Compare unlike fractions using 1 as a benchmark with this printable math worksheet.

Let's solve this step-by-step using benchmarks, specifically 1 as a reference point. The goal is to compare each pair of fractions by determining whether each fraction is greater than, less than, or equal to 1, and then use that information to compare them.

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🔍 Strategy:

- If a fraction is greater than 1, its numerator is greater than its denominator.
- If a fraction is less than 1, its numerator is less than its denominator.
- If a fraction is equal to 1, numerator = denominator.

We'll compare the two fractions in each pair based on their relationship to 1.

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✔ Left Column:

#### 1. $\frac{5}{7} \quad \square \quad \frac{5}{3}$

- $\frac{5}{7}$: $5 < 7$ → < 1
- $\frac{5}{3}$: $5 > 3$ → > 1

So, $\frac{5}{7} < \frac{5}{3}$
👉 Answer: <

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#### 2. $\frac{3}{2} \quad \square \quad \frac{1}{3}$

- $\frac{3}{2}$: $3 > 2$ → > 1
- $\frac{1}{3}$: $1 < 3$ → < 1

So, $\frac{3}{2} > \frac{1}{3}$
👉 Answer: >

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#### 3. $\frac{9}{7} \quad \square \quad \frac{3}{5}$

- $\frac{9}{7}$: $9 > 7$ → > 1
- $\frac{3}{5}$: $3 < 5$ → < 1

So, $\frac{9}{7} > \frac{3}{5}$
👉 Answer: >

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#### 4. $\frac{6}{5} \quad \square \quad \frac{6}{9}$

- $\frac{6}{5}$: $6 > 5$ → > 1
- $\frac{6}{9}$: $6 < 9$ → < 1

So, $\frac{6}{5} > \frac{6}{9}$
👉 Answer: >

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#### 5. $\frac{8}{7} \quad \square \quad \frac{1}{6}$

- $\frac{8}{7}$: $8 > 7$ → > 1
- $\frac{1}{6}$: $1 < 6$ → < 1

So, $\frac{8}{7} > \frac{1}{6}$
👉 Answer: >

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✔ Right Column:

#### 6. $\frac{1}{4} \quad \square \quad \frac{6}{2}$

- $\frac{1}{4}$: $1 < 4$ → < 1
- $\frac{6}{2} = 3$ → > 1

So, $\frac{1}{4} < \frac{6}{2}$
👉 Answer: <

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#### 7. $\frac{9}{8} \quad \square \quad \frac{3}{7}$

- $\frac{9}{8}$: $9 > 8$ → > 1
- $\frac{3}{7}$: $3 < 7$ → < 1

So, $\frac{9}{8} > \frac{3}{7}$
👉 Answer: >

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#### 8. $\frac{5}{15} \quad \square \quad \frac{1}{3}$

- $\frac{5}{15} = \frac{1}{3}$ → = 1/3, so it's < 1
- $\frac{1}{3}$: also < 1

But let’s simplify:
- $\frac{5}{15} = \frac{1}{3}$ → they are equal

So, $\frac{5}{15} = \frac{1}{3}$
👉 Answer: =

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#### 9. $\frac{24}{6} \quad \square \quad \frac{28}{7}$

Simplify both:
- $\frac{24}{6} = 4$
- $\frac{28}{7} = 4$

So, both are equal to 4, which is > 1

Thus, $\frac{24}{6} = \frac{28}{7}$
👉 Answer: =

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#### 10. $\frac{10}{12} \quad \square \quad \frac{11}{10}$

- $\frac{10}{12}$: $10 < 12$ → < 1
- $\frac{11}{10}$: $11 > 10$ → > 1

So, $\frac{10}{12} < \frac{11}{10}$
👉 Answer: <

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| $\frac{5}{7} \quad \square \quad \frac{5}{3}$ | < |
| $\frac{3}{2} \quad \square \quad \frac{1}{3}$ | > |
| $\frac{9}{7} \quad \square \quad \frac{3}{5}$ | > |
| $\frac{6}{5} \quad \square \quad \frac{6}{9}$ | > |
| $\frac{8}{7} \quad \square \quad \frac{1}{6}$ | > |
| $\frac{1}{4} \quad \square \quad \frac{6}{2}$ | < |
| $\frac{9}{8} \quad \square \quad \frac{3}{7}$ | > |
| $\frac{5}{15} \quad \square \quad \frac{1}{3}$ | = |
| $\frac{24}{6} \quad \square \quad \frac{28}{7}$ | = |
| $\frac{10}{12} \quad \square \quad \frac{11}{10}$ | < |

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🧠 Summary:

We used 1 as a benchmark to quickly determine whether each fraction was greater than, less than, or equal to 1. Then we compared the two fractions based on their position relative to 1.

This method is efficient for comparing unlike fractions without finding common denominators — especially when one fraction is clearly greater than 1 and the other less than 1.

Let me know if you'd like a visual explanation or practice problems!