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Comparing Fractions

Compare fractions using common denominators

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Comparing Fractions

Same Denominator

When fractions have the same denominator, compare numerators:

38<58\frac{3}{8} < \frac{5}{8}

(3 parts < 5 parts)

Different Denominators

Find a common denominator first, then compare:

Example: Compare 12\frac{1}{2} and 25\frac{2}{5}

Common denominator is 10:

  • 12=510\frac{1}{2} = \frac{5}{10}
  • 25=410\frac{2}{5} = \frac{4}{10}

Since 510>410\frac{5}{10} > \frac{4}{10}, we know 12>25\frac{1}{2} > \frac{2}{5}

Using Benchmarks

Compare to common fractions:

  • Is it close to 00, 12\frac{1}{2}, or 11?

Example:

  • 18\frac{1}{8} is close to 0
  • 78\frac{7}{8} is close to 1

So 78>18\frac{7}{8} > \frac{1}{8} (obviously!)

Tips

  • Same numerator? Smaller denominator = larger fraction
    • 34>38\frac{3}{4} > \frac{3}{8}

📚 Practice Problems

1Problem 1easy

❓ Question:

Which is greater: 27\frac{2}{7} or 57\frac{5}{7}?

💡 Show Solution

Solution:

Same denominator - compare numerators:

2<52 < 5

So 27<57\frac{2}{7} < \frac{5}{7}

Answer: 57\frac{5}{7} is greater

2Problem 2easy

❓ Question:

Which is greater: 27\frac{2}{7} or 57\frac{5}{7}?

💡 Show Solution

Solution:

Same denominator - compare numerators:

2<52 < 5

So 27<57\frac{2}{7} < \frac{5}{7}

Answer: 57\frac{5}{7} is greater

3Problem 3medium

❓ Question:

Which is greater: 13\frac{1}{3} or 14\frac{1}{4}?

💡 Show Solution

Solution:

Same numerator (1) - smaller denominator wins:

Think: 13\frac{1}{3} of a pizza is bigger than 14\frac{1}{4} of a pizza

Common denominator (12):

  • 13=412\frac{1}{3} = \frac{4}{12}
  • 14=312\frac{1}{4} = \frac{3}{12}

Answer: 13\frac{1}{3} is greater

4Problem 4medium

❓ Question:

Which is greater: 13\frac{1}{3} or 14\frac{1}{4}?

💡 Show Solution

Solution:

Same numerator (1) - smaller denominator wins:

Think: 13\frac{1}{3} of a pizza is bigger than 14\frac{1}{4} of a pizza

Common denominator (12):

  • 13=412\frac{1}{3} = \frac{4}{12}
  • 14=312\frac{1}{4} = \frac{3}{12}

Answer: 13\frac{1}{3} is greater

5Problem 5hard

❓ Question:

Order from least to greatest: 12\frac{1}{2}, 38\frac{3}{8}, 56\frac{5}{6}

💡 Show Solution

Solution:

Find common denominator (24):

  • 12=1224\frac{1}{2} = \frac{12}{24}
  • 38=924\frac{3}{8} = \frac{9}{24}
  • 56=2024\frac{5}{6} = \frac{20}{24}

Order: 924<1224<2024\frac{9}{24} < \frac{12}{24} < \frac{20}{24}

Answer: 38,12,56\frac{3}{8}, \frac{1}{2}, \frac{5}{6}

6Problem 6hard

❓ Question:

Order from least to greatest: 12\frac{1}{2}, 38\frac{3}{8}, 56\frac{5}{6}

💡 Show Solution

Solution:

Find common denominator (24):

  • 12=1224\frac{1}{2} = \frac{12}{24}
  • 38=924\frac{3}{8} = \frac{9}{24}
  • 56=2024\frac{5}{6} = \frac{20}{24}

Order: 924<1224<2024\frac{9}{24} < \frac{12}{24} < \frac{20}{24}

Answer: 38,12,56\frac{3}{8}, \frac{1}{2}, \frac{5}{6}

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Equivalent FractionsAdding and Subtracting FractionsAdding Fractions with Like DenominatorsMultiplying Fractions by Whole NumbersMultiplying Fractions by Whole Numbers

❓ Frequently Asked Questions

What is Comparing Fractions?▾
Compare fractions using common denominators
How can I study Comparing Fractions effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Comparing Fractions study guide free?▾
Yes — all study notes, flashcards, and practice problems for Comparing Fractions on Study Mondo are free to access. No account is needed.
What course covers Comparing Fractions?▾
Comparing Fractions is part of the Grade 4 Math course on Study Mondo, specifically in the Fractions section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Comparing Fractions?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.