Complete Comparing Fractions Worksheet for Grade 5

Master advanced fraction comparison methods: same numerator, same denominator, unlike denominators, mixed numbers, improper fractions, decimal conversions, and complex comparison strategies through this comprehensive worksheet with 30 detailed exercises designed specifically for grade 5 students.

Comparing Fractions Worksheet Grade 5
Learning Progress: Advanced Fraction Comparison

30 exercises completed | Ready for assessment

Exercise Problems (Grade 5 Level)
1.
3/7 _____ 4/9
<
2.
5/8 _____ 7/11
<
3.
2/3 _____ 5/6
<
4.
7/12 _____ 5/8
<
5.
11/15 _____ 7/9
>
6.
4/5 _____ 9/10
<
7.
8/13 _____ 5/8
<
8.
6/7 _____ 11/12
<
9.
3/4 _____ 7/10
>
10.
9/14 _____ 5/7
<
11.
1 2/3 _____ 5/3
=
12.
2 1/4 _____ 9/4
=
13.
1 3/5 _____ 8/5
=
14.
0.6 _____ 3/5
=
15.
0.75 _____ 3/4
=
16.
0.4 _____ 2/5
=
17.
2 3/4 _____ 2.75
=
18.
1 1/2 _____ 1.6
<
19.
0.8 _____ 4/5
=
20.
0.333... _____ 1/3
=
21.
13/16 _____ 7/8
<
22.
17/20 _____ 4/5
>
23.
19/24 _____ 5/6
<
24.
23/30 _____ 4/5
<
25.
29/36 _____ 5/6
>
26.
31/40 _____ 3/4
>
27.
37/48 _____ 3/4
<
28.
41/48 _____ 7/8
>
29.
43/56 _____ 3/4
<
30.
47/60 _____ 5/6
<
Solutions: Problems 1-5
Problem 1: 3/7 vs 4/9 (Cross Multiplication)

Method: Cross multiplication

3/7 vs 4/9

3×9 = 27 and 4×7 = 28

Since 27 < 28, then 3/7 < 4/9.

Problem 2: 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 3: 2/3 vs 5/6 (Common Denominator)

Method: Find common denominator (LCM of 3 and 6 is 6)

2/3 = (2×2)/(3×2) = 4/6

5/6 = 5/6

Since 4 < 5, then 4/6 < 5/6, so 2/3 < 5/6.

3/7
4/9
Solutions: Problems 6-10
Problem 6: 4/5 vs 9/10 (Common Denominator)

Method: Find common denominator (LCM of 5 and 10 is 10)

4/5 = (4×2)/(5×2) = 8/10

9/10 = 9/10

Since 8 < 9, then 8/10 < 9/10, so 4/5 < 9/10.

Problem 7: 8/13 vs 5/8 (Cross Multiplication)

Method: Cross multiplication

8/13 vs 5/8

8×8 = 64 and 5×13 = 65

Since 64 < 65, then 8/13 < 5/8.

Problem 8: 6/7 vs 11/12 (Cross Multiplication)

Method: Cross multiplication

6/7 vs 11/12

6×12 = 72 and 11×7 = 77

Since 72 < 77, then 6/7 < 11/12.

6/8
5/6
Grade 5 Fraction Comparison Guide
Complete Summary for Grade 5 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
  • Mixed Numbers: Whole numbers combined with fractions
  • Improper Fractions: Fractions where numerator ≥ denominator
  • Decimal Conversion: Converting fractions to decimals for comparison

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, cross multiplication, or decimal conversion
  3. Apply the method: Perform the necessary calculations
  4. Compare results: Determine which fraction is greater
  5. Convert mixed numbers: Change to improper fractions if needed
  6. 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)
  • Grade 5: 2 1/4 vs 9/4 (mixed numbers to improper)
  • Advanced Grade 5: 0.75 vs 3/4 (decimal to fraction conversion)

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
  • Convert mixed numbers to improper fractions before comparing
  • Convert fractions to decimals when denominators are large
  • 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
  • Incorrect conversion of mixed numbers to improper fractions
  • Decimal conversion errors

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"
  • "Mixed number: whole × denominator + numerator"
  • "Convert to same form before comparing"
Grade 5 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).

Mixed Numbers: A whole number combined with a proper fraction (e.g., 2 1/3).

Improper Fractions: Fractions where the numerator is greater than or equal to the denominator (e.g., 7/3).

