Free worksheets for comparing or ordering fractions - Free Printable

Let's solve each problem on the Comparing Fractions Worksheet step by step. We need to compare the given fractions and determine whether one is greater than (>), less than (<), or equal to (=) the other.

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1a. $\frac{7}{13} \quad \boxed{?} \quad \frac{6}{14}$

- Simplify $\frac{6}{14}$:
$$
\frac{6}{14} = \frac{3}{7}
$$

- Compare $\frac{7}{13}$ and $\frac{3}{7}$

We can use cross-multiplication:
$$
7 \times 7 = 49,\quad 13 \times 3 = 39
$$
Since $49 > 39$, then $\frac{7}{13} > \frac{3}{7}$, so:
$$
\frac{7}{13} > \frac{6}{14}
$$

✔ Answer: >

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1b. $\frac{7}{13} \quad \boxed{?} \quad \frac{1}{14}$

Compare $\frac{7}{13}$ and $\frac{1}{14}$

Cross-multiply:
$$
7 \times 14 = 98,\quad 13 \times 1 = 13
$$
Since $98 > 13$, then $\frac{7}{13} > \frac{1}{14}$

✔ Answer: >

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1c. $\frac{4}{9} \quad \boxed{?} \quad \frac{7}{12}$

Cross-multiply:
$$
4 \times 12 = 48,\quad 9 \times 7 = 63
$$
Since $48 < 63$, then $\frac{4}{9} < \frac{7}{12}$

✔ Answer: <

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2a. $\frac{4}{10} \quad \boxed{?} \quad \frac{1}{7}$

Simplify $\frac{4}{10} = \frac{2}{5}$

Now compare $\frac{2}{5}$ and $\frac{1}{7}$

Cross-multiply:
$$
2 \times 7 = 14,\quad 5 \times 1 = 5
$$
Since $14 > 5$, then $\frac{2}{5} > \frac{1}{7}$ → $\frac{4}{10} > \frac{1}{7}$

✔ Answer: >

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2b. $\frac{6}{9} \quad \boxed{?} \quad \frac{12}{13}$

Simplify $\frac{6}{9} = \frac{2}{3}$

Compare $\frac{2}{3}$ and $\frac{12}{13}$

Cross-multiply:
$$
2 \times 13 = 26,\quad 3 \times 12 = 36
$$
Since $26 < 36$, then $\frac{2}{3} < \frac{12}{13}$

✔ Answer: <

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2c. $\frac{5}{7} \quad \boxed{?} \quad \frac{6}{14}$

Simplify $\frac{6}{14} = \frac{3}{7}$

Now compare $\frac{5}{7}$ and $\frac{3}{7}$

Same denominator → compare numerators: $5 > 3$

So $\frac{5}{7} > \frac{3}{7}$ → $\frac{5}{7} > \frac{6}{14}$

✔ Answer: >

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3a. $\frac{15}{16} \quad \boxed{?} \quad \frac{9}{11}$

Cross-multiply:
$$
15 \times 11 = 165,\quad 16 \times 9 = 144
$$
Since $165 > 144$, then $\frac{15}{16} > \frac{9}{11}$

✔ Answer: >

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3b. $\frac{7}{14} \quad \boxed{?} \quad \frac{1}{5}$

Simplify $\frac{7}{14} = \frac{1}{2}$

Compare $\frac{1}{2}$ and $\frac{1}{5}$

Since $\frac{1}{2} = 0.5$ and $\frac{1}{5} = 0.2$, clearly $0.5 > 0.2$

So $\frac{1}{2} > \frac{1}{5}$ → $\frac{7}{14} > \frac{1}{5}$

✔ Answer: >

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3c. $\frac{8}{16} \quad \boxed{?} \quad \frac{13}{14}$

Simplify $\frac{8}{16} = \frac{1}{2}$

Compare $\frac{1}{2}$ and $\frac{13}{14}$

$\frac{1}{2} = 0.5$, $\frac{13}{14} \approx 0.9286$

Clearly $0.5 < 0.9286$, so $\frac{1}{2} < \frac{13}{14}$

Thus, $\frac{8}{16} < \frac{13}{14}$

✔ Answer: <

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1a | > |
| 1b | > |
| 1c | < |
| 2a | > |
| 2b | < |
| 2c | > |
| 3a | > |
| 3b | > |
| 3c | < |

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📝 Summary of Methods Used:

- Cross-multiplication: Multiply numerator of first fraction by denominator of second, and vice versa.
- Simplification: Reduce fractions before comparing.
- Common denominators: Useful when possible (e.g., same denominator).
- Decimal conversion: For quick estimation.

This worksheet helps build skills in fraction comparison, which is essential for algebra and higher math.