The image you've uploaded is a completed worksheet titled
"Ordering Fractions from Least to Greatest". It contains 12 boxes, each with three fractions (or mixed numbers) that have been correctly ordered from least to greatest. Below is an explanation of how each set was solved and why the orderings are correct.
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🔍 General Strategy for Ordering Fractions:
To compare and order fractions:
1.
Same denominators: Compare numerators directly.
2.
Same numerators: The fraction with the larger denominator is smaller.
3.
Different numerators and denominators: Find a common denominator or convert to decimals.
Let’s go through each box and explain the logic.
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✔ Box 1: $\frac{5}{3}, \frac{4}{3}, \frac{2}{3}$
- All have same denominator: 3
- Compare numerators: $2 < 4 < 5$
- So: $\boxed{\frac{2}{3} < \frac{4}{3} < \frac{5}{3}}$ ✔️
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✔ Box 2: $\frac{3}{11}, \frac{3}{8}, \frac{3}{5}$
- Same numerator: 3
- Larger denominator → smaller fraction
- $11 > 8 > 5$, so $\frac{3}{11} < \frac{3}{8} < \frac{3}{5}$
- So: $\boxed{\frac{3}{11} < \frac{3}{8} < \frac{3}{5}}$ ✔️
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✔ Box 3: $\frac{2}{7}, \frac{6}{7}, \frac{10}{7}$
- Same denominator: 7
- Numerators: $2 < 6 < 10$
- So: $\boxed{\frac{2}{7} < \frac{6}{7} < \frac{10}{7}}$ ✔️
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✔ Box 4: $\frac{2}{5}, \frac{3}{7}, \frac{4}{9}$
- Different denominators → find common denominator or use decimal approximations:
- $\frac{2}{5} = 0.4$
- $\frac{3}{7} \approx 0.4286$
- $\frac{4}{9} \approx 0.4444$
- So: $0.4 < 0.4286 < 0.4444$
- Therefore: $\boxed{\frac{2}{5} < \frac{3}{7} < \frac{4}{9}}$ ✔️
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✔ Box 5: $\frac{15}{2}, \frac{13}{2}, \frac{17}{2}$
- Same denominator: 2
- Numerators: $13 < 15 < 17$
- So: $\boxed{\frac{13}{2} < \frac{15}{2} < \frac{17}{2}}$ ✔️
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✔ Box 6: $\frac{13}{3}, \frac{16}{3}, \frac{5}{3}$
- Same denominator: 3
- Numerators: $5 < 13 < 16$
- So: $\boxed{\frac{5}{3} < \frac{13}{3} < \frac{16}{3}}$ ✔️
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✔ Box 7: $\frac{2}{19}, \frac{2}{17}, \frac{2}{13}$
- Same numerator: 2
- Larger denominator → smaller value
- $19 > 17 > 13$, so $\frac{2}{19} < \frac{2}{17} < \frac{2}{13}$
- So: $\boxed{\frac{2}{19} < \frac{2}{17} < \frac{2}{13}}$ ✔️
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✔ Box 8: $2\frac{3}{5}, 2\frac{1}{5}, 3\frac{2}{5}$
- Convert to improper fractions or compare whole parts first:
- $2\frac{1}{5} = 2.2$
- $2\frac{3}{5} = 2.6$
- $3\frac{2}{5} = 3.4$
- So: $2.2 < 2.6 < 3.4$
- Thus: $\boxed{2\frac{1}{5} < 2\frac{3}{5} < 3\frac{2}{5}}$ ✔️
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✔ Box 9: $\frac{3}{8}, \frac{6}{8}, \frac{5}{8}$
- Same denominator: 8
- Numerators: $3 < 5 < 6$
- So: $\boxed{\frac{3}{8} < \frac{5}{8} < \frac{6}{8}}$ ✔️
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✔ Box 10: $\frac{11}{14}, \frac{3}{14}, \frac{9}{14}$
- Same denominator: 14
- Numerators: $3 < 9 < 11$
- So: $\boxed{\frac{3}{14} < \frac{9}{14} < \frac{11}{14}}$ ✔️
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✔ Box 11: $4\frac{1}{8}, 5\frac{3}{8}, 9\frac{5}{8}$
- Whole numbers: 4, 5, 9 → clearly increasing
- So: $\boxed{4\frac{1}{8} < 5\frac{3}{8} < 9\frac{5}{8}}$ ✔️
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✔ Box 12: $7\frac{1}{6}, 4\frac{5}{6}, 2\frac{1}{6}$
- Whole numbers: 2, 4, 7
- So: $2\frac{1}{6} < 4\frac{5}{6} < 7\frac{1}{6}$
- Even though $\frac{5}{6} > \frac{1}{6}$, the whole number dominates
- So: $\boxed{2\frac{1}{6} < 4\frac{5}{6} < 7\frac{1}{6}}$ ✔️
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✔ Final Assessment:
✔ All answers on the worksheet are
correct.
This worksheet demonstrates key fraction comparison techniques:
- Comparing like denominators
- Comparing like numerators
- Using decimal conversions
- Handling mixed numbers
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🎯 Summary:
The worksheet is well-designed and correctly completed. Each ordering follows sound mathematical reasoning. Students practicing this will develop strong skills in comparing and ordering fractions.
If you’d like, I can generate a similar worksheet or explain any particular concept in more depth!
Parent Tip: Review the logic above to help your child master the concept of least to greatest fractions worksheet.