Cross Multiplication: a/b vs c/d → Compare a×d vs b×c
Cross Multiplication Method
Mixed to Improper: a b/c = (a×c + b)/c
Mixed Number Conversion
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
Mixed to Improper
a b/c
(a×c + 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.
Mixed Numbers
Whole numbers combined with fractions that need conversion to improper fractions for comparison.
Decimal Conversion
Converting fractions to decimals for easier comparison when denominators are large.
Tip 1: Always find the LCM for the most efficient common denominator.
Tip 2: Use cross multiplication for quick comparisons.
Tip 3: Convert mixed numbers to improper fractions 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, improper mixed number conversion.
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

• Mixed to improper: a b/c = (a×c + b)/c

Solutions: Problems 11-30
Problems 11-15 Solutions
Problem 11: 1 2/3 vs 5/3 (Mixed Number Conversion)

Method: Convert mixed number to improper fraction

1 2/3 = (1×3 + 2)/3 = 5/3

Since both equal 5/3, then 1 2/3 = 5/3.

Problem 12: 2 1/4 vs 9/4 (Mixed Number Conversion)

Method: Convert mixed number to improper fraction

2 1/4 = (2×4 + 1)/4 = 9/4

Since both equal 9/4, then 2 1/4 = 9/4.

Problem 13: 1 3/5 vs 8/5 (Mixed Number Conversion)

Method: Convert mixed number to improper fraction

1 3/5 = (1×5 + 3)/5 = 8/5

Since both equal 8/5, then 1 3/5 = 8/5.

Problem 14: 0.6 vs 3/5 (Decimal Conversion)

Method: Convert decimal to fraction or fraction to decimal

0.6 = 6/10 = 3/5

Since both equal 3/5, then 0.6 = 3/5.

Problem 15: 0.75 vs 3/4 (Decimal Conversion)

Method: Convert decimal to fraction or fraction to decimal

0.75 = 75/100 = 3/4

Since both equal 3/4, then 0.75 = 3/4.

Problems 16-20 Solutions
Problem 16: 0.4 vs 2/5 (Decimal Conversion)

Method: Convert decimal to fraction or fraction to decimal

0.4 = 4/10 = 2/5

Since both equal 2/5, then 0.4 = 2/5.

Problem 17: 2 3/4 vs 2.75 (Mixed Number Conversion)

Method: Convert mixed number to decimal

2 3/4 = 2 + 3/4 = 2 + 0.75 = 2.75

Since both equal 2.75, then 2 3/4 = 2.75.

Problem 18: 1 1/2 vs 1.6 (Mixed Number Conversion)

Method: Convert mixed number to decimal

1 1/2 = 1 + 1/2 = 1 + 0.5 = 1.5

Since 1.5 < 1.6, then 1 1/2 < 1.6.

Problem 19: 0.8 vs 4/5 (Decimal Conversion)

Method: Convert decimal to fraction or fraction to decimal

0.8 = 8/10 = 4/5

Since both equal 4/5, then 0.8 = 4/5.

Problem 20: 0.333... vs 1/3 (Decimal Conversion)

Method: Recognize repeating decimal

0.333... = 1/3

Since both equal 1/3, then 0.333... = 1/3.

Problems 21-25 Solutions
Problem 21: 13/16 vs 7/8 (Common Denominator)

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

13/16 = 13/16

7/8 = (7×2)/(8×2) = 14/16

Since 13 < 14, then 13/16 < 14/16, so 13/16 < 7/8.

Problem 22: 17/20 vs 4/5 (Common Denominator)

Method: Find common denominator (LCM of 20 and 5 is 20)

17/20 = 17/20

4/5 = (4×4)/(5×4) = 16/20

Since 17 > 16, then 17/20 > 16/20, so 17/20 > 4/5.

Problem 23: 19/24 vs 5/6 (Common Denominator)

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

19/24 = 19/24

5/6 = (5×4)/(6×4) = 20/24

Since 19 < 20, then 19/24 < 20/24, so 19/24 < 5/6.

Problem 24: 23/30 vs 4/5 (Common Denominator)

Method: Find common denominator (LCM of 30 and 5 is 30)

23/30 = 23/30

4/5 = (4×6)/(5×6) = 24/30

Since 23 < 24, then 23/30 < 24/30, so 23/30 < 4/5.

Problem 25: 29/36 vs 5/6 (Common Denominator)

Method: Find common denominator (LCM of 36 and 6 is 36)

29/36 = 29/36

5/6 = (5×6)/(6×6) = 30/36

Since 29 < 30, then 29/36 < 30/36, so 29/36 < 5/6.

