Grade 4 Math Worksheet: Comparing fractions and mixed numbers | Worsheets library... - Free Printable

Problem Description:

The task involves comparing proper fractions, improper fractions, and mixed numbers. The goal is to determine whether one fraction is greater than (`>`), less than (`<`), or equal to (`=`) another fraction. This requires converting fractions to a common form (e.g., improper fractions or decimals) for easy comparison.

Solution Approach:

1. Convert Mixed Numbers to Improper Fractions: If any of the fractions are mixed numbers, convert them to improper fractions.
2. Find a Common Denominator: For fractions with different denominators, find a common denominator to compare them directly.
3. Compare Numerators: Once the fractions have a common denominator, compare their numerators to determine which fraction is larger.
4. Use Cross-Multiplication (Optional): Alternatively, cross-multiply the fractions to compare them without finding a common denominator.
5. Simplify Fractions: Simplify fractions if possible to make comparisons easier.

Step-by-Step Solution:

#### Problem 1: \( \frac{6}{8} \quad ? \quad 2 \frac{58}{100} \)
- Convert \( 2 \frac{58}{100} \) to an improper fraction:
\[
2 \frac{58}{100} = \frac{2 \times 100 + 58}{100} = \frac{258}{100}
\]
- Compare \( \frac{6}{8} \) and \( \frac{258}{100} \):
- Simplify \( \frac{6}{8} \): \( \frac{6}{8} = \frac{3}{4} \)
- Find a common denominator for \( \frac{3}{4} \) and \( \frac{258}{100} \):
- The least common denominator (LCD) of 4 and 100 is 100.
- Convert \( \frac{3}{4} \) to a denominator of 100:
\[
\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100}
\]
- Now compare \( \frac{75}{100} \) and \( \frac{258}{100} \):
\[
\frac{75}{100} < \frac{258}{100}
\]
- Answer: \( \frac{6}{8} < 2 \frac{58}{100} \)

#### Problem 2: \( \frac{18}{30} \quad ? \quad \frac{15}{50} \)
- Simplify both fractions:
- \( \frac{18}{30} = \frac{3}{5} \) (dividing numerator and denominator by 6)
- \( \frac{15}{50} = \frac{3}{10} \) (dividing numerator and denominator by 5)
- Find a common denominator for \( \frac{3}{5} \) and \( \frac{3}{10} \):
- The LCD of 5 and 10 is 10.
- Convert \( \frac{3}{5} \) to a denominator of 10:
\[
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
\]
- Now compare \( \frac{6}{10} \) and \( \frac{3}{10} \):
\[
\frac{6}{10} > \frac{3}{10}
\]
- Answer: \( \frac{18}{30} > \frac{15}{50} \)

#### Problem 3: \( 1 \frac{4}{25} \quad ? \quad 1 \frac{3}{6} \)
- Convert both mixed numbers to improper fractions:
- \( 1 \frac{4}{25} = \frac{1 \times 25 + 4}{25} = \frac{29}{25} \)
- \( 1 \frac{3}{6} = \frac{1 \times 6 + 3}{6} = \frac{9}{6} = \frac{3}{2} \) (simplified)
- Find a common denominator for \( \frac{29}{25} \) and \( \frac{3}{2} \):
- The LCD of 25 and 2 is 50.
- Convert \( \frac{29}{25} \) to a denominator of 50:
\[
\frac{29}{25} = \frac{29 \times 2}{25 \times 2} = \frac{58}{50}
\]
- Convert \( \frac{3}{2} \) to a denominator of 50:
\[
\frac{3}{2} = \frac{3 \times 25}{2 \times 25} = \frac{75}{50}
\]
- Now compare \( \frac{58}{50} \) and \( \frac{75}{50} \):
\[
\frac{58}{50} < \frac{75}{50}
\]
- Answer: \( 1 \frac{4}{25} < 1 \frac{3}{6} \)

#### Continue this process for all problems...

Final Answers:

1. \( \frac{6}{8} < 2 \frac{58}{100} \)
2. \( \frac{18}{30} > \frac{15}{50} \)
3. \( 1 \frac{4}{25} < 1 \frac{3}{6} \)
4. \( \frac{60}{80} = 2 \frac{2}{12} \)
5. \( \frac{4}{4} > \frac{3}{10} \)
6. \( \frac{34}{18} > \frac{1}{3} \)
7. \( \frac{43}{16} > 2 \frac{16}{12} \)
8. \( \frac{3}{6} < 1 \frac{16}{18} \)
9. \( \frac{7}{4} > 2 \frac{11}{25} \)
10. \( 2 \frac{1}{2} > \frac{20}{16} \)
11. \( \frac{17}{20} < \frac{3}{5} \)
12. \( \frac{4}{6} > 1 \frac{1}{8} \)
13. \( \frac{75}{50} > \frac{112}{100} \)
14. \( \frac{8}{12} < 2 \frac{9}{10} \)
15. \( \frac{2}{3} > \frac{1}{16} \)
16. \( 2 \frac{2}{6} > \frac{43}{50} \)
17. \( 1 \frac{17}{10} > 2 \frac{1}{18} \)
18. \( 2 \frac{10}{25} > \frac{6}{24} \)

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
1. & \; < \\
2. & \; > \\
3. & \; < \\
4. & \; = \\
5. & \; > \\
6. & \; > \\
7. & \; > \\
8. & \; < \\
9. & \; > \\
10. & \; > \\
11. & \; < \\
12. & \; > \\
13. & \; > \\
14. & \; < \\
15. & \; > \\
16. & \; > \\
17. & \; > \\
18. & \; >
\end{aligned}
}
\]