Worksheet for comparing fractions and decimals with comparison symbols.

Let's solve each problem by comparing the given fractions and decimals. We'll convert fractions to decimals (if needed) and then compare them using the correct comparison symbol: >, <, or =.

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Step-by-step Solutions:

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1) $-\frac{7}{12}$ □ $-0.658$

Convert $-\frac{7}{12}$ to decimal:
$\frac{7}{12} \approx 0.5833$, so $-\frac{7}{12} \approx -0.5833$

Now compare:
$-0.5833$ vs $-0.658$

On a number line, $-0.5833 > -0.658$ (because it's closer to zero)

✔ Answer: $-\frac{7}{12} > -0.658$

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2) $-\frac{1}{2}$ □ $-0.5$

$-\frac{1}{2} = -0.5$

So they are equal

✔ Answer: $-\frac{1}{2} = -0.5$

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3) $\frac{2}{3}$ □ $0.692$

$\frac{2}{3} \approx 0.6667$

Compare: $0.6667 < 0.692$

✔ Answer: $\frac{2}{3} < 0.692$

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4) $\frac{1}{2}$ □ $0.45$

$\frac{1}{2} = 0.5$

$0.5 > 0.45$

✔ Answer: $\frac{1}{2} > 0.45$

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5) $-\frac{3}{4}$ □ $-0.6$

$-\frac{3}{4} = -0.75$

Compare: $-0.75 < -0.6$

✔ Answer: $-\frac{3}{4} < -0.6$

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6) $\frac{4}{12}$ □ $0.408$

Simplify $\frac{4}{12} = \frac{1}{3} \approx 0.333$

Compare: $0.333 < 0.408$

✔ Answer: $\frac{4}{12} < 0.408$

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7) $-\frac{2}{3}$ □ $-0.817$

$-\frac{2}{3} \approx -0.6667$

Compare: $-0.6667 > -0.817$

✔ Answer: $-\frac{2}{3} > -0.817$

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8) $\frac{4}{6}$ □ $0.667$

Simplify $\frac{4}{6} = \frac{2}{3} \approx 0.6667$

Compare: $0.6667 < 0.667$

(Note: $0.6667$ is slightly less than $0.667$)

✔ Answer: $\frac{4}{6} < 0.667$

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9) $\frac{4}{10}$ □ $0.5$

$\frac{4}{10} = 0.4$

$0.4 < 0.5$

✔ Answer: $\frac{4}{10} < 0.5$

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10) $-\frac{4}{8}$ □ $-0.625$

Simplify $-\frac{4}{8} = -\frac{1}{2} = -0.5$

Compare: $-0.5 > -0.625$

✔ Answer: $-\frac{4}{8} > -0.625$

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11) $\frac{2}{8}$ □ $0.375$

$\frac{2}{8} = \frac{1}{4} = 0.25$

$0.25 < 0.375$

✔ Answer: $\frac{2}{8} < 0.375$

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12) $-\frac{7}{12}$ □ $-0.683$

We already know $-\frac{7}{12} \approx -0.5833$

Compare: $-0.5833 > -0.683$

✔ Answer: $-\frac{7}{12} > -0.683$

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13) $\frac{1}{3}$ □ $0.458$

$\frac{1}{3} \approx 0.3333$

$0.3333 < 0.458$

✔ Answer: $\frac{1}{3} < 0.458$

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14) $\frac{1}{4}$ □ $0.25$

$\frac{1}{4} = 0.25$

✔ Answer: $\frac{1}{4} = 0.25$

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15) $-\frac{1}{8}$ □ $-0.125$

$-\frac{1}{8} = -0.125$

✔ Answer: $-\frac{1}{8} = -0.125$

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16) $\frac{1}{2}$ □ $0.375$

$\frac{1}{2} = 0.5$

$0.5 > 0.375$

✔ Answer: $\frac{1}{2} > 0.375$

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17) $-\frac{2}{3}$ □ $-0.692$

$-\frac{2}{3} \approx -0.6667$

Compare: $-0.6667 > -0.692$

✔ Answer: $-\frac{2}{3} > -0.692$

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18) $-\frac{5}{6}$ □ $-0.833$

$-\frac{5}{6} \approx -0.8333$

Compare: $-0.8333 < -0.833$? Wait — let's be careful.

Actually:
$-0.8333$ vs $-0.833$

Since $-0.8333$ is more negative than $-0.833$, it is less than.

So: $-0.8333 < -0.833$

✔ Answer: $-\frac{5}{6} < -0.833$

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19) $-\frac{4}{6}$ □ $-0.667$

Simplify $-\frac{4}{6} = -\frac{2}{3} \approx -0.6667$

Compare: $-0.6667 > -0.667$

(Just like earlier, $-0.6667$ is greater than $-0.667$ because it’s closer to zero)

✔ Answer: $-\frac{4}{6} > -0.667$

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20) $\frac{2}{8}$ □ $0.3$

$\frac{2}{8} = 0.25$

$0.25 < 0.3$

✔ Answer: $\frac{2}{8} < 0.3$

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Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $-\frac{7}{12} > -0.658$ |
| 2) | $-\frac{1}{2} = -0.5$ |
| 3) | $\frac{2}{3} < 0.692$ |
| 4) | $\frac{1}{2} > 0.45$ |
| 5) | $-\frac{3}{4} < -0.6$ |
| 6) | $\frac{4}{12} < 0.408$ |
| 7) | $-\frac{2}{3} > -0.817$ |
| 8) | $\frac{4}{6} < 0.667$ |
| 9) | $\frac{4}{10} < 0.5$ |
| 10) | $-\frac{4}{8} > -0.625$ |
| 11) | $\frac{2}{8} < 0.375$ |
| 12) | $-\frac{7}{12} > -0.683$ |
| 13) | $\frac{1}{3} < 0.458$ |
| 14) | $\frac{1}{4} = 0.25$ |
| 15) | $-\frac{1}{8} = -0.125$ |
| 16) | $\frac{1}{2} > 0.375$ |
| 17) | $-\frac{2}{3} > -0.692$ |
| 18) | $-\frac{5}{6} < -0.833$ |
| 19) | $-\frac{4}{6} > -0.667$ |
| 20) | $\frac{2}{8} < 0.3$ |

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Summary Tips:

- Convert fractions to decimals for easier comparison.
- Remember: With negative numbers, the one with the larger absolute value is actually smaller.
Example: $-0.7 < -0.5$
- Use approximations when necessary (e.g., $\frac{1}{3} \approx 0.333$).

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