Fractions — Operations, Conversion & Comparison - Exam Answer Templates
Mastering fraction problems in exams requires not just mathematical accuracy but also clear, structured presentation of solutions. In Philippine entrance exams like UPCAT, CSE, and NMAT, partial credit is awarded based on proper methodology, clear steps, and correct final answers. These templates show you exactly how to structure your responses for maximum marks across different question types.
Answer templates
Convert 3¾ to an improper fraction.
Examiner tip
Even for 1-mark questions, show the multiplication and addition steps clearly
Model answer
3¾ = (3 × 4 + 3)/4 = 15/4
Answer structure
- Show the conversion formula and calculate [1 mark]
Scoring breakdown
Criteria
Correct conversion using the formula (whole × denominator + numerator)/denominator
Common mark deductions
- Not showing the multiplication step
- Incorrect arithmetic
- Not simplifying when needed
Key phrases to include
- multiply
- add
- improper fraction
Add: 2/3 + 1/4
Examiner tip
Always state the LCD clearly - this is a common marking point
Model answer
Step 1: Find LCD of 3 and 4 = 12
Step 2: 2/3 + 1/4 = 8/12 + 3/12 = 11/12
Answer structure
- Find the LCD [1 mark]
- Convert fractions and add [1 mark]
Scoring breakdown
Criteria
Correctly identifying LCD as 12
Criteria
Proper conversion and addition to get 11/12
Common mark deductions
- Wrong LCD calculation
- Conversion errors
- Not adding numerators correctly
Key phrases to include
- LCD
- convert
- add numerators
Arrange in ascending order: 3/5, 2/3, 7/10
Examiner tip
Show each conversion step separately for clarity and partial marks
Model answer
Step 1: Find LCD of 5, 3, and 10 = 30
Step 2: Convert to equivalent fractions:
3/5 = 18/30, 2/3 = 20/30, 7/10 = 21/30
Step 3: Ascending order: 18/30 < 20/30 < 21/30
Therefore: 3/5 < 2/3 < 7/10
Answer structure
- Find LCD of all denominators [1 mark]
- Convert all fractions to equivalent fractions [1 mark]
- Arrange in correct order [1 mark]
Scoring breakdown
Criteria
Correctly finding LCD = 30
Criteria
Accurate conversion of all three fractions
Criteria
Correct final arrangement with proper notation
Common mark deductions
- Wrong LCD
- Conversion errors
- Incorrect final order
- Missing inequality symbols
Key phrases to include
- LCD
- equivalent fractions
- ascending order
Multiply: 2⅓ × 1¾
Examiner tip
Label each conversion clearly to avoid confusion
Model answer
Step 1: Convert to improper fractions:
2⅓ = 7/3, 1¾ = 7/4
Step 2: Multiply: 7/3 × 7/4 = 49/12
Step 3: Convert to mixed number: 49/12 = 4 1/12
Answer structure
- Convert mixed numbers to improper fractions [1 mark]
- Multiply the fractions [1 mark]
- Convert answer back to mixed number [1 mark]
Scoring breakdown
Criteria
Correct conversion: 2⅓ = 7/3 and 1¾ = 7/4
Criteria
Proper multiplication: 7/3 × 7/4 = 49/12
Criteria
Final conversion: 49/12 = 4 1/12
Common mark deductions
- Conversion errors
- Multiplication mistakes
- Not converting final answer
Key phrases to include
- improper fractions
- multiply
- mixed number
Divide: 3/4 ÷ 2/5
Examiner tip
Always state 'reciprocal method' to show your understanding
Model answer
Step 1: Use reciprocal method: 3/4 ÷ 2/5 = 3/4 × 5/2
Step 2: Multiply: 3/4 × 5/2 = 15/8 = 1⅞
Answer structure
- Apply reciprocal method [1 mark]
- Calculate and simplify [1 mark]
Scoring breakdown
Criteria
Correctly showing 3/4 ÷ 2/5 = 3/4 × 5/2
Criteria
Accurate multiplication and final answer 1⅞
Common mark deductions
- Not using reciprocal
- Multiplication errors
- Not converting to mixed number
Key phrases to include
- reciprocal
- multiply
- invert
Simplify 24/36 to its lowest terms.
Examiner tip
Show the GCF calculation method for full marks
Model answer
Step 1: Find GCF of 24 and 36
24 = 2³ × 3, 36 = 2² × 3²
GCF = 2² × 3 = 12
Step 2: Divide both by GCF: 24/36 = (24÷12)/(36÷12) = 2/3
Answer structure
- Find the GCF of numerator and denominator [1 mark]
- Divide both by GCF to get simplified form [1 mark]
Scoring breakdown
Criteria
Correctly identifying GCF = 12
Criteria
Proper division to get 2/3
Common mark deductions
- Wrong GCF calculation
- Division errors
- Not reaching lowest terms
Key phrases to include
- GCF
- lowest terms
- divide
Convert 0.75 to a fraction in lowest terms.
