Civil Service Exam basic operations: fractions, decimals, percentages, PEMDAS.
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Basic operations is the mechanics layer of the Numerical Ability subtest, and it is one of the three official Numerical Ability topics (basic operations, number sequence, word problems). The CSC does not publish a per-topic breakdown, so any specific percentage you see online is an estimate, not an official figure. What matters is that a chunk of the paper is pure arithmetic (fractions, decimals, percentages, order of operations) with no word-problem disguise. This is where the most points are won or lost per hour of study, because the trick is recognition ("that's a percentage-to-fraction conversion") not problem-solving. Memorize the shortcuts below, drill them for a week, and you'll solve these items in 15-30 seconds each.
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Quick facts
- Primary subtest
- Numerical Ability
- Calculator
- Not allowed
- Official scope
- Basic operations, number sequence, word problems
- Difficulty to improve
- Low (pure mechanics)
Primary keyword: civil service exam basic operations
What gets tested: the four families
Every basic-operations item falls into one of four families. Percentages tend to show up often in published reviewers, so it is worth weighting your study there, but treat that as a study heuristic, not an official weighting.
| Family | What gets tested |
|---|---|
| Fractions | Add, subtract, multiply, divide. Convert mixed numbers and improper fractions. Simplify to lowest terms. Tested raw ("compute 3/4 + 5/6") and inside larger expressions. |
| Decimals | Add, subtract, multiply, divide. Round to a place. Convert decimals to fractions and back. The trap is counting decimal places: 0.3 × 0.04 = 0.012, not 0.12 or 0.0012. |
| Percentages | Compute a percentage of a number, find what percentage one number is of another, compute percentage changes. |
| Order of operations (PEMDAS/MDAS) | Compute mixed-operation expressions. The CSC uses MDAS more often than PEMDAS because exponents are rare on the paper. |
The shortcuts: memorize these cold
These are the conversions and methods that turn 30-second problems into 5-second ones. Start with the percentage-to-fraction table. Computing 25% of 360 by long division is slow; recognizing it as 360 ÷ 4 = 90 is instant.
| Percentage | Fraction |
|---|---|
| 10% | 1/10 |
| 12.5% | 1/8 |
| 20% | 1/5 |
| 25% | 1/4 |
| 33⅓% | 1/3 |
| 50% | 1/2 |
| 66⅔% | 2/3 |
| 75% | 3/4 |
| Decimal | Percentage |
|---|---|
| 0.45 | 45% |
| 0.06 | 6% |
| 1.25 | 125% |
- 1
Fraction addition with unlike denominators
Find the least common denominator, convert both fractions, then add. Example, 1/4 + 2/3: LCD = 12, so 1/4 = 3/12 and 2/3 = 8/12, and the sum is 3/12 + 8/12 = 11/12. Skipping the LCD step and adding numerators directly is the most common error.
- 2
Percentage of a percentage
Convert each to a decimal and multiply. Example, 20% of 30% of 500 = 0.20 × 0.30 × 500 = 30. Always multiply percentages as decimals. Never add or subtract them.
- 3
Reverse percentages (finding the original)
If a value increased by 25% to reach 200, the original is NOT 200 − 25 = 175. The factor for a 25% increase is 1.25, so the original = 200 ÷ 1.25 = 160. The factor is always the multiplier: 25% increase → 1.25, 25% decrease → 0.75.
The percentage change trap: the most common exam mistake
Here is the classic setup. "A price goes up 20%, then down 20%. Net change?" Most test-takers answer 0%. That's wrong. The 20% decrease applies to the new, larger price, not the original:
100 → ×1.20 → 120 → ×0.80 → 96
Net change is a 4% decrease. The rule is simple: percentage changes multiply as factors, they don't add as percentages.
| Change | Factor |
|---|---|
| 20% increase | 1.20 |
| 20% decrease | 0.80 |
| Net multiplier | 1.20 × 0.80 = 0.96 |
Expect this on your paper This is the most-tested trap in basic operations because the wrong answer (0%) is the intuitive one. Expect at least one item like this on any paper. Always multiply factors.
How to drill
One focused week is enough to lock this down. Here is the day-by-day plan.
- 1
Days 1-2: percentage-fraction conversions
Make flashcards for the eight conversions in the shortcuts section. Drill until you can name the fraction in under one second when shown the percentage (and vice versa). This is the highest-ROI study you can do on the entire numerical subtest.
- 2
Days 3-4: fractions and decimals
Twenty mixed items per day. Look up every rule you miss and keep a one-page error log. By day four, you should be at 90%+ accuracy untimed.
- 3
Days 5-6: percentages
Forty items per day, including percentage-of-percentage, percentage change, and reverse-percentage items. Force yourself to use the multiplier method, not addition or subtraction.
