Problem: Comparing Fractions Worksheet
The task is to compare the given fractions using the symbols
> (greater than) and
< (less than). Additionally, shading diagrams can be used to help visualize the comparisons.
Solution:
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1. Compare \( \frac{1}{4} \) and \( \frac{3}{4} \)
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Fractions: \( \frac{1}{4} \) and \( \frac{3}{4} \)
-
Comparison: Both fractions have the same denominator (4). When the denominators are the same, the fraction with the larger numerator is greater.
- \( 1 < 3 \), so \( \frac{1}{4} < \frac{3}{4} \).
Answer: \( \frac{1}{4} < \frac{3}{4} \)
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2. Compare \( \frac{4}{5} \) and \( \frac{2}{5} \)
-
Fractions: \( \frac{4}{5} \) and \( \frac{2}{5} \)
-
Comparison: Both fractions have the same denominator (5). When the denominators are the same, the fraction with the larger numerator is greater.
- \( 4 > 2 \), so \( \frac{4}{5} > \frac{2}{5} \).
Answer: \( \frac{4}{5} > \frac{2}{5} \)
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3. Compare \( \frac{7}{8} \) and \( \frac{5}{8} \)
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Fractions: \( \frac{7}{8} \) and \( \frac{5}{8} \)
-
Comparison: Both fractions have the same denominator (8). When the denominators are the same, the fraction with the larger numerator is greater.
- \( 7 > 5 \), so \( \frac{7}{8} > \frac{5}{8} \).
Answer: \( \frac{7}{8} > \frac{5}{8} \)
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4. Compare \( \frac{1}{6} \) and \( \frac{3}{6} \)
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Fractions: \( \frac{1}{6} \) and \( \frac{3}{6} \)
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Comparison: Both fractions have the same denominator (6). When the denominators are the same, the fraction with the larger numerator is greater.
- \( 1 < 3 \), so \( \frac{1}{6} < \frac{3}{6} \).
Answer: \( \frac{1}{6} < \frac{3}{6} \)
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5. Compare \( \frac{5}{10} \) and \( \frac{8}{10} \)
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Fractions: \( \frac{5}{10} \) and \( \frac{8}{10} \)
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Comparison: Both fractions have the same denominator (10). When the denominators are the same, the fraction with the larger numerator is greater.
- \( 5 < 8 \), so \( \frac{5}{10} < \frac{8}{10} \).
Answer: \( \frac{5}{10} < \frac{8}{10} \)
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6. Compare \( \frac{9}{12} \) and \( \frac{3}{12} \)
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Fractions: \( \frac{9}{12} \) and \( \frac{3}{12} \)
-
Comparison: Both fractions have the same denominator (12). When the denominators are the same, the fraction with the larger numerator is greater.
- \( 9 > 3 \), so \( \frac{9}{12} > \frac{3}{12} \).
Answer: \( \frac{9}{12} > \frac{3}{12} \)
Final Answers:
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. \( \frac{9}{12} > \frac{3}{12} \)
Boxed Final Answer:
\[
\boxed{
\begin{aligned}
1. & \quad \frac{1}{4} < \frac{3}{4} \\
2. & \quad \frac{4}{5} > \frac{2}{5} \\
3. & \quad \frac{7}{8} > \frac{5}{8} \\
4. & \quad \frac{1}{6} < \frac{3}{6} \\
5. & \quad \frac{5}{10} < \frac{8}{10} \\
6. & \quad \frac{9}{12} > \frac{3}{12}
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of comparing and ordering fractions worksheet 4th grade.