Problems 26-30 Solutions
Problem 26: 31/40 vs 3/4 (Common Denominator)

Method: Find common denominator (LCM of 40 and 4 is 40)

31/40 = 31/40

3/4 = (3×10)/(4×10) = 30/40

Since 31 > 30, then 31/40 > 30/40, so 31/40 > 3/4.

Problem 27: 37/48 vs 3/4 (Common Denominator)

Method: Find common denominator (LCM of 48 and 4 is 48)

37/48 = 37/48

3/4 = (3×12)/(4×12) = 36/48

Since 37 > 36, then 37/48 > 36/48, so 37/48 > 3/4.

Problem 28: 41/48 vs 7/8 (Common Denominator)

Method: Find common denominator (LCM of 48 and 8 is 48)

41/48 = 41/48

7/8 = (7×6)/(8×6) = 42/48

Since 41 < 42, then 41/48 < 42/48, so 41/48 < 7/8.

Problem 29: 43/56 vs 3/4 (Common Denominator)

Method: Find common denominator (LCM of 56 and 4 is 56)

43/56 = 43/56

3/4 = (3×14)/(4×14) = 42/56

Since 43 > 42, then 43/56 > 42/56, so 43/56 > 3/4.

Problem 30: 47/60 vs 5/6 (Common Denominator)

Method: Find common denominator (LCM of 60 and 6 is 60)

47/60 = 47/60

5/6 = (5×10)/(6×10) = 50/60

Since 47 < 50, then 47/60 < 50/60, so 47/60 < 5/6.

25/48
1/2
Grade 5 Assessment Preparation
Advanced Fraction Comparison Mastery
Grade 5 Skills Checklist
Key definitions:

Advanced fraction comparison: Determining which fraction is greater, lesser, or equal through systematic analysis using multiple methods appropriate for grade 5 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

Mixed numbers: Whole numbers combined with fractions that need conversion for comparison

Decimal conversion: Converting fractions to decimals for easier comparison

Grade 5 methodology:
  1. Examine the fractions: Identify numerators, denominators, mixed numbers, or decimals
  2. Choose the best method: Same numerator, same denominator, common denominator, cross multiplication, decimal conversion, or mixed number conversion
  3. Apply the method: Perform the necessary calculations
  4. Compare results: Determine which fraction is greater
  5. Convert if needed: Change mixed numbers to improper fractions or decimals
  6. Verify with visual model: Draw a picture if needed
  7. 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: Convert mixed numbers to improper fractions 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, improper mixed number conversion.
Assessment prep: Master all methods, practice with unlike denominators, mixed numbers, decimals, understand equivalent fractions.
Grade 5 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

• Mixed numbers: Convert to improper fractions first

• Decimal conversion: Convert to same form for comparison

• Always check with visual models

Grade 5 Fraction Comparison Mastery

Grade 5 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
  • Mixed numbers: Convert to improper fractions first
  • Decimal conversion: Convert to same form for comparison
  • 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 converting mixed numbers to improper fractions. How do I do that?

Answer: Converting mixed numbers to improper fractions follows this simple formula:

Formula: a b/c = (a×c + b)/c

Steps:

  1. Multiply the whole number by the denominator
  2. Add the numerator to the result
  3. Put the sum over the original denominator

Example: 2 3/4

  • Step 1: 2 × 4 = 8
  • Step 2: 8 + 3 = 11
  • Step 3: 11/4
  • So 2 3/4 = 11/4

This makes comparing mixed numbers much easier!

Question: My child is struggling with decimal conversions. When should they convert fractions to decimals?

Answer: Converting fractions to decimals is especially useful when:

  1. Denominators are large primes: Hard to find common denominators
  2. Quick comparisons: You need an answer fast
  3. Calculator available: Makes conversion easy
  4. Word problems: Decimals are more intuitive for some contexts

Common conversions to remember:

  • 1/2 = 0.5
  • 1/4 = 0.25, 3/4 = 0.75
  • 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8
  • 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875

Decimal conversion provides another method for comparing fractions!

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

Answer: Here are effective practice strategies for grade 5 fraction comparison:

  • Daily practice: 20-25 minutes per day is ideal
  • Multiple methods: Practice common denominator, cross multiplication, decimal conversion, and mixed number conversion
  • Real-world examples: Use recipes, measurements, and money to illustrate fractions
  • Games and apps: Make learning fun with fraction comparison games
  • Worksheets: Provide variety in difficulty levels
  • Word problems: Apply fraction comparison in context

Weekly schedule suggestion:

  • Monday/Wednesday/Friday: Focus on common denominator method
  • Tuesday/Thursday: Focus on cross multiplication and decimal conversion
  • Saturday: Mixed practice with visual models
  • Sunday: Word problems and review

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