Comparing fractions, 4th grade | 4th grade Math Worksheet ... - Free Printable

Problem Overview:

The task involves comparing fractions and determining which fraction is greater or if they are equal. The worksheet provides a step-by-step approach to solving these problems, using the concept of finding a common denominator.

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Step-by-Step Solution:

#### Part 1: Comparing Fractions
We are given two fractions and need to determine which one is greater. The method involves finding a common denominator for the fractions.

##### Example from the Worksheet:
- Compare \( \frac{3}{5} \) and \( \frac{4}{6} \).

1. Find the Least Common Denominator (LCD):
- The denominators are 5 and 6.
- The least common multiple (LCM) of 5 and 6 is 30.
- So, the LCD is 30.

2. Convert Each Fraction to an Equivalent Fraction with the LCD:
- For \( \frac{3}{5} \):
\[
\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}
\]
- For \( \frac{4}{6} \):
\[
\frac{4}{6} = \frac{4 \times 5}{6 \times 5} = \frac{20}{30}
\]

3. Compare the Numerators:
- The fractions are now \( \frac{18}{30} \) and \( \frac{20}{30} \).
- Since \( 18 < 20 \), we have \( \frac{18}{30} < \frac{20}{30} \).

4. Conclusion:
- \( \frac{3}{5} < \frac{4}{6} \).

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#### Part 2: Applying the Method to Other Problems
Now, let's solve the remaining problems using the same approach.

##### Problem 1: \( \frac{2}{3} \) or \( \frac{3}{4} \)
1. Find the LCD:
- Denominators are 3 and 4.
- LCM of 3 and 4 is 12.
- So, the LCD is 12.

2. Convert Each Fraction:
- For \( \frac{2}{3} \):
\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\]
- For \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

3. Compare the Numerators:
- The fractions are \( \frac{8}{12} \) and \( \frac{9}{12} \).
- Since \( 8 < 9 \), we have \( \frac{8}{12} < \frac{9}{12} \).

4. Conclusion:
- \( \frac{2}{3} < \frac{3}{4} \).

##### Problem 2: \( \frac{5}{6} \) or \( \frac{7}{8} \)
1. Find the LCD:
- Denominators are 6 and 8.
- LCM of 6 and 8 is 24.
- So, the LCD is 24.

2. Convert Each Fraction:
- For \( \frac{5}{6} \):
\[
\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}
\]
- For \( \frac{7}{8} \):
\[
\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}
\]

3. Compare the Numerators:
- The fractions are \( \frac{20}{24} \) and \( \frac{21}{24} \).
- Since \( 20 < 21 \), we have \( \frac{20}{24} < \frac{21}{24} \).

4. Conclusion:
- \( \frac{5}{6} < \frac{7}{8} \).

##### Problem 3: \( \frac{3}{5} \) or \( \frac{4}{7} \)
1. Find the LCD:
- Denominators are 5 and 7.
- LCM of 5 and 7 is 35.
- So, the LCD is 35.

2. Convert Each Fraction:
- For \( \frac{3}{5} \):
\[
\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}
\]
- For \( \frac{4}{7} \):
\[
\frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35}
\]

3. Compare the Numerators:
- The fractions are \( \frac{21}{35} \) and \( \frac{20}{35} \).
- Since \( 21 > 20 \), we have \( \frac{21}{35} > \frac{20}{35} \).

4. Conclusion:
- \( \frac{3}{5} > \frac{4}{7} \).

##### Problem 4: \( \frac{2}{3} \) or \( \frac{5}{6} \)
1. Find the LCD:
- Denominators are 3 and 6.
- LCM of 3 and 6 is 6.
- So, the LCD is 6.

2. Convert Each Fraction:
- For \( \frac{2}{3} \):
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
- For \( \frac{5}{6} \):
\[
\frac{5}{6} = \frac{5}{6}
\]

3. Compare the Numerators:
- The fractions are \( \frac{4}{6} \) and \( \frac{5}{6} \).
- Since \( 4 < 5 \), we have \( \frac{4}{6} < \frac{5}{6} \).

4. Conclusion:
- \( \frac{2}{3} < \frac{5}{6} \).

##### Problem 5: \( \frac{3}{4} \) or \( \frac{5}{8} \)
1. Find the LCD:
- Denominators are 4 and 8.
- LCM of 4 and 8 is 8.
- So, the LCD is 8.

2. Convert Each Fraction:
- For \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]
- For \( \frac{5}{8} \):
\[
\frac{5}{8} = \frac{5}{8}
\]

3. Compare the Numerators:
- The fractions are \( \frac{6}{8} \) and \( \frac{5}{8} \).
- Since \( 6 > 5 \), we have \( \frac{6}{8} > \frac{5}{8} \).

