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Academy11+

⚖️ Equivalent Fractions

Learn to find and create equivalent fractions. Understand how different fractions can represent the same part of a whole.

Beginner Level
30-40 minutes
Fraction Foundation

What are Equivalent Fractions?

Equivalent fractions represent the same value! ⚖️

Equivalent fractions are different fractions that represent the same part of a whole. They have different numerators and denominators but equal values. Understanding equivalent fractions is the foundation for working with fractions.

Same Value
Different forms

Fractions that represent the same part of a whole. They have equal values but different numerators and denominators.

Multiplication
Scale up

Multiply numerator and denominator by the same number to create equivalent fractions. This scales the fraction up.

Division
Simplify

Divide numerator and denominator by the same number to simplify fractions. This creates equivalent fractions in simplest form.

Key Concepts

Equal Values

Equivalent fractions represent the same part of a whole. They have equal values but different numerators and denominators.

Multiplication Method

Multiply both numerator and denominator by the same number to create equivalent fractions. This scales the fraction up.

Simplification

Divide both numerator and denominator by the same number to simplify fractions. This creates equivalent fractions in simplest form.

Detailed Examples

Example 1: Creating Equivalent Fractions

Multiply by Same Number

Original: 1/2
Multiply by 2: 1×2/2×2
Result: 2/4
Multiply by 3: 1×3/2×3
Result: 3/6
Rule: Multiply both by same number

Equivalent Fractions

• 1/2 = 2/4 = 3/6 = 4/8
• All represent the same value
• Different numerators and denominators
• Can be created by multiplying
• Can be simplified by dividing

Example 2: Simplifying Fractions

Divide by Common Factor

Original: 8/12
Common factor: 4
Divide: 8÷4/12÷4
Result: 2/3
Rule: Divide both by common factor

Simplification Tips

• Find the greatest common factor
• Divide numerator and denominator
• Keep dividing until no common factors
• Check if fraction is in simplest form
• Always check your answer

Example 3: Finding Missing Numbers

Cross-Multiplication Method

Problem: 2/3 = ?/12
Cross-multiply: 2 × 12 = 3 × ?
24 = 3 × ?
? = 24 ÷ 3 = 8
Answer: 2/3 = 8/12
Rule: Cross-multiply to find missing number

Cross-Multiplication

• If a/b = c/d, then a×d = b×c
• Use to find missing numbers
• Use to check if fractions are equivalent
• Works for any equivalent fractions
• Always check your answer

Interactive Activities

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Activity 1: Equivalent Fraction Finder

Find equivalent fractions by multiplying or dividing.

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Activity 2: Fraction Simplifier

Simplify fractions to their lowest terms.

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Activity 3: Missing Number Finder

Find missing numbers in equivalent fractions.

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Activity 4: Equivalent Fraction Quiz

Test your knowledge with interactive questions.

Practice Questions

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4 practice questions on this topic, from easy to 11+ level. Reading the guide is free for everyone; practice is for members, and signing up is free.

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Tips and Tricks

Creating Equivalent Fractions

  • • Multiply numerator and denominator by same number
  • • This scales the fraction up
  • • The value stays the same
  • • Use any whole number except 0
  • • Check your answer makes sense

Simplifying Fractions

  • • Find the greatest common factor
  • • Divide numerator and denominator by it
  • • Keep dividing until no common factors
  • • Check if fraction is in simplest form
  • • Always check your answer

Cross-Multiplication

  • • If a/b = c/d, then a×d = b×c
  • • Use to find missing numbers
  • • Use to check if fractions are equivalent
  • • Works for any equivalent fractions
  • • Always check your answer

Memory Tricks

  • • "Multiply both by same number"
  • • "Divide by common factors"
  • • "Cross-multiply to check"
  • • "Always simplify to lowest terms"
  • • "Check your answer makes sense"