Ordering Rational Numbers Color by Number - Free Printable

Let's solve each section of the "Comparing and Ordering Fractions" worksheet step by step.

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1. First Row

#### a) $\frac{3}{4}, \frac{1}{4}, \frac{2}{4}$
All have the same denominator (4), so compare numerators:
$3 > 2 > 1$ → $\frac{3}{4} > \frac{2}{4} > \frac{1}{4}$ ✔
Already given.

#### b) $\frac{7}{8}, \frac{6}{8}, \frac{9}{8}$
Same denominator (8):
Numerators: $9 > 7 > 6$ → $\frac{9}{8} > \frac{7}{8} > \frac{6}{8}$

✔ Answer: $\boxed{\frac{9}{8} > \frac{7}{8} > \frac{6}{8}}$

#### c) $\frac{2}{15}, \frac{8}{15}, \frac{10}{15}$
Same denominator (15):
$10 > 8 > 2$ → $\frac{10}{15} > \frac{8}{15} > \frac{2}{15}$

✔ Answer: $\boxed{\frac{10}{15} > \frac{8}{15} > \frac{2}{15}}$

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2. Second Row

#### d) $\frac{6}{9}, \frac{6}{4}, \frac{6}{7}$
All have numerator 6, so compare denominators.
For same numerator, larger denominator = smaller fraction.

- $\frac{6}{4} = 1.5$
- $\frac{6}{7} \approx 0.857$
- $\frac{6}{9} = \frac{2}{3} \approx 0.666$

So: $\frac{6}{9} < \frac{6}{7} < \frac{6}{4}$

✔ Answer: $\boxed{\frac{6}{9} < \frac{6}{7} < \frac{6}{4}}$

#### e) $\frac{3}{5}, \frac{5}{6}, \frac{2}{9}$
Different denominators — find common denominator or convert to decimals.

- $\frac{3}{5} = 0.6$
- $\frac{5}{6} \approx 0.833$
- $\frac{2}{9} \approx 0.222$

So: $\frac{2}{9} < \frac{3}{5} < \frac{5}{6}$

✔ Answer: $\boxed{\frac{2}{9} < \frac{3}{5} < \frac{5}{6}}$

#### f) $\frac{4}{9}, \frac{4}{3}, \frac{4}{5}$
Same numerator (4), so compare denominators:

- $\frac{4}{3} \approx 1.333$
- $\frac{4}{5} = 0.8$
- $\frac{4}{9} \approx 0.444$

So: $\frac{4}{9} < \frac{4}{5} < \frac{4}{3}$

✔ Answer: $\boxed{\frac{4}{9} < \frac{4}{5} < \frac{4}{3}}$

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3. Third Row

#### g) $\frac{14}{7}, \frac{14}{3}, \frac{14}{9}$
Same numerator (14), so larger denominator = smaller value.

- $\frac{14}{7} = 2$
- $\frac{14}{3} \approx 4.666$
- $\frac{14}{9} \approx 1.555$

So: $\frac{14}{9} < \frac{14}{7} < \frac{14}{3}$

✔ Answer: $\boxed{\frac{14}{9} < \frac{14}{7} < \frac{14}{3}}$

#### h) $\frac{8}{9}, \frac{1}{3}, 6\frac{1}{2}$
Convert all to decimals:

- $\frac{8}{9} \approx 0.888$
- $\frac{1}{3} \approx 0.333$
- $6\frac{1}{2} = 6.5$

So: $6\frac{1}{2} > \frac{8}{9} > \frac{1}{3}$

✔ Answer: $\boxed{6\frac{1}{2} > \frac{8}{9} > \frac{1}{3}}$

#### i) $1\frac{1}{5}, 2\frac{1}{4}, \frac{3}{7}$
Convert to improper fractions or decimals:

- $1\frac{1}{5} = 1.2$
- $2\frac{1}{4} = 2.25$
- $\frac{3}{7} \approx 0.4286$

So: $\frac{3}{7} < 1\frac{1}{5} < 2\frac{1}{4}$

✔ Answer: $\boxed{\frac{3}{7} < 1\frac{1}{5} < 2\frac{1}{4}}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1b | $\frac{9}{8} > \frac{7}{8} > \frac{6}{8}$ |
| 1c | $\frac{10}{15} > \frac{8}{15} > \frac{2}{15}$ |
| 2d | $\frac{6}{9} < \frac{6}{7} < \frac{6}{4}$ |
| 2e | $\frac{2}{9} < \frac{3}{5} < \frac{5}{6}$ |
| 2f | $\frac{4}{9} < \frac{4}{5} < \frac{4}{3}$ |
| 3g | $\frac{14}{9} < \frac{14}{7} < \frac{14}{3}$ |
| 3h | $6\frac{1}{2} > \frac{8}{9} > \frac{1}{3}$ |
| 3i | $\frac{3}{7} < 1\frac{1}{5} < 2\frac{1}{4}$ |

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📝 Summary Tips:

- Same denominator: Compare numerators.
- Same numerator: Larger denominator → smaller fraction.
- Different numerators/denominators: Convert to decimals or use LCM to compare.

Let me know if you'd like this as a printable answer sheet!