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Equivalent Fractions

Find fractions that represent the same value

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Equivalent Fractions

What Are Equivalent Fractions?

Fractions that look different but have the same value:

12=24=36=48\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}

All of these equal one-half!

Creating Equivalent Fractions

Method 1: Multiply

Multiply both numerator and denominator by the same number:

23=2×23×2=46\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}

23=2×53×5=1015\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}

Method 2: Divide (Simplifying)

Divide both numerator and denominator by the same number:

68=6÷28÷2=34\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}

Simplest Form

A fraction is in simplest form when the numerator and denominator have no common factors except 1:

  • 34\frac{3}{4} is in simplest form
  • 68\frac{6}{8} is NOT (it can simplify to 34\frac{3}{4})

Why Is This Useful?

  • Comparing fractions
  • Adding and subtracting fractions
  • Understanding the same amount in different ways

📚 Practice Problems

1Problem 1easy

❓ Question:

Find an equivalent fraction for 13\frac{1}{3} by multiplying by 2.

💡 Show Solution

Solution:

Multiply both top and bottom by 2:

1×23×2=26\frac{1 \times 2}{3 \times 2} = \frac{2}{6}

Answer: 26\frac{2}{6}

2Problem 2easy

❓ Question:

Find an equivalent fraction for 13\frac{1}{3} by multiplying by 2.

💡 Show Solution

Solution:

Multiply both top and bottom by 2:

1×23×2=26\frac{1 \times 2}{3 \times 2} = \frac{2}{6}

Answer: 26\frac{2}{6}

3Problem 3medium

❓ Question:

Simplify 812\frac{8}{12} to simplest form.

💡 Show Solution

Solution:

Find a common factor of 8 and 12: Both divide by 4:

8÷412÷4=23\frac{8 \div 4}{12 \div 4} = \frac{2}{3}

Answer: 23\frac{2}{3}

4Problem 4medium

❓ Question:

Simplify 812\frac{8}{12} to simplest form.

💡 Show Solution

Solution:

Find a common factor of 8 and 12: Both divide by 4:

8÷412÷4=23\frac{8 \div 4}{12 \div 4} = \frac{2}{3}

Answer: 23\frac{2}{3}

5Problem 5hard

❓ Question:

Are 35\frac{3}{5} and 1220\frac{12}{20} equivalent? Explain.

💡 Show Solution

Solution:

Check by simplifying 1220\frac{12}{20}:

Find common factor (both divide by 4): 12÷420÷4=35\frac{12 \div 4}{20 \div 4} = \frac{3}{5}

Since 1220\frac{12}{20} simplifies to 35\frac{3}{5}, they are equivalent!

Answer: Yes, they are equivalent

6Problem 6hard

❓ Question:

Are 35\frac{3}{5} and 1220\frac{12}{20} equivalent? Explain.

💡 Show Solution

Solution:

Check by simplifying 1220\frac{12}{20}:

Find common factor (both divide by 4): 12÷420÷4=35\frac{12 \div 4}{20 \div 4} = \frac{3}{5}

Since 1220\frac{12}{20} simplifies to 35\frac{3}{5}, they are equivalent!

Answer: Yes, they are equivalent

Explain using:
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Comparing Fractions
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📌 Related Topics in Fractions

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

❓ Frequently Asked Questions

What is Equivalent Fractions?▾
Find fractions that represent the same value
How can I study Equivalent 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 Equivalent Fractions study guide free?▾
Yes — all study notes, flashcards, and practice problems for Equivalent Fractions on Study Mondo are free to access. No account is needed.
What course covers Equivalent Fractions?▾
Equivalent 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 Equivalent 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.