1}{4}$
5. $\frac{1}{5} < \frac{2}{8}$
6. $\frac{1}{4} < \frac{4}{6}$
7. $\frac{1}{3} < \frac{3}{5}$
8. $\frac{1}{8} < \frac{1}{4}$
9. $\frac{2}{3} > \frac{1}{8}$

10. Color 1 square.
11. Color 3 squares.
12. Color 3 squares.
13. Color 1 square.

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. < \\
2. > \\
3. > \\
4. > \\
5. < \\
6. < \\
7. < \\
8. < \\
9. > \\
\text{Coloring: } 1, 3, 3, 1
\end{array}
}
\]