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Comparing Unlike FractionsFREEWorksheet Generator(Grade 4)

Q: What is the core learning objective for comparing unlike fractions?

Compare two fractions with different numerators and different denominators using benchmark fractions, common denominators, and cross-multiplication, recording results with symbols . This directly aligns with Common Core Standard CCSS.MATH.CONTENT.4.NF.A.2.

Q: How does the unlimited comparing unlike fractions worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of comparing unlike fractions problems with unique numbers. No two worksheets are ever the same — perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

Q: Are these comparing unlike fractions worksheets free to print with answer keys?

Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.

Comparing Unlike Fractions worksheets (Grade 4) with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems.

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Set:

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Set A • 10 Qs

PanMaths.comComparing Unlike Fractions Worksheets • Set A (Medium)

Name: __________________________

Date: _____________ Period: ____

Score: _____ / 10

1.38___35

= ______

Workspace:

2.28___14

= ______

Workspace:

3.16___57

= ______

Workspace:

4.15___34

= ______

Workspace:

5.610___35

= ______

Workspace:

6.47___46

= ______

Workspace:

7.18___14

= ______

Workspace:

8.37___49

= ______

Workspace:

9.12___36

= ______

Workspace:

10.14___23

= ______

Workspace:

PanMaths.com • Free Math Worksheet Generator • Set A (Medium)Page 1 of 2

PanMaths.comAnswer Key & Worked Solutions • Set A (Medium)

Answer Key

Total Problems: 10

1.38___35

= <

1. Cross-Multiply (Butterfly Method): (3 × 5) vs (3 × 8) ➔ 15 vs 24

2. Convert to Common Denominator (40): 3/8 = 15/40; 3/5 = 24/40

3. Comparison: 3/8 < 3/5 ✅

2.28___14

= =

1. Cross-Multiply (Butterfly Method): (2 × 4) vs (1 × 8) ➔ 8 vs 8

2. Convert to Common Denominator (8): 2/8 = 2/8; 1/4 = 2/8

3. Comparison: 2/8 = 1/4 ✅

3.16___57

= <

1. Cross-Multiply (Butterfly Method): (1 × 7) vs (5 × 6) ➔ 7 vs 30

2. Convert to Common Denominator (42): 1/6 = 7/42; 5/7 = 30/42

3. Comparison: 1/6 < 5/7 ✅

4.15___34

= <

1. Cross-Multiply (Butterfly Method): (1 × 4) vs (3 × 5) ➔ 4 vs 15

2. Convert to Common Denominator (20): 1/5 = 4/20; 3/4 = 15/20

3. Comparison: 1/5 < 3/4 ✅

5.610___35

= =

1. Cross-Multiply (Butterfly Method): (6 × 5) vs (3 × 10) ➔ 30 vs 30

2. Convert to Common Denominator (10): 6/10 = 6/10; 3/5 = 6/10

3. Comparison: 6/10 = 3/5 ✅

6.47___46

= <

1. Cross-Multiply (Butterfly Method): (4 × 6) vs (4 × 7) ➔ 24 vs 28

2. Convert to Common Denominator (42): 4/7 = 24/42; 4/6 = 28/42

3. Comparison: 4/7 < 4/6 ✅

7.18___14

= <

1. Cross-Multiply (Butterfly Method): (1 × 4) vs (1 × 8) ➔ 4 vs 8

2. Convert to Common Denominator (8): 1/8 = 1/8; 1/4 = 2/8

3. Comparison: 1/8 < 1/4 ✅

8.37___49

= <

1. Cross-Multiply (Butterfly Method): (3 × 9) vs (4 × 7) ➔ 27 vs 28

2. Convert to Common Denominator (63): 3/7 = 27/63; 4/9 = 28/63

3. Comparison: 3/7 < 4/9 ✅

9.12___36

= =

1. Cross-Multiply (Butterfly Method): (1 × 6) vs (3 × 2) ➔ 6 vs 6

2. Convert to Common Denominator (6): 1/2 = 3/6; 3/6 = 3/6

3. Comparison: 1/2 = 3/6 ✅

10.14___23

= <

1. Cross-Multiply (Butterfly Method): (1 × 3) vs (2 × 4) ➔ 3 vs 8

2. Convert to Common Denominator (12): 1/4 = 3/12; 2/3 = 8/12

3. Comparison: 1/4 < 2/3 ✅

PanMaths.com • Answer Key & Worked SolutionsPage 2 of 2

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Worksheet Info

Categorygrade-4

Grade LevelGrade 4

DifficultyEasy, Medium, Hard, Sprint

Time5-10 min

CCSS CodeCCSS.MATH.CONTENT.4.NF.A.2

Skills Practiced

✓ Comparing Unlike Fractions

Key Strategies

🎯 Benchmark Reasoning (Comparing to 1/2): Check whether each fraction is less than, equal to, or greater than 1/2. If 3/8 < 1/2 and 5/8 > 1/2, then 3/8 < 5/8 immediately without calculating common denominators.
🦋 Cross-Multiplication (Butterfly Method): Multiply the numerator of the first fraction by the denominator of the second (a × d) and compare to the product of the second numerator and first denominator (c × b).
📊 Convert to Common Denominators (LCD): Find the Least Common Denominator (LCD) of both fractions, convert them to equivalent forms, and compare the resulting numerators directly.
📏 Same Numerator Reasoning: If two fractions share the same numerator, the fraction with the smaller denominator is larger because the whole is divided into larger slices (e.g., 3/4 > 3/8).

🎮 Interactive Warm-Up

Fraction Pizza Slinger Arcade

Warm up with 60 seconds of rapid mental math practice before printing!

