Complete Comparing Fractions Worksheet for Grade 4

Master advanced fraction comparison methods: same numerator, same denominator, unlike denominators, cross multiplication, and mixed comparison strategies through this comprehensive worksheet with 25 detailed exercises designed specifically for grade 4 students.

Comparing Fractions Worksheet Grade 4
Learning Progress: Advanced Fraction Comparison

25 exercises completed | Ready for assessment

Exercise Problems (Grade 4 Level)
1.
2/3 _____ 3/4
<
2.
5/6 _____ 7/8
<
3.
1/4 _____ 2/8
=
4.
3/5 _____ 4/7
>
5.
2/9 _____ 1/6
>
6.
7/10 _____ 5/7
>
7.
1/3 _____ 3/9
=
8.
4/9 _____ 5/12
>
9.
3/8 _____ 2/5
<
10.
6/11 _____ 5/9
<
11.
2/7 _____ 3/10
>
12.
5/8 _____ 7/11
>
13.
4/6 _____ 6/9
=
14.
1/5 _____ 2/11
>
15.
8/15 _____ 5/9
<
16.
7/12 _____ 3/5
>
17.
3/14 _____ 2/9
<
18.
9/16 _____ 5/8
<
19.
4/11 _____ 3/8
<
20.
5/13 _____ 3/7
<
21.
6/17 _____ 4/11
<
22.
8/21 _____ 3/7
<
23.
7/18 _____ 5/12
>
24.
9/20 _____ 4/9
>
25.
11/24 _____ 5/11
>
Solutions: Problems 1-5
Problem 1: 2/3 vs 3/4 (Unlike Denominators)

Method: Find common denominator (LCM of 3 and 4 is 12)

2/3 = (2×4)/(3×4) = 8/12

3/4 = (3×3)/(4×3) = 9/12

Since 8 < 9, then 8/12 < 9/12, so 2/3 < 3/4.

Problem 2: 5/6 vs 7/8 (Unlike Denominators)

Method: Find common denominator (LCM of 6 and 8 is 24)

5/6 = (5×4)/(6×4) = 20/24

7/8 = (7×3)/(8×3) = 21/24

Since 20 < 21, then 20/24 < 21/24, so 5/6 < 7/8.

Problem 3: 1/4 vs 2/8 (Equivalent Fractions)

Method: Simplify 2/8 to lowest terms

2/8 = (2÷2)/(8÷2) = 1/4

Since both fractions equal 1/4, then 1/4 = 2/8.

2/3
3/4
Solutions: Problems 6-10
Problem 6: 7/10 vs 5/7 (Unlike Denominators)

Method: Cross multiplication

7/10 vs 5/7

7×7 = 49 and 5×10 = 50

Since 49 < 50, then 7/10 < 5/7.

Problem 7: 1/3 vs 3/9 (Equivalent Fractions)

Method: Simplify 3/9 to lowest terms

3/9 = (3÷3)/(9÷3) = 1/3

Since both fractions equal 1/3, then 1/3 = 3/9.

Problem 8: 4/9 vs 5/12 (Unlike Denominators)

Method: Find common denominator (LCM of 9 and 12 is 36)

4/9 = (4×4)/(9×4) = 16/36

5/12 = (5×3)/(12×3) = 15/36

Since 16 > 15, then 16/36 > 15/36, so 4/9 > 5/12.

4/9
5/12
Grade 4 Fraction Comparison Guide
Complete Summary for Grade 4 Students

Core Concepts and Definitions

Fractions are numbers that represent parts of a whole. A fraction has two parts: the numerator (top number) tells how many parts we have, and the denominator (bottom number) tells how many equal parts the whole is divided into.

Advanced Rules and Principles

  • Same Denominator Rule: When denominators are equal, compare numerators directly
  • Same Numerator Rule: When numerators are equal, compare denominators inversely
  • Common Denominator Method: Convert fractions to have the same denominator, then compare numerators
  • Cross Multiplication: For a/b vs c/d, compare a×d vs b×c
  • Equivalent Fractions: Fractions that represent the same value

Step-by-Step Methods

  1. Examine the fractions: Check if numerators or denominators are the same
  2. Choose the method: Same denominator, same numerator, common denominator, or cross multiplication
  3. Apply the method: Perform the necessary calculations
  4. Compare results: Determine which fraction is greater
  5. Draw a picture: Verify with visual model if needed

Examples from Simple to Advanced

  • Simple: 1/2 vs 1/3 (same numerator)
  • Intermediate: 2/5 vs 3/5 (same denominator)
  • Advanced: 2/3 vs 3/4 (find common denominator)
  • Complex: 7/12 vs 5/9 (cross multiplication)

Tips and Tricks

  • Always start by looking at the numerators and denominators
  • Find the LCM of denominators for common denominator method
  • Use cross multiplication for quick comparisons
  • Check if fractions can be simplified first
  • Draw pie charts or bar models to verify answers

Common Mistakes to Avoid

  • Comparing denominators directly when numerators are the same
  • Not finding the correct common denominator
  • Mistakes in cross multiplication
  • Forgetting to adjust the numerator when changing the denominator

Key Notes for Memorization

  • "Same bottom, compare tops: bigger top wins"
  • "Same top, smaller bottom wins: fewer pieces = bigger pieces"
  • "Cross multiply: multiply diagonally and compare"
  • "Find LCM for common denominator method"
Grade 4 Advanced Concepts

Least Common Multiple (LCM): The smallest number that is a multiple of both denominators. Use prime factorization or listing multiples to find LCM.

