Civil Service Exam (Subprofessional) Numerical Ability — Fractions — Operations, Conversion & ComparisonExam Answer Templates
Exam-style answer templates for Fractions — Operations, Conversion & Comparison — how to answer Civil Service Exam (Subprofessional) Numerical Ability questions when Civil Service Commission (CSC) asks about this chapter. Use these as your mental checklist on exam day.
Exam context
Civil Service Commission (CSC) runs the Career Service Examination — Subprofessional Level on Bi-annual — March and August 2026. Its Numerical Ability section sits under a "~25% weightage" weighting, and Fractions — Operations, Conversion & Comparison is the 2nd chapter in the 9-chapter Civil Service Exam (Subprofessional) Numerical Ability rotation. The Civil Service Exam (Subprofessional) passing mark is 80%, and the most recent 2026 paper drew about 17 questions from Numerical Ability.
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.
Templates
Convert 3¾ to an improper fraction.
Marks
1
Topic
Fraction Conversion
Difficulty
easy
Template Id
T1
Examiner Tip
Even for 1-mark questions, show the multiplication and addition steps clearly
Model Answer
3¾ = (3 × 4 + 3)/4 = 15/4
Question Type
very_short_answer
Answer Structure
- Show the conversion formula and calculate [1 mark]
Scoring Breakdown
Marks
1
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
Marks
2
Topic
Addition of Fractions
Difficulty
easy
Template Id
T2
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
Question Type
short_answer
Answer Structure
- Find the LCD [1 mark]
- Convert fractions and add [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly identifying LCD as 12
Marks
1
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
Marks
3
Topic
Comparing Fractions
Difficulty
medium
Template Id
T3
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
Question Type
short_answer
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
Marks
1
Criteria
Correctly finding LCD = 30
Marks
1
Criteria
Accurate conversion of all three fractions
Marks
1
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
Marks
3
Topic
Multiplication of Fractions
Difficulty
medium
Template Id
T4
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
Question Type
short_answer
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
Marks
1
Criteria
Correct conversion: 2⅓ = 7/3 and 1¾ = 7/4
Marks
1
Criteria
Proper multiplication: 7/3 × 7/4 = 49/12
Marks
1
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
Marks
2
Topic
Division of Fractions
Difficulty
easy
Template Id
T5
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
Question Type
short_answer
Answer Structure
- Apply reciprocal method [1 mark]
- Calculate and simplify [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly showing 3/4 ÷ 2/5 = 3/4 × 5/2
Marks
1
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.
Marks
2
Topic
Simplifying Fractions
Difficulty
easy
Template Id
T6
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
Question Type
short_answer
Answer Structure
- Find the GCF of numerator and denominator [1 mark]
- Divide both by GCF to get simplified form [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly identifying GCF = 12
Marks
1
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.
Marks
2
Topic
Decimal to Fraction Conversion
Difficulty
easy
Template Id
T7
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
Question Type
short_answer
Answer Structure
- Convert decimal to fraction with denominator 100 [1 mark]
- Simplify to lowest terms [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly writing 0.75 = 75/100
Marks
1
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?
Marks
3
Topic
Word Problems - Addition
Difficulty
medium
Template Id
T8
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.
Question Type
short_answer
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
Marks
1
Criteria
Recognizing this is an addition problem
Marks
1
Criteria
Correct LCD = 15 and proper conversion
Marks
1
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?
Marks
5
Topic
Word Problems - Multiplication
Difficulty
medium
Template Id
T9
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.
Question Type
long_answer
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
Marks
1
Criteria
Correct conversion: 2¼ = 9/4 and 1½ = 3/2
Marks
1
Criteria
Proper setup: 9/4 × 3/2
Marks
1
Criteria
Accurate multiplication: 27/8
Marks
1
Criteria
Correct conversion: 27/8 = 3⅜
Marks
1
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 =.
Marks
2
Topic
Comparing Fractions
Difficulty
easy
Template Id
T10
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
Question Type
short_answer
Answer Structure
- Find LCD and convert fractions [1 mark]
- Compare and write correct symbol [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct LCD = 24 and accurate conversions
Marks
1
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
Marks
3
Topic
Subtraction of Mixed Numbers
Difficulty
medium
Template Id
T11
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
Question Type
short_answer
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
Marks
1
Criteria
Correct conversions: 5⅔ = 17/3 and 2¾ = 11/4
Marks
1
Criteria
Proper LCD = 12 and subtraction: 35/12
Marks
1
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?
Marks
3
Topic
Fraction Operations in Comparison
Difficulty
medium
Template Id
T12
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.
Question Type
short_answer
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
Marks
1
Criteria
Correct calculation: 3/4 of 80 = 60
Marks
1
Criteria
Correct calculation: 5/6 of 72 = 60
Marks
1
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?
Marks
5
Topic
Complex Word Problems
Difficulty
hard
Template Id
T13
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.
Question Type
long_answer
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
Marks
1
Criteria
Recognizing initial water = 3/5 of tank
Marks
1
Criteria
Correct calculation: water used = 1/4 × 3/5 = 3/20
Marks
1
Criteria
Proper setup: 3/5 - 3/20
Marks
1
Criteria
Accurate calculation: 9/20
Marks
1
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.
Marks
1
Topic
Improper to Mixed Conversion
Difficulty
easy
Template Id
T14
Examiner Tip
Show the division step briefly even for 1-mark questions
Model Answer
13 ÷ 4 = 3 remainder 1, so 13/4 = 3¼
Question Type
very_short_answer
Answer Structure
- Perform division and express as mixed number [1 mark]
Scoring Breakdown
Marks
1
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
Marks
3
Topic
Addition of Multiple Fractions
Difficulty
medium
Template Id
T15
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
Question Type
short_answer
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
Marks
1
Criteria
Correct LCD = 24
Marks
1
Criteria
Accurate conversion of all three fractions
Marks
1
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
Dos
- Show key step clearly
- Write final answer
- Use proper notation
Donts
- Skip showing any work
- Make careless arithmetic errors
- Forget to simplify
Marks
1
Strategy
Direct application of formulas or simple conversions with minimal working
Expected Length
1-2 lines
Time Allocation
30-60 seconds
Dos
- Label each step
- Show LCD calculations
- Verify final answer
Donts
- Combine multiple steps
- Skip intermediate results
- Forget units in word problems
Marks
2
Strategy
Two clear steps with intermediate results shown
Expected Length
3-4 lines
Time Allocation
1-2 minutes
Dos
- Number your steps
- Show all conversions
- State final conclusion clearly
Donts
- Rush through calculations
- Skip conversion steps
- Leave answers unsimplified
Marks
3
Strategy
Three distinct steps with clear progression and proper explanations
Expected Length
4-6 lines
Time Allocation
2-3 minutes
Dos
- Break into logical steps
- Explain your reasoning
- Include units throughout
- Double-check calculations
Donts
- Jump steps
- Mix up different methods
- Forget to answer the actual question
- Leave working unclear
Marks
5
Strategy
Comprehensive solution with detailed working, clear logic, and complete explanations
Expected Length
8-12 lines
Time Allocation
4-6 minutes
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
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