4. Conclusion:
- \( \frac{3}{4} > \frac{5}{8} \).

##### Problem 6: \( \frac{4}{5} \) or \( \frac{7}{10} \)
1. Find the LCD:
- Denominators are 5 and 10.
- LCM of 5 and 10 is 10.
- So, the LCD is 10.

2. Convert Each Fraction:
- For \( \frac{4}{5} \):
\[
\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
\]
- For \( \frac{7}{10} \):
\[
\frac{7}{10} = \frac{7}{10}
\]

3. Compare the Numerators:
- The fractions are \( \frac{8}{10} \) and \( \frac{7}{10} \).
- Since \( 8 > 7 \), we have \( \frac{8}{10} > \frac{7}{10} \).

4. Conclusion:
- \( \frac{4}{5} > \frac{7}{10} \).

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#### Part 3: Identifying Equal Fractions
We need to identify pairs of fractions that are equal.

##### Problem: Which two fractions in each pair are equal?
1. \( \frac{1}{2} \) or \( \frac{2}{4} \):
- Convert \( \frac{2}{4} \) to its simplest form:
\[
\frac{2}{4} = \frac{1}{2}
\]
- Conclusion: \( \frac{1}{2} = \frac{2}{4} \).

2. \( \frac{3}{4} \) or \( \frac{6}{8} \):
- Convert \( \frac{6}{8} \) to its simplest form:
\[
\frac{6}{8} = \frac{3}{4}
\]
- Conclusion: \( \frac{3}{4} = \frac{6}{8} \).

3. \( \frac{2}{3} \) or \( \frac{4}{6} \):
- Convert \( \frac{4}{6} \) to its simplest form:
\[
\frac{4}{6} = \frac{2}{3}
\]
- Conclusion: \( \frac{2}{3} = \frac{4}{6} \).

4. \( \frac{5}{6} \) or \( \frac{10}{12} \):
- Convert \( \frac{10}{12} \) to its simplest form:
\[
\frac{10}{12} = \frac{5}{6}
\]
- Conclusion: \( \frac{5}{6} = \frac{10}{12} \).

5. \( \frac{3}{5} \) or \( \frac{6}{10} \):
- Convert \( \frac{6}{10} \) to its simplest form:
\[
\frac{6}{10} = \frac{3}{5}
\]
- Conclusion: \( \frac{3}{5} = \frac{6}{10} \).

6. \( \frac{4}{5} \) or \( \frac{8}{10} \):
- Convert \( \frac{8}{10} \) to its simplest form:
\[
\frac{8}{10} = \frac{4}{5}
\]
- Conclusion: \( \frac{4}{5} = \frac{8}{10} \).

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#### Part 4: Ordering Fractions
Finally, we need to order the fractions from least to greatest.

##### Problem: Order \( \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5} \).
1. Find the LCD:
- Denominators are 2, 3, 4, and 5.
- LCM of 2, 3, 4, and 5 is 60.
- So, the LCD is 60.

2. Convert Each Fraction:
- For \( \frac{1}{2} \):
\[
\frac{1}{2} = \frac{1 \times 30}{2 \times 30} = \frac{30}{60}
\]
- For \( \frac{2}{3} \):
\[
\frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60}
\]
- For \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}
\]
- For \( \frac{4}{5} \):
\[
\frac{4}{5} = \frac{4 \times 12}{5 \times 12} = \frac{48}{60}
\]

3. Compare the Numerators:
- The fractions are \( \frac{30}{60}, \frac{40}{60}, \frac{45}{60}, \frac{48}{60} \).
- In ascending order: \( 30 < 40 < 45 < 48 \).

4. Conclusion:
- The ordered fractions are:
\[
\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}
\]

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Final Answers:

1. \( \frac{2}{3} < \frac{3}{4} \)
2. \( \frac{5}{6} < \frac{7}{8} \)
3. \( \frac{3}{5} > \frac{4}{7} \)
4. \( \frac{2}{3} < \frac{5}{6} \)
5. \( \frac{3}{4} > \frac{5}{8} \)
6. \( \frac{4}{5} > \frac{7}{10} \)

Equal fractions:
1. \( \frac{1}{2} = \frac{2}{4} \)
2. \( \frac{3}{4} = \frac{6}{8} \)
3. \( \frac{2}{3} = \frac{4}{6} \)
4. \( \frac{5}{6} = \frac{10}{12} \)
5. \( \frac{3}{5} = \frac{6}{10} \)
6. \( \frac{4}{5} = \frac{8}{10} \)

Ordered fractions:
\[
\boxed{\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}}
\]