Greatest Common Factor (GCF): Used to simplify fractions to lowest terms.

Equivalent Fractions: Fractions that represent the same value (e.g., 1/2 = 2/4 = 3/6).

Cross Multiplication: a/b vs c/d → Compare a×d vs b×c
Cross Multiplication Method
Common Denominator: a/b vs c/d → Convert to (a×n)/(b×n) vs (c×m)/(d×m)
Common Denominator Method
Same Denominator
a/c vs b/c
Compare numerators: a vs b
Same Numerator
a/b vs a/c
Compare denominators: b vs c (inversely)
Cross Multiplication
a/b vs c/d
Compare a×d vs b×c
Common Denominator Method
Convert fractions to have the same denominator, then compare numerators directly.
Cross Multiplication
Multiply numerator of first fraction by denominator of second fraction, and vice versa.
Equivalent Fractions
Fractions that represent the same value but have different numerators and denominators.
Tip 1: Always find the LCM for the most efficient common denominator.
Tip 2: Use cross multiplication for quick comparisons.
Tip 3: Check if fractions can be simplified before comparing.
Tip 4: Draw visual models to verify your answers.
Common errors: Forgetting to adjust numerators when changing denominators, incorrect LCM calculation, cross multiplication mistakes.
Key insight: The relationship between numerator and denominator determines fraction size.
Essential formulas:

• Same denominator: a/c vs b/c → Compare a vs b

• Same numerator: a/b vs a/c → Compare b vs c inversely

• Cross multiplication: a/b vs c/d → Compare a×d vs b×c

• Common denominator: Convert to same denominator, then compare numerators

Solutions: Problems 11-25
Problems 11-15 Solutions
Problem 11: 2/7 vs 3/10 (Cross Multiplication)

Method: Cross multiplication

2/7 vs 3/10

2×10 = 20 and 3×7 = 21

Since 20 < 21, then 2/7 < 3/10.

Problem 12: 5/8 vs 7/11 (Cross Multiplication)

Method: Cross multiplication

5/8 vs 7/11

5×11 = 55 and 7×8 = 56

Since 55 < 56, then 5/8 < 7/11.

Problem 13: 4/6 vs 6/9 (Equivalent Fractions)

Method: Simplify both fractions

4/6 = (4÷2)/(6÷2) = 2/3

6/9 = (6÷3)/(9÷3) = 2/3

Since both equal 2/3, then 4/6 = 6/9.

Problem 14: 1/5 vs 2/11 (Cross Multiplication)

Method: Cross multiplication

1/5 vs 2/11

1×11 = 11 and 2×5 = 10

Since 11 > 10, then 1/5 > 2/11.

Problem 15: 8/15 vs 5/9 (Common Denominator)

Method: Find common denominator (LCM of 15 and 9 is 45)

8/15 = (8×3)/(15×3) = 24/45

5/9 = (5×5)/(9×5) = 25/45

Since 24 < 25, then 24/45 < 25/45, so 8/15 < 5/9.

Problems 16-20 Solutions
Problem 16: 7/12 vs 3/5 (Cross Multiplication)

Method: Cross multiplication

7/12 vs 3/5

7×5 = 35 and 3×12 = 36

Since 35 < 36, then 7/12 < 3/5.

Problem 17: 3/14 vs 2/9 (Cross Multiplication)

Method: Cross multiplication

3/14 vs 2/9

3×9 = 27 and 2×14 = 28

Since 27 < 28, then 3/14 < 2/9.

Problem 18: 9/16 vs 5/8 (Common Denominator)

Method: Find common denominator (LCM of 16 and 8 is 16)

9/16 = 9/16

5/8 = (5×2)/(8×2) = 10/16

Since 9 < 10, then 9/16 < 10/16, so 9/16 < 5/8.

Problem 19: 4/11 vs 3/8 (Cross Multiplication)

Method: Cross multiplication

4/11 vs 3/8

4×8 = 32 and 3×11 = 33

Since 32 < 33, then 4/11 < 3/8.

Problem 20: 5/13 vs 3/7 (Cross Multiplication)

Method: Cross multiplication

5/13 vs 3/7

5×7 = 35 and 3×13 = 39

Since 35 < 39, then 5/13 < 3/7.

Problems 21-25 Solutions
Problem 21: 6/17 vs 4/11 (Cross Multiplication)

Method: Cross multiplication

6/17 vs 4/11

6×11 = 66 and 4×17 = 68

Since 66 < 68, then 6/17 < 4/11.