Examiner tip
Always check if the fraction can be simplified further
Model answer
Step 1: 0.75 = 75/100
Step 2: Simplify by GCF: GCF of 75 and 100 = 25
75/100 = (75÷25)/(100÷25) = 3/4
Answer structure
- Convert decimal to fraction with denominator 100 [1 mark]
- Simplify to lowest terms [1 mark]
Scoring breakdown
Criteria
Correctly writing 0.75 = 75/100
Criteria
Proper simplification to 3/4
Common mark deductions
- Wrong initial fraction
- Incorrect simplification
- Not finding GCF
Key phrases to include
- decimal to fraction
- simplify
- lowest terms
Maria ate 2/5 of a pizza and her brother ate 1/3 of the same pizza. What fraction of the pizza did they eat altogether?
Examiner tip
Always restate the question in your final answer for word problems
Model answer
Step 1: Add the fractions eaten: 2/5 + 1/3
Step 2: Find LCD of 5 and 3 = 15
Step 3: 2/5 + 1/3 = 6/15 + 5/15 = 11/15
Therefore, they ate 11/15 of the pizza altogether.
Answer structure
- Identify the operation needed (addition) [1 mark]
- Find LCD and convert fractions [1 mark]
- Add fractions and state final answer [1 mark]
Scoring breakdown
Criteria
Recognizing this is an addition problem
Criteria
Correct LCD = 15 and proper conversion
Criteria
Final answer 11/15 with proper conclusion
Common mark deductions
- Wrong operation
- LCD errors
- Missing final statement
- No units
Key phrases to include
- add
- LCD
- altogether
A recipe calls for 2¼ cups of flour. If you want to make 1½ times the recipe, how much flour do you need?
Examiner tip
Show every step clearly in word problems - each step typically earns marks
Model answer
Step 1: Convert mixed numbers to improper fractions
2¼ = (2×4+1)/4 = 9/4
1½ = (1×2+1)/2 = 3/2
Step 2: Set up multiplication
Flour needed = 2¼ × 1½ = 9/4 × 3/2
Step 3: Multiply the fractions
9/4 × 3/2 = (9×3)/(4×2) = 27/8
Step 4: Convert to mixed number
27 ÷ 8 = 3 remainder 3
27/8 = 3⅜
Therefore, you need 3⅜ cups of flour.
Answer structure
- Convert mixed numbers to improper fractions [1 mark]
- Set up the multiplication correctly [1 mark]
- Perform the multiplication [1 mark]
- Convert back to mixed number [1 mark]
- State final answer with units [1 mark]
Scoring breakdown
Criteria
Correct conversion: 2¼ = 9/4 and 1½ = 3/2
Criteria
Proper setup: 9/4 × 3/2
Criteria
Accurate multiplication: 27/8
Criteria
Correct conversion: 27/8 = 3⅜
Criteria
Complete answer with units and conclusion
Common mark deductions
- Conversion errors
- Setup mistakes
- Arithmetic errors
- Missing units
- No final statement
Key phrases to include
- convert
- multiply
- mixed number
- cups
Compare 7/12 and 5/8 using the symbol <, >, or =.
Examiner tip
Always show the converted fractions before stating the comparison
Model answer
Step 1: Find LCD of 12 and 8 = 24
Step 2: Convert: 7/12 = 14/24 and 5/8 = 15/24
Step 3: Since 14/24 < 15/24, therefore 7/12 < 5/8
Answer structure
- Find LCD and convert fractions [1 mark]
- Compare and write correct symbol [1 mark]
Scoring breakdown
Criteria
Correct LCD = 24 and accurate conversions
Criteria
Proper comparison: 7/12 < 5/8
Common mark deductions
- Wrong LCD
- Conversion errors
- Incorrect comparison symbol
Key phrases to include
- LCD
- convert
- compare
Subtract: 5⅔ - 2¾
Examiner tip
Double-check your conversion arithmetic - it's a common error point
Model answer
Step 1: Convert to improper fractions:
5⅔ = 17/3, 2¾ = 11/4
Step 2: Find LCD of 3 and 4 = 12
Step 3: 17/3 - 11/4 = 68/12 - 33/12 = 35/12 = 2 11/12
Answer structure
- Convert mixed numbers to improper fractions [1 mark]
- Find LCD and subtract [1 mark]
- Convert final answer to mixed number [1 mark]
Scoring breakdown
Criteria
Correct conversions: 5⅔ = 17/3 and 2¾ = 11/4
Criteria
Proper LCD = 12 and subtraction: 35/12
Criteria
Final conversion: 35/12 = 2 11/12
Common mark deductions
- Conversion errors
- Wrong LCD
- Subtraction mistakes
- Not converting final answer
Key phrases to include
- improper fractions
- LCD
- subtract
- mixed number
Which is greater: 3/4 of 80 or 5/6 of 72?
Examiner tip
Remember that 'of' means multiplication in fraction problems
Model answer
Step 1: Calculate 3/4 of 80
3/4 × 80 = (3 × 80)/4 = 240/4 = 60
Step 2: Calculate 5/6 of 72
5/6 × 72 = (5 × 72)/6 = 360/6 = 60
Step 3: Compare: 60 = 60
Therefore, both values are equal.
