Comparing Fractions Worksheet - Free Printable

It looks like you've uploaded an image of a completed worksheet titled *"Comparing Fractions Sheet 1 Answers"*, which shows the correct answers for comparing pairs of fractions using the symbols:
- `>` (greater than)
- `<` (less than)
- `=` (equal to)

Since this is an answer key, it already provides the solutions. However, I can help explain how to solve each type of problem and give a step-by-step method for comparing fractions.

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🔍 How to Compare Fractions

To compare two fractions, follow these steps:

#### ✔ Step 1: Check if they have the same denominator
- If yes → Compare numerators directly.
- Larger numerator = larger fraction.
- If no → Find a common denominator or use cross-multiplication.

#### ✔ Step 2: Use Cross-Multiplication (if denominators differ)
For fractions $\frac{a}{b}$ and $\frac{c}{d}$:
- Multiply $a \times d$ and $c \times b$
- Compare the results:
- If $a \times d > c \times b$, then $\frac{a}{b} > \frac{c}{d}$
- If $a \times d < c \times b$, then $\frac{a}{b} < \frac{c}{d}$
- If equal, then the fractions are equal.

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Let’s go through a few examples from your sheet to show how it works:

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📌 Example 1: $\frac{1}{2} \ ? \ \frac{1}{3}$

- Use cross-multiplication:
- $1 \times 3 = 3$
- $1 \times 2 = 2$
- Since $3 > 2$, then $\frac{1}{2} > \frac{1}{3}$ ✔

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📌 Example 2: $\frac{1}{5} \ ? \ \frac{1}{4}$

- $1 \times 4 = 4$
- $1 \times 5 = 5$
- $4 < 5$, so $\frac{1}{5} < \frac{1}{4}$ ✔

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📌 Example 4: $\frac{2}{4} \ ? \ \frac{1}{2}$

- Simplify both:
- $\frac{2}{4} = \frac{1}{2}$
- So, $\frac{2}{4} = \frac{1}{2}$ ✔

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📌 Example 6: $\frac{2}{9} \ ? \ \frac{5}{9}$

- Same denominator → compare numerators:
- $2 < 5$, so $\frac{2}{9} < \frac{5}{9}$ ✔

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📌 Example 15: $\frac{4}{8} \ ? \ \frac{1}{2}$

- Simplify $\frac{4}{8} = \frac{1}{2}$
- So, $\frac{4}{8} = \frac{1}{2}$ ✔

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📌 Example 17: $\frac{1}{10} \ ? \ \frac{1}{4}$

- $1 \times 4 = 4$
- $1 \times 10 = 10$
- $4 < 10$, so $\frac{1}{10} < \frac{1}{4}$ ✔

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📌 Example 20: $\frac{2}{3} \ ? \ \frac{2}{5}$

- Numerators are same → compare denominators:
- Smaller denominator = larger fraction
- $3 < 5$, so $\frac{2}{3} > \frac{2}{5}$ ✔

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📌 Example 23: $\frac{8}{9} \ ? \ \frac{5}{9}$

- Same denominator → compare numerators:
- $8 > 5$, so $\frac{8}{9} > \frac{5}{9}$ ✔

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🔚 Summary

This worksheet tests understanding of:
- Fraction equivalence
- Comparing fractions with different denominators
- Understanding that a larger denominator means smaller pieces (when numerators are equal)

All the answers in the image are correct, and the logic above explains why each comparison holds true.

If you’d like, I can generate a similar worksheet for practice or explain any specific problem in more detail!