Problem 22: 8/21 vs 3/7 (Common Denominator)

Method: Find common denominator (LCM of 21 and 7 is 21)

8/21 = 8/21

3/7 = (3×3)/(7×3) = 9/21

Since 8 < 9, then 8/21 < 9/21, so 8/21 < 3/7.

Problem 23: 7/18 vs 5/12 (Common Denominator)

Method: Find common denominator (LCM of 18 and 12 is 36)

7/18 = (7×2)/(18×2) = 14/36

5/12 = (5×3)/(12×3) = 15/36

Since 14 < 15, then 14/36 < 15/36, so 7/18 < 5/12.

Problem 24: 9/20 vs 4/9 (Cross Multiplication)

Method: Cross multiplication

9/20 vs 4/9

9×9 = 81 and 4×20 = 80

Since 81 > 80, then 9/20 > 4/9.

Problem 25: 11/24 vs 5/11 (Cross Multiplication)

Method: Cross multiplication

11/24 vs 5/11

11×11 = 121 and 5×24 = 120

Since 121 > 120, then 11/24 > 5/11.

5/12
7/17
Grade 4 Assessment Preparation
Advanced Fraction Comparison Mastery
Grade 4 Skills Checklist
Key definitions:

Advanced fraction comparison: Determining which fraction is greater, lesser, or equal through systematic analysis using multiple methods appropriate for grade 4 level

Common denominator: Converting fractions to have the same denominator to enable direct comparison of numerators

Cross multiplication: A method to compare fractions without converting to common denominators

Grade 4 methodology:
  1. Examine the fractions: Identify numerators and denominators
  2. Choose the best method: Same numerator, same denominator, common denominator, or cross multiplication
  3. Apply the method: Perform the necessary calculations
  4. Compare results: Determine which fraction is greater
  5. Verify with visual model: Draw a picture if needed
  6. Write the answer: Use >, <, or = symbols
Tip 1: Always find the LCM for the most efficient common denominator.
Tip 2: Use cross multiplication for quick comparisons.
Tip 3: Check if fractions can be simplified before comparing.
Tip 4: Draw pie charts or bar models to verify answers.
Common errors: Forgetting to adjust numerators when changing denominators, incorrect LCM calculation, cross multiplication mistakes.
Assessment prep: Master all methods, practice with unlike denominators, understand equivalent fractions.
Grade 4 reference:

• Same denominator: Compare numerators directly

• Same numerator: Compare denominators inversely

• Cross multiplication: a/b vs c/d → Compare a×d vs b×c

• Common denominator: Convert then compare numerators

• Always check with visual models

Grade 4 Fraction Comparison Mastery

Grade 4 Skills: Mastering advanced fraction comparison through multiple methods.

  • Same denominator: Easy - just compare numerators
  • Same numerator: Remember - smaller denominator wins
  • Cross multiplication: Quick method for unlike denominators
  • Common denominator: Convert then compare numerators
  • Visual models: Use pie charts and bar models to confirm answers
  • Regular practice: Daily practice leads to mastery

Questions & Answers

Question: I'm having trouble finding the common denominator. How do I know what number to use?

Answer: The common denominator is called the Least Common Multiple (LCM). Here's how to find it:

  1. List the multiples: Write multiples of each denominator until you find a common one
  2. Example: For 1/4 and 1/6, multiples of 4 are 4, 8, 12, 16... and multiples of 6 are 6, 12, 18...
  3. Find the smallest: The smallest number that appears in both lists is 12
  4. Alternative method: Multiply denominators together (works but may not be the LCM)

For 1/4 and 1/6: LCM is 12, so convert 1/4 = 3/12 and 1/6 = 2/12, then compare 3/12 vs 2/12.

Practice with smaller numbers first, then work up to larger denominators!

Question: My child is struggling with cross multiplication. When should they use this method?

Answer: Cross multiplication is especially useful when:

  1. Denominators are large: Finding LCM might be difficult
  2. Quick comparisons: You need an answer fast
  3. Unlike denominators: No obvious common denominator

How to do it:

  • For a/b vs c/d, multiply a×d and b×c
  • Compare the two products
  • Whichever product is larger corresponds to the larger fraction

Example: 2/5 vs 3/7

  • 2×7 = 14 and 3×5 = 15
  • Since 15 > 14, then 3/7 > 2/5

Cross multiplication always works but may involve larger numbers!

Question: How can I help my child practice these advanced fraction comparison skills?

Answer: Here are effective practice strategies for grade 4 fraction comparison:

  • Daily practice: 15-20 minutes per day is ideal
  • Multiple methods: Practice both common denominator and cross multiplication
  • Real-world examples: Use food, time, money to illustrate fractions
  • Games and apps: Make learning fun with fraction comparison games
  • Worksheets: Provide variety in difficulty levels

Weekly schedule suggestion:

  • Monday/Wednesday/Friday: Focus on common denominator method
  • Tuesday/Thursday: Focus on cross multiplication method
  • Saturday: Mixed practice with visual models
  • Sunday: Review and light practice

Remember: Consistent practice with immediate feedback is key to mastery!