Answer structure
- Calculate first fraction of its number [1 mark]
- Calculate second fraction of its number [1 mark]
- Compare and state conclusion [1 mark]
Scoring breakdown
Criteria
Correct calculation: 3/4 of 80 = 60
Criteria
Correct calculation: 5/6 of 72 = 60
Criteria
Proper comparison and conclusion that they are equal
Common mark deductions
- Arithmetic errors
- Wrong interpretation of 'of'
- Missing comparison
- No conclusion
Key phrases to include
- of means multiply
- calculate
- compare
A tank is 3/5 full of water. If 1/4 of the water is used, what fraction of the tank contains water now?
Examiner tip
Clearly state what each fraction represents relative to the tank capacity
Model answer
Step 1: Initial water in tank = 3/5 of tank
Step 2: Water used = 1/4 of the water in tank
Water used = 1/4 × 3/5 = 3/20 of tank
Step 3: Water remaining = Initial water - Water used
Water remaining = 3/5 - 3/20
Step 4: Find LCD of 5 and 20 = 20
3/5 = 12/20
Water remaining = 12/20 - 3/20 = 9/20
Therefore, 9/20 of the tank contains water now.
Answer structure
- Identify initial water fraction [1 mark]
- Calculate water used as fraction of tank [1 mark]
- Set up subtraction for remaining water [1 mark]
- Find LCD and subtract correctly [1 mark]
- State final answer with proper units [1 mark]
Scoring breakdown
Criteria
Recognizing initial water = 3/5 of tank
Criteria
Correct calculation: water used = 1/4 × 3/5 = 3/20
Criteria
Proper setup: 3/5 - 3/20
Criteria
Accurate calculation: 9/20
Criteria
Complete final answer with units
Common mark deductions
- Misunderstanding the problem
- Calculation errors
- Wrong operation
- Missing units
- Incomplete explanation
Key phrases to include
- initial
- used
- remaining
- of tank
Express 13/4 as a mixed number.
Examiner tip
Show the division step briefly even for 1-mark questions
Model answer
13 ÷ 4 = 3 remainder 1, so 13/4 = 3¼
Answer structure
- Perform division and express as mixed number [1 mark]
Scoring breakdown
Criteria
Correct conversion showing 13/4 = 3¼
Common mark deductions
- Division errors
- Wrong mixed number format
Key phrases to include
- divide
- remainder
- mixed number
Find the sum: 1/6 + 1/8 + 1/12
Examiner tip
When adding multiple fractions, organize your work clearly to avoid errors
Model answer
Step 1: Find LCD of 6, 8, and 12
LCM(6,8,12) = 24
Step 2: Convert to equivalent fractions:
1/6 = 4/24, 1/8 = 3/24, 1/12 = 2/24
Step 3: Add: 4/24 + 3/24 + 2/24 = 9/24 = 3/8
Answer structure
- Find LCD of all three denominators [1 mark]
- Convert all fractions to equivalent fractions [1 mark]
- Add and simplify [1 mark]
Scoring breakdown
Criteria
Correct LCD = 24
Criteria
Accurate conversion of all three fractions
Criteria
Proper addition and simplification to 3/8
Common mark deductions
- Wrong LCD calculation
- Conversion errors
- Addition mistakes
- Not simplifying final answer
Key phrases to include
- LCD
- equivalent fractions
- add
- simplify
Mark wise strategy
Direct application of formulas or simple conversions with minimal working
Do
- Show key step clearly
- Write final answer
- Use proper notation
Don't
- Skip showing any work
- Make careless arithmetic errors
- Forget to simplify
Two clear steps with intermediate results shown
Do
- Label each step
- Show LCD calculations
- Verify final answer
Don't
- Combine multiple steps
- Skip intermediate results
- Forget units in word problems
Three distinct steps with clear progression and proper explanations
Do
- Number your steps
- Show all conversions
- State final conclusion clearly
Don't
- Rush through calculations
- Skip conversion steps
- Leave answers unsimplified
Comprehensive solution with detailed working, clear logic, and complete explanations
Do
- Break into logical steps
- Explain your reasoning
- Include units throughout
- Double-check calculations
Don't
- Jump steps
- Mix up different methods
- Forget to answer the actual question
- Leave working unclear
General answer writing tips
- Always show your complete working, even for simple calculations - examiners award marks for correct methodology
- Use proper fraction notation and simplify all final answers to lowest terms
- Label each step clearly when converting between mixed numbers and improper fractions
- Include units in word problems and box your final answer for easy identification
- When comparing fractions, show the LCD calculation process step by step
- Draw clear diagrams for fraction visualization when appropriate
- Use the reciprocal method notation clearly in division problems
- Check your answer by substitution or estimation to avoid careless errors
Diagrams
Fraction Operations Overview
Complete overview of all fraction operations covered in the chapter, showing relationships between different types of problems
Adding Fractions Step-by-Step Process
Decision tree showing the complete process for adding any two fractions, whether they have the same or different denominators
Word Problem Solution Strategy
Systematic approach to solving fraction word problems, helping students identify the correct operation and organize their solution