Comparing Fractions Worksheets - Free Printable

To solve the problem of comparing fractions using the pie models, we need to analyze each pair of fractions and determine whether one is greater than (>), less than (<), or equal to (=) the other. Here's a step-by-step explanation:

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Step 1: Understand the Pie Models

Each pie model represents a fraction. The whole circle represents "1," and the shaded portion represents the numerator of the fraction. The denominator tells us how many equal parts the circle is divided into.

For example:
- If a circle is divided into 4 equal parts and 3 parts are shaded, the fraction is \( \frac{3}{4} \).

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Step 2: Compare Each Pair of Fractions

We will compare each pair of fractions by analyzing their numerators and denominators, as well as their visual representations in the pie models.

#### Row 1:
1. Left: \( \frac{3}{4} \)
- The circle is divided into 4 parts, and 3 parts are shaded.
2. Right: \( \frac{1}{2} \)
- The circle is divided into 2 parts, and 1 part is shaded.
3. Comparison:
- \( \frac{3}{4} \) is larger than \( \frac{1}{2} \) because \( \frac{3}{4} = 0.75 \) and \( \frac{1}{2} = 0.5 \).
- Answer: \( > \)

#### Row 2:
1. Left: \( \frac{1}{3} \)
- The circle is divided into 3 parts, and 1 part is shaded.
2. Right: \( \frac{1}{4} \)
- The circle is divided into 4 parts, and 1 part is shaded.
3. Comparison:
- \( \frac{1}{3} \) is larger than \( \frac{1}{4} \) because \( \frac{1}{3} \approx 0.333 \) and \( \frac{1}{4} = 0.25 \).
- Answer: \( > \)

#### Row 3:
1. Left: \( \frac{2}{5} \)
- The circle is divided into 5 parts, and 2 parts are shaded.
2. Right: \( \frac{1}{2} \)
- The circle is divided into 2 parts, and 1 part is shaded.
3. Comparison:
- \( \frac{2}{5} = 0.4 \) and \( \frac{1}{2} = 0.5 \).
- \( \frac{2}{5} \) is smaller than \( \frac{1}{2} \).
- Answer: \( < \)

#### Row 4:
1. Left: \( \frac{3}{8} \)
- The circle is divided into 8 parts, and 3 parts are shaded.
2. Right: \( \frac{1}{4} \)
- The circle is divided into 4 parts, and 1 part is shaded.
3. Comparison:
- \( \frac{3}{8} = 0.375 \) and \( \frac{1}{4} = 0.25 \).
- \( \frac{3}{8} \) is larger than \( \frac{1}{4} \).
- Answer: \( > \)

#### Row 5:
1. Left: \( \frac{5}{6} \)
- The circle is divided into 6 parts, and 5 parts are shaded.
2. Right: \( \frac{7}{8} \)
- The circle is divided into 8 parts, and 7 parts are shaded.
3. Comparison:
- \( \frac{5}{6} \approx 0.833 \) and \( \frac{7}{8} = 0.875 \).
- \( \frac{5}{6} \) is smaller than \( \frac{7}{8} \).
- Answer: \( < \)

#### Row 6:
1. Left: \( \frac{3}{5} \)
- The circle is divided into 5 parts, and 3 parts are shaded.
2. Right: \( \frac{2}{3} \)
- The circle is divided into 3 parts, and 2 parts are shaded.
3. Comparison:
- \( \frac{3}{5} = 0.6 \) and \( \frac{2}{3} \approx 0.667 \).
- \( \frac{3}{5} \) is smaller than \( \frac{2}{3} \).
- Answer: \( < \)

#### Row 7:
1. Left: \( \frac{7}{10} \)
- The circle is divided into 10 parts, and 7 parts are shaded.
2. Right: \( \frac{3}{4} \)
- The circle is divided into 4 parts, and 3 parts are shaded.
3. Comparison:
- \( \frac{7}{10} = 0.7 \) and \( \frac{3}{4} = 0.75 \).
- \( \frac{7}{10} \) is smaller than \( \frac{3}{4} \).
- Answer: \( < \)

#### Row 8:
1. Left: \( \frac{5}{8} \)
- The circle is divided into 8 parts, and 5 parts are shaded.
2. Right: \( \frac{3}{5} \)
- The circle is divided into 5 parts, and 3 parts are shaded.
3. Comparison:
- \( \frac{5}{8} = 0.625 \) and \( \frac{3}{5} = 0.6 \).
- \( \frac{5}{8} \) is larger than \( \frac{3}{5} \).
- Answer: \( > \)

#### Row 9:
1. Left: \( \frac{4}{5} \)
- The circle is divided into 5 parts, and 4 parts are shaded.
2. Right: \( \frac{7}{8} \)
- The circle is divided into 8 parts, and 7 parts are shaded.
3. Comparison:
- \( \frac{4}{5} = 0.8 \) and \( \frac{7}{8} = 0.875 \).
- \( \frac{4}{5} \) is smaller than \( \frac{7}{8} \).
- Answer: \( < \)

#### Row 10:
1. Left: \( \frac{5}{6} \)
- The circle is divided into 6 parts, and 5 parts are shaded.
2. Right: \( \frac{3}{4} \)
- The circle is divided into 4 parts, and 3 parts are shaded.
3. Comparison:
- \( \frac{5}{6} \approx 0.833 \) and \( \frac{3}{4} = 0.75 \).
- \( \frac{5}{6} \) is larger than \( \frac{3}{4} \).
- Answer: \( > \)

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Final Answers:

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

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Boxed Answer:

\[
\boxed{>, >, <, >, <, <, <, >, <, >}
\]