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Related Worksheets

📄 Equivalent Fractions & SimplifyingView →📄 Adding & Subtracting Like FractionsView →📄 Multiplying Fractions by Whole NumbersView →📄 Decimals: Tenths and HundredthsView →📄 Decimals on a Number LineView →📄 Comparing & Ordering DecimalsView →

📜 Standard: CCSS.MATH.CONTENT.4.NF.A.2🔗 CCSS.MATH.CONTENT.3.NF.A.3.D

Mastering Comparing Unlike Fractions: Core Concepts & Mental Models

Comparing fractions with different denominators requires students to establish a common basis of comparison. Under CCSS 4.NF.A.2, students develop reasoning through benchmark fractions (like 0, 1/2, and 1), common denominators (LCD), and cross-multiplication (the butterfly method).

Worked Example & SolutionTeacher Step-by-Step Method

📝 Problem: Compare 3/4 and 5/6 using <, >, or =.

Worked Solution: 1. Method 1 (LCD): Denominators 4 and 6 have LCD = 12. Convert: 3/4 = (3 × 3)/(4 × 3) = 9/12; 5/6 = (5 × 2)/(6 × 2) = 10/12. Compare numerators: 9 < 10, so 9/12 < 10/12. 2. Method 2 (Cross-Multiplication): 3 × 6 = 18 and 5 × 4 = 20. Since 18 < 20, 3/4 < 5/6. Final Answer: 3/4 < 5/6.

💡 Essential Strategies for Comparing Unlike Fractions

🎯 Benchmark Reasoning (Comparing to 1/2)

Check whether each fraction is less than, equal to, or greater than 1/2. If 3/8 < 1/2 and 5/8 > 1/2, then 3/8 < 5/8 immediately without calculating common denominators.

🦋 Cross-Multiplication (Butterfly Method)

Multiply the numerator of the first fraction by the denominator of the second (a × d) and compare to the product of the second numerator and first denominator (c × b).

📊 Convert to Common Denominators (LCD)

Find the Least Common Denominator (LCD) of both fractions, convert them to equivalent forms, and compare the resulting numerators directly.

📏 Same Numerator Reasoning

If two fractions share the same numerator, the fraction with the smaller denominator is larger because the whole is divided into larger slices (e.g., 3/4 > 3/8).

⚠️ Common Mistakes & Teacher Fixes

⚠️Comparing numerators without converting denominators

Why students stumble: Assuming the fraction with the larger numerator is always greater (e.g., thinking 3/8 > 2/3 because 3 > 2).

Teacher Fix: Never compare numerators until both fractions share the same denominator, or use cross-multiplication.

Example: 3/8 = 9/24 and 2/3 = 16/24. 9/24 < 16/24, so 3/8 < 2/3.

⚠️Thinking larger denominators mean larger numbers

Why students stumble: Applying whole number intuition to fractional parts (thinking 1/8 > 1/4 because 8 > 4).

Teacher Fix: Remember that more slices mean each individual slice is smaller. 1/4 of a pizza is twice as big as 1/8.

Example: 1/4 > 1/8.

⚠️Cross-multiplying in the wrong direction

Why students stumble: Assigning the product to the denominator rather than the numerator.

Teacher Fix: Always multiply upward: start at the bottom denominator and multiply into the top numerator. The product belongs to that numerator.

Example: In 3/4 vs 2/5, 5 × 3 = 15 (belongs to 3/4) and 4 × 2 = 8 (belongs to 2/5). Since 15 > 8, 3/4 > 2/5.

📖 Key Mathematical Vocabulary

Unlike Denominators

Fractions that have different numbers in their bottom positions, meaning their wholes are divided into different numbers of parts.

Benchmark Fraction

A well-known reference fraction (such as 1/2, 1/4, or 3/4) used to judge the relative size of other fractions.

Cross-Multiplication

A quick method of comparing two fractions (a/b and c/d) by evaluating a × d versus b × c.

Inequality Symbols

Mathematical signs used to indicate order: < (less than), > (greater than), and = (equal to).

❓ Frequently Asked Questions

How do you solve a comparing unlike fractions problem step by step?

Here is a worked example: "Compare 3/4 and 5/6 using <, >, or =.". Solution: 1. Method 1 (LCD): Denominators 4 and 6 have LCD = 12. Convert: 3/4 = (3 × 3)/(4 × 3) = 9/12; 5/6 = (5 × 2)/(6 × 2) = 10/12. Compare numerators: 9 < 10, so 9/12 < 10/12. 2. Method 2 (Cross-Multiplication): 3 × 6 = 18 and 5 × 4 = 20. Since 18 < 20, 3/4 < 5/6. Final Answer: 3/4 < 5/6.

What is the core learning objective for comparing unlike fractions?

Compare two fractions with different numerators and different denominators using benchmark fractions, common denominators, and cross-multiplication, recording results with symbols <, =, or >. This directly aligns with Common Core Standard CCSS.MATH.CONTENT.4.NF.A.2.

What is the most common mistake students make with comparing unlike fractions?

A frequent pitfall is: "Comparing numerators without converting denominators". Why students stumble: Assuming the fraction with the larger numerator is always greater (e.g., thinking 3/8 > 2/3 because 3 > 2). How to fix it: Never compare numerators until both fractions share the same denominator, or use cross-multiplication. (Example: 3/8 = 9/24 and 2/3 = 16/24. 9/24 < 16/24, so 3/8 < 2/3.)

How does the unlimited comparing unlike fractions worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of comparing unlike fractions problems with unique numbers. No two worksheets are ever the same — perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

Are these comparing unlike fractions worksheets free to print with answer keys?

Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.