Review of Fractions Worksheet - Comprehensive Practice for 4th Graders

Comprehensive fractions worksheet covering all essential concepts: equivalent fractions, comparing fractions, operations, and conversions with detailed solutions and practice problems.

Worksheet Problems 1 to 3
Fraction Review Worksheet
30 Points Total
Problem Set A: Equivalent Fractions
Problem 1: Finding Equivalent Fractions
Complete each equivalent fraction. Show your work and explain the process.
3/4 = ?/8
2/5 = 4/?
6/9 = ?/3
Definition:

Equivalent fractions: Fractions that represent the same value by multiplying or dividing both numerator and denominator by the same number.

Method for finding equivalent fractions:
  1. Look at the denominators to find the relationship
  2. Determine what number the original denominator was multiplied by
  3. Multiply the numerator by the same number
  4. Verify using cross multiplication
Problem 1
3/4 = 6/8
Problem 2
2/5 = 4/10
Problem 3
6/9 = 2/3
Problem 1: 3/4 = ?/8

Find relationship: 4 × 2 = 8

Apply to numerator: 3 × 2 = 6

Result: 3/4 = 6/8

Problem 2: 2/5 = 4/?

Find relationship: 2 × 2 = 4

Apply to denominator: 5 × 2 = 10

Result: 2/5 = 4/10

Problem 3: 6/9 = ?/3

Find relationship: 9 ÷ 3 = 3

Apply to numerator: 6 ÷ 3 = 2

Result: 6/9 = 2/3

3/4
6/8
3/4 = 6/8
Answers:

1) 3/4 = 6/8 (multiplied by 2)

2) 2/5 = 4/10 (multiplied by 2)

3) 6/9 = 2/3 (divided by 3)

Points: 6/6
Problem Set B: Comparing Fractions
Problem 2: Comparing Fractions
Compare each pair of fractions using <, >, or =. Show your work using at least two different methods.
2/3 ___ 3/4
1/2 ___ 2/4
5/6 ___ 4/5
Definition:

Comparing fractions: Determining which fraction is larger, smaller, or if they are equal using various methods.

Problem 1
2/3 < 3/4
Problem 2
1/2 = 2/4
Problem 3
5/6 > 4/5
Problem 1: 2/3 vs 3/4 (Cross multiplication)

2 × 4 = 8 and 3 × 3 = 9

Since 8 < 9, 2/3 < 3/4

Problem 2: 1/2 vs 2/4 (Simplification)

2/4 = 1/2, so 1/2 = 2/4

Problem 3: 5/6 vs 4/5 (Common denominator)

LCM of 6 and 5 is 30

5/6 = 25/30 and 4/5 = 24/30

Since 25 > 24, 5/6 > 4/5

2/3
3/4
2/3 < 3/4
Answers:

1) 2/3 < 3/4 (cross multiplication: 8 < 9)

2) 1/2 = 2/4 (simplification: 2/4 = 1/2)

3) 5/6 > 4/5 (common denominator: 25/30 > 24/30)

Points: 6/6
Problem Set C: Simplifying Fractions
Problem 3: Simplifying to Lowest Terms
Simplify each fraction to its lowest terms. Show all your work and explain how you know it's in lowest terms.
8/12
15/25
18/24
Definition:

Simplifying fractions: Reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD).

Problem 1
8/12 = 2/3
Problem 2
15/25 = 3/5
Problem 3
18/24 = 3/4
Problem 1: 8/12

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12

GCD: 4

8/12 = (8÷4)/(12÷4) = 2/3

Problem 2: 15/25

Factors of 15: 1, 3, 5, 15

Factors of 25: 1, 5, 25

GCD: 5

15/25 = (15÷5)/(25÷5) = 3/5

Problem 3: 18/24

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

GCD: 6

18/24 = (18÷6)/(24÷6) = 3/4

2/3
8/12 = 2/3
Answers:

1) 8/12 = 2/3 (divided by GCD of 4)

2) 15/25 = 3/5 (divided by GCD of 5)

3) 18/24 = 3/4 (divided by GCD of 6)

Points: 6/6
Worksheet Problems 4 to 5
Problem Set D: Fraction Operations
Problem 4: Adding and Subtracting Fractions
Perform each operation. Remember to show your work and simplify if possible.
1/4 + 2/4
5/8 - 3/8
2/5 + 1/5
Definition:

Adding/subtracting fractions with same denominator: Add or subtract the numerators and keep the denominator unchanged.

Method for same denominator operations:
  1. Add or subtract the numerators only
  2. Keep the same denominator
  3. Simplify the result if possible
Problem 1
1/4 + 2/4 = 3/4
Problem 2
5/8 - 3/8 = 2/8 = 1/4
Problem 3
2/5 + 1/5 = 3/5
Problem 1: 1/4 + 2/4

Add numerators: 1 + 2 = 3

Keep denominator: 4

Result: 3/4

Problem 2: 5/8 - 3/8

Subtract numerators: 5 - 3 = 2

Keep denominator: 8

Result: 2/8 = 1/4 (simplified by dividing by GCD of 2)

Problem 3: 2/5 + 1/5

Add numerators: 2 + 1 = 3

Keep denominator: 5

Result: 3/5

1/4
2/4
3/4
1/4 + 2/4 = 3/4
Answers:

1) 1/4 + 2/4 = 3/4

2) 5/8 - 3/8 = 2/8 = 1/4

3) 2/5 + 1/5 = 3/5

Points: 6/6
Problem Set E: Word Problems
Problem 5: Real-World Applications
Solve each word problem. Show your work and write your answer in a complete sentence.
Maria ate 2/3 of her sandwich. How much is left?
Tom painted 1/4 of a fence. His friend painted 1/2 of the same fence. What fraction did they paint together?
Definition:

Word problems: Real-world scenarios that require mathematical analysis and solution using fraction concepts.

