Finding Equivalent Fractions Worksheets for 4th Grade Students

Complete collection of finding equivalent fractions worksheets: 15 practice problems with step-by-step solutions and visual models for 4th grade students.

Finding Equivalent Fractions - Basic Level

Instructions:

Complete each problem by finding the equivalent fraction. Use the method: multiply both numerator and denominator by the same number. Show your work.

1 Basic Equivalent Fraction
1
Find an equivalent fraction for 1/2 by multiplying by 2.
1/2
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1/2 × 2/2 = ?
Work shown:

Step 1: Multiply numerator by 2: 1 × 2 = 2

Step 2: Multiply denominator by 2: 2 × 2 = 4

Step 3: So 1/2 × 2/2 = 2/4

Therefore: 1/2 = 2/4

Verification:

1/2 = 0.5, 2/4 = 0.5 ✓

2 Basic Equivalent Fraction
2
Find an equivalent fraction for 2/3 by multiplying by 3.
2/3
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2/3 × 3/3 = ?
Work shown:

Step 1: Multiply numerator by 3: 2 × 3 = 6

Step 2: Multiply denominator by 3: 3 × 3 = 9

Step 3: So 2/3 × 3/3 = 6/9

Therefore: 2/3 = 6/9

Verification:

2/3 ≈ 0.667, 6/9 ≈ 0.667 ✓

3 Basic Equivalent Fraction
3
Find an equivalent fraction for 3/4 by multiplying by 2.
3/4
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3/4 × 2/2 = ?
Work shown:

Step 1: Multiply numerator by 2: 3 × 2 = 6

Step 2: Multiply denominator by 2: 4 × 2 = 8

Step 3: So 3/4 × 2/2 = 6/8

Therefore: 3/4 = 6/8

Verification:

3/4 = 0.75, 6/8 = 0.75 ✓

4 Basic Equivalent Fraction
4
Find an equivalent fraction for 4/5 by multiplying by 3.
4/5
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4/5 × 3/3 = ?
Work shown:

Step 1: Multiply numerator by 3: 4 × 3 = 12

Step 2: Multiply denominator by 3: 5 × 3 = 15

Step 3: So 4/5 × 3/3 = 12/15

Therefore: 4/5 = 12/15

Verification:

4/5 = 0.8, 12/15 = 0.8 ✓

Finding Equivalent Fractions - Intermediate Level
5 Finding Missing Numerators
5
Find the missing numerator: 2/3 = ?/6
2/3
2/3
=
?/6
?/6
Work shown:

Step 1: Look at the denominators: 3 → 6

Step 2: 3 × 2 = 6, so multiply by 2

Step 3: Multiply numerator by the same number: 2 × 2 = 4

Step 4: So 2/3 = 4/6

Verification:

2/3 = 0.667, 4/6 = 0.667 ✓

6 Finding Missing Denominators
6
Find the missing denominator: 3/4 = 6/?
3/4
3/4
=
6/?
6/?
Work shown:

Step 1: Look at the numerators: 3 → 6

Step 2: 3 × 2 = 6, so multiply by 2

Step 3: Multiply denominator by the same number: 4 × 2 = 8

Step 4: So 3/4 = 6/8

Verification:

3/4 = 0.75, 6/8 = 0.75 ✓

7 Multiple Operations
7
Find two equivalent fractions for 1/2.
1/2
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🍕
1/2 × 2/2 = 2/4
1/2 × 3/3 = 3/6
Work shown:

Step 1: Multiply 1/2 by 2/2: (1×2)/(2×2) = 2/4

Step 2: Multiply 1/2 by 3/3: (1×3)/(2×3) = 3/6

Step 3: So 1/2 = 2/4 = 3/6

Verification:

1/2 = 0.5, 2/4 = 0.5, 3/6 = 0.5 ✓

8 Simplifying Fractions
8
Simplify 6/8 to its lowest terms.
6/8
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6/8 ÷ 2/2 = 3/4
Work shown:

Step 1: Find the GCF of 6 and 8 (GCF = 2)

Step 2: Divide numerator by 2: 6 ÷ 2 = 3

Step 3: Divide denominator by 2: 8 ÷ 2 = 4

Step 4: So 6/8 = 3/4

Verification:

6/8 = 0.75, 3/4 = 0.75 ✓

Finding Equivalent Fractions - Advanced Level + Answer Key
9 Advanced Equivalent Fraction
9
Find an equivalent fraction for 5/6 by multiplying by 4.
5/6
🎂
🎂
🎂
🎂
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5/6 × 4/4 = ?
Work shown:

Step 1: Multiply numerator by 4: 5 × 4 = 20

Step 2: Multiply denominator by 4: 6 × 4 = 24

Step 3: So 5/6 × 4/4 = 20/24

Therefore: 5/6 = 20/24

Verification:

5/6 ≈ 0.833, 20/24 ≈ 0.833 ✓

10 Advanced Equivalent Fraction
10
Find an equivalent fraction for 7/9 by multiplying by 5.
7/9
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⭐
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7/9 × 5/5 = ?
Work shown:

Step 1: Multiply numerator by 5: 7 × 5 = 35

Step 2: Multiply denominator by 5: 9 × 5 = 45

Step 3: So 7/9 × 5/5 = 35/45

Therefore: 7/9 = 35/45

Verification:

7/9 ≈ 0.778, 35/45 ≈ 0.778 ✓

11 Cross-Multiplication Check
11
Are 3/7 and 9/21 equivalent fractions?
3/7
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⭐
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⭐
⭐
⭐
9/21
⭐
⭐
⭐
⭐
⭐
⭐
⭐
⭐
⭐
⭐
⭐
⭐
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Work shown:

Step 1: Cross multiply: 3 × 21 = 63

Step 2: Cross multiply: 7 × 9 = 63

Step 3: Since 63 = 63, the fractions are equivalent

Step 4: So 3/7 = 9/21

Verification:

3/7 ≈ 0.429, 9/21 ≈ 0.429 ✓

Complete Answer Key:
  • 1. 1/2 = 2/4
  • 2. 2/3 = 6/9
  • 3. 3/4 = 6/8
  • 4. 4/5 = 12/15
  • 5. 2/3 = 4/6
  • 6. 3/4 = 6/8
  • 7. 1/2 = 2/4 = 3/6
  • 8. 6/8 = 3/4
  • 9. 5/6 = 20/24
  • 10. 7/9 = 35/45
  • 11. Yes, 3/7 = 9/21
  • 12. 8/12 = 2/3
  • 13. 4/10 = 8/20
  • 14. 15/20 = 3/4
  • 15. 2/5 = 6/15
    • Finding Equivalent Fractions - Complete Guide
    a/b = (a × n)/(b × n) = (a ÷ d)/(b ÷ d)
    Equivalent Fractions Formula
    Finding Equivalent Fractions - Complete Guide
    Core Definitions
  • Equivalent Fractions: Fractions that represent the same value
  • Numerator: The top number in a fraction
  • Denominator: The bottom number in a fraction
  • Simplifying: Making fractions smaller by dividing
  • Expanding: Making fractions larger by multiplying
    • Core Rules and Principles
  • Rule 1: Multiply both numerator and denominator by the same number
  • Rule 2: Divide both numerator and denominator by the same number
  • Rule 3: The value of the fraction stays the same
  • Rule 4: Only multiply or divide, never add or subtract
  • Rule 5: Use cross-multiplication to verify equivalence
    • Step-by-Step Methods
  • Method 1: Multiplication - Multiply top and bottom by same number
  • Method 2: Division - Divide top and bottom by same number
  • Method 3: Cross-multiplication - Check if fractions are equivalent
  • Method 4: GCF method - Simplify by dividing by greatest common factor
  • Method 5: Visual method - Draw fraction models to compare
    • Examples (Progressive Difficulty)
  • Basic: 1/2 = 2/4 (multiply by 2)
  • Simple: 2/3 = 4/6 (multiply by 2)
  • Medium: 6/8 = 3/4 (divide by 2)
  • Advanced: 12/18 = 2/3 (divide by GCF 6)
  • Complex: 15/25 = 3/5 (divide by GCF 5)
    • Tips and Tricks
  • Tip 1: Always check your answer by converting to decimals
  • Tip 2: Use visual models to understand the concept
  • Tip 3: Remember to do the same operation to both numerator and denominator
  • Tip 4: Practice with small numbers first
  • Tip 5: Look for patterns in multiplication tables
    • Common Pitfalls to Avoid
  • Pitfall 1: Adding or subtracting instead of multiplying or dividing
  • Pitfall 2: Only changing the numerator or denominator
  • Pitfall 3: Forgetting to verify the answer
  • Pitfall 4: Using different numbers for numerator and denominator
  • Pitfall 5: Not simplifying to lowest terms when possible
    • Key Notes for Memorization
  • Remember: Equivalent fractions have the same value
  • Always multiply or divide both parts by the same number
  • Use cross-multiplication to check: a/b = c/d if a×d = b×c
  • To simplify, divide by the greatest common factor
  • Equivalent fractions are like different names for the same amount
    • Real-World Applications
  • Sharing food portions equally
  • Measuring ingredients in recipes
  • Comparing prices per unit
  • Understanding time fractions
  • Working with percentages
  • Scaling measurements
    • 1/2
    1/2
    =
    2/4
    2/4
    =
    4/8
    4/8
    All represent the same amount!
    Verification:

    1/2 = 0.5, 2/4 = 0.5, 4/8 = 0.5 ✓

    Questions & Answers

    Question: Why do equivalent fractions have the same value even though they look different?

    Answer: Great question! Equivalent fractions represent the same portion of a whole. Think of it like this:

    • 1/2 of a pizza is the same as 2/4 of a pizza
    • We cut the pizza differently, but the amount is the same
    • When you multiply or divide both numerator and denominator by the same number, you're just changing how you count the pieces, not the actual amount

    Example: 1/2 = 2/4 because both represent half of something!

    Question: How can I help my child practice finding equivalent fractions?

    Answer: Here are effective strategies:

    • Use visual aids: Draw circles or rectangles divided into different parts
    • Use real objects: Cut pizzas, pies, or chocolate bars to demonstrate
    • Practice with games: Fraction matching games or apps
    • Connect to daily life: Cooking, sharing food, telling time
    • Start simple: Begin with halves, thirds, and quarters

    Hands-on activities make abstract concepts more concrete!

    Question: How do I know if I found the right equivalent fraction?

    Answer: Here are verification methods:

    • Convert to decimals: Divide numerator by denominator for both fractions
    • Cross-multiply: If a/b = c/d, then a×d should equal b×c
    • Visual check: Draw models to compare the amounts
    • Common sense: Does the answer make sense?

    Example: To check if 2/3 = 4/6, cross multiply: 2×6 = 12, 3×4 = 12. Since 12 = 12, they are equivalent!