This is a worksheet for comparing fractions. The task is to compare each pair of fractions using the greater than (`>`) or less than (`<`) sign and to use the provided diagrams to help visualize the comparison.
I will solve each problem one by one, explaining the reasoning based on the fractions and the visual aids.
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Problem 1: $\frac{1}{4}$ ___ $\frac{3}{4}$
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Analysis: Both fractions have the same denominator (4). When denominators are the same, we only need to compare the numerators. Since $1 < 3$, it follows that $\frac{1}{4} < \frac{3}{4}$.
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Visual Aid: The diagram below has two rows of 4 boxes each. For $\frac{1}{4}$, you would shade 1 box in the top row. For $\frac{3}{4}$, you would shade 3 boxes in the bottom row. Clearly, 3 shaded boxes are more than 1 shaded box.
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Answer: $\frac{1}{4} < \frac{3}{4}$
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Problem 2: $\frac{4}{5}$ ___ $\frac{2}{5}$
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Analysis: Both fractions have the same denominator (5). Comparing the numerators, $4 > 2$, so $\frac{4}{5} > \frac{2}{5}$.
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Visual Aid: The diagram has two rows of 5 boxes. For $\frac{4}{5}$, shade 4 boxes; for $\frac{2}{5}$, shade 2 boxes. Four shaded boxes are more than two.
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Answer: $\frac{4}{5} > \frac{2}{5}$
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Problem 3: $\frac{7}{8}$ ___ $\frac{5}{8}$
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Analysis: Same denominator (8). Since $7 > 5$, we have $\frac{7}{8} > \frac{5}{8}$.
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Visual Aid: Two rows of 8 boxes. Shade 7 for the first fraction and 5 for the second. Seven is clearly more than five.
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Answer: $\frac{7}{8} > \frac{5}{8}$
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Problem 4: $\frac{1}{6}$ ___ $\frac{3}{6}$
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Analysis: Same denominator (6). Comparing numerators, $1 < 3$, so $\frac{1}{6} < \frac{3}{6}$.
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Visual Aid: Two rows of 6 boxes. Shade 1 for the first and 3 for the second. Three shaded boxes are more than one.
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Answer: $\frac{1}{6} < \frac{3}{6}$
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Problem 5: $\frac{5}{10}$ ___ $\frac{8}{10}$
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Analysis: Same denominator (10). Since $5 < 8$, it follows that $\frac{5}{10} < \frac{8}{10}$.
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Visual Aid: Two rows of 10 boxes. Shade 5 for the first and 8 for the second. Eight is more than five.
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Answer: $\frac{5}{10} < \frac{8}{10}$
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Problem 6: $\frac{9}{12}$ ___ $\frac{3}{12}$
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Analysis: Same denominator (12). Since $9 > 3$, we have $\frac{9}{12} > \frac{3}{12}$.
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Visual Aid: Two rows of 12 boxes. Shade 9 for the first and 3 for the second. Nine is clearly more than three.
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Answer: $\frac{9}{12} > \frac{3}{12}$
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Final Answer:
Here are the completed comparisons for the worksheet:
1. $\frac{1}{4} < \frac{3}{4}$
2. $\frac{4}{5} > \frac{2}{5}$
3. $\frac{7}{8} > \frac{5}{8}$
4. $\frac{1}{6} < \frac{3}{6}$
5. $\frac{5}{10} < \frac{8}{10}$
6. $\frac{9}{12} > \frac{3}{12}$
Parent Tip: Review the logic above to help your child master the concept of order fractions worksheet.