Problem 1
1 - 2/3 = 1/3
Problem 2
1/4 + 1/2 = 3/4
Problem 1: Maria's sandwich

Total sandwich = 1

Eaten = 2/3

Left = 1 - 2/3 = 3/3 - 2/3 = 1/3

Problem 2: Fence painting

Tom painted: 1/4

Friend painted: 1/2 = 2/4

Total: 1/4 + 2/4 = 3/4

2/3 eaten
1/3 left
1 - 2/3 = 1/3
Answers:

1) Maria has 1/3 of her sandwich left.

2) Together, Tom and his friend painted 3/4 of the fence.

Points: 6/6
Complete Worksheet Review
\( \frac{a}{b} = \frac{a \times n}{b \times n} = \frac{a ÷ m}{b ÷ m} \)
Fraction Operations Formula
Key concepts covered:

Equivalent fractions: Understanding that different fractions can represent the same value by multiplying or dividing both numerator and denominator by the same number.

Comparing fractions: Methods for determining which fraction is larger, smaller, or equal using common denominators or cross multiplication.

Simplifying fractions: Reducing fractions to lowest terms by dividing by the greatest common divisor.

Fraction operations: Adding and subtracting fractions with the same denominator.

Word problems: Applying fraction concepts to real-world scenarios.

Problem-solving strategies:
  1. Read carefully: Understand what the question is asking
  2. Plan your approach: Decide which method to use
  3. Show your work: Write out all steps clearly
  4. Check your answer: Verify using alternative methods
  5. State the answer: Answer the specific question asked
For equivalent fractions: Find the relationship between denominators first, then apply to numerators.
For comparing fractions: Use common denominators or cross multiplication.
For simplifying: Always check that GCD of final numerator and denominator is 1.
For operations: Only possible when denominators are the same.
For verification: Use cross multiplication or decimal conversion to check answers.
Common errors: Forgetting to apply operations to both numerator and denominator, not simplifying completely, computational mistakes.
Success criteria: Showing all work, getting correct answers, explaining reasoning clearly.
Review focus: Practice problems that combine multiple concepts and require multi-step solutions.
Core principles:

• Conservation principle: The value of a fraction remains unchanged when equivalent fractions are created

• Proportionality: Operations must be applied equally to numerator and denominator

• Verification: Always check answers using alternative methods

• Clarity: Show all work and explain reasoning clearly

• Application: Connect fraction concepts to real-world scenarios

\( \frac{a}{b} = \frac{c}{d} \iff ad = bc \)
Cross Product Property
Scoring Guide:

Problem 1: 6 points (2 points per equivalent fraction)

Problem 2: 6 points (2 points per comparison)

Problem 3: 6 points (2 points per simplification)

Problem 4: 6 points (2 points per operation)

Problem 5: 6 points (3 points per word problem)

Total: 30 points

Post-worksheet review strategies:
  1. Review incorrect answers: Understand why you made mistakes
  2. Practice similar problems: Work on areas where you struggled
  3. Ask for help: Clarify concepts you don't understand
  4. Connect concepts: See how different fraction topics relate
  5. Build confidence: Celebrate what you learned and accomplished
All Worksheet Answers:

Problem 1: 3/4 = 6/8, 2/5 = 4/10, 6/9 = 2/3

Problem 2: 2/3 < 3/4, 1/2 = 2/4, 5/6 > 4/5

Problem 3: 8/12 = 2/3, 15/25 = 3/5, 18/24 = 3/4

Problem 4: 1/4 + 2/4 = 3/4, 5/8 - 3/8 = 1/4, 2/5 + 1/5 = 3/5

Problem 5: 1/3 left, 3/4 painted together

Questions & Answers

Question: How do I know which method to use when comparing fractions? Should I always find common denominators?

Answer: You have several options for comparing fractions:

  • Cross multiplication: Usually fastest for two fractions (multiply diagonally)
  • Common denominators: Good when denominators are small or have obvious LCM
  • Decimal conversion: Useful for checking answers or when comfortable with division

For 2/3 vs 5/8:

Cross multiplication: 2×8=16 vs 3×5=15, so 16>15, meaning 2/3 > 5/8

Choose the method that feels most comfortable and efficient for the specific numbers you're working with!

Question: My child often forgets to simplify fractions. How can I help them remember?

Answer: Here are some strategies to help:

  1. Make it routine: Always ask "Can this be simplified?" after working with fractions
  2. Use the "check" method: Look for common factors of numerator and denominator
  3. Practice divisibility rules: Numbers ending in 0,2,4,6,8 are divisible by 2
  4. Visual cues: Draw models to see if parts can be grouped together

Remind your child that simplified fractions are easier to work with and often required in final answers!

Regular practice with simplification will make it more automatic over time.

Question: When solving multi-step fraction problems, how do I stay organized?

Answer: Organization is key for multi-step problems:

  1. Read the entire problem first: Understand what's being asked
  2. Break into steps: Identify what needs to be done in order
  3. Write each step clearly: Don't skip steps, even if they seem simple
  4. Label your work: Keep track of what each calculation represents
  5. Check as you go: Verify each step before moving to the next

For the pizza problem:

Step 1: Add slices eaten

Step 2: Write as fraction

Step 3: Simplify

Step 4: Find equivalent fraction

This systematic approach prevents confusion and helps catch errors!