- 4
Day 7: timed mixed set
Forty items in twenty-five minutes. Faster than exam pace, on purpose. If you can hit 90% at this speed, you've fully internalized the shortcuts.
Worked examples
These items are written specifically for this guide. The actual practice bank pulls from a separate pool of original CSE-style items reviewed by passers.
Item 01
Compute: 3/4 + 5/6
- A8/10
- B15/24
- C19/12Correct
- D1 5/12
Solution
- 1
Find the LCD
LCD of 4 and 6 is 12.
- 2
Rewrite each fraction
3/4 = 9/12 5/6 = 10/12
- 3
Add numerators
9/12 + 10/12 = 19/12
Answer
19/12 (or 1 7/12 as a mixed number)
Trap to watch. Option A (8/10) adds numerators and denominators separately, which is invalid. Option B (15/24) uses 24 as the denominator instead of 12. Option D (1 5/12) miscomputes the mixed-number conversion.
Item 02
What is 15% of 240?
- A30
- B36Correct
- C40
- D48
Solution
- 1
Break 15% into 10% + 5%
10% of 240 = 24 5% of 240 = half of 10% = 12
- 2
Add the parts
24 + 12 = 36
Answer
36
Trap to watch. Direct method: 15% = 0.15, so 0.15 × 240 = 36. The 10%+5% breakdown works on any 15% problem and is faster than computing 0.15 × N by hand.
Item 03
Compute: 0.4 × 0.05
- A0.002
- B0.02Correct
- C0.2
- D2.0
Solution
- 1
Multiply the digits, ignore decimals
4 × 5 = 20
- 2
Count total decimal places
0.4 has 1 0.05 has 2 Total: 3
- 3
Place the decimal
20 with 3 decimal places = 0.020 = 0.02
Answer
0.02
Trap to watch. Option A (0.002) adds one extra decimal place. Option C (0.2) only counts one factor's decimals. Always count the total across ALL factors.
Item 04
A shirt originally costs ₱500. It is marked down 20%, then marked down another 10% from the sale price. What is the final price?
- A₱350
- B₱360Correct
- C₱370
- D₱400
Solution
- 1
Convert each discount to a factor
20% off → factor 0.80 10% off → factor 0.90
- 2
Multiply the factors
0.80 × 0.90 = 0.72
- 3
Apply to original price
500 × 0.72 = ₱360
Answer
₱360
Trap to watch. Option A (₱350) is the trap of adding the discounts: 500 × (1 − 0.20 − 0.10) = 500 × 0.70 = 350. Wrong because the second discount applies to the smaller sale price, not the original.
Item 05
Compute: 24 + 8 ÷ 4 × 2 − 3
- A5
- B7
- C13
- D25Correct
Solution
- 1
Do division first (left-to-right)
8 ÷ 4 = 2 Expression becomes: 24 + 2 × 2 − 3
- 2
Then multiplication
2 × 2 = 4 Expression becomes: 24 + 4 − 3
- 3
Finally addition/subtraction left-to-right
24 + 4 = 28 28 − 3 = 25
Answer
25
Trap to watch. Option C (13) treats the operations strictly left-to-right and ignores MDAS precedence. Always do × and ÷ before + and −, even when they appear later in the expression.
Item 06
A jacket originally priced at ₱800 was sold at a 25% discount. What was the sale price?
- A₱500
- B₱575
- C₱600Correct
- D₱650
Solution
- 1
Recognize 25% as 1/4
25% = 1/4
- 2
Compute 25% of 800
800 ÷ 4 = 200
- 3
Subtract from original
800 − 200 = ₱600
Answer
₱600
Trap to watch. Equivalent direct method: 800 × 0.75 = ₱600. The fraction shortcut (25% = 1/4) is faster than decimal multiplication; memorize all eight percentage-fraction conversions.
Item 07
After a 40% increase, a property is valued at ₱2,800,000. What was the original value?
- A₱1,680,000
- B₱2,000,000Correct
- C₱2,240,000
- D₱2,400,000
Solution
- 1
Identify the factor
40% increase → factor 1.40
- 2
Divide the new value by the factor
2,800,000 ÷ 1.40 = 2,000,000
- 3
Verify by going forward
2,000,000 × 1.40 = 2,800,000 ✓
Answer
₱2,000,000
Trap to watch. Option A (1,680,000) is the trap of subtracting 40% of the final value: 2,800,000 × 0.60 = 1,680,000. Wrong because 40% of the ORIGINAL was added, not 40% of the final. Always divide by the factor; never multiply by (1 − rate).
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The civil service exam basic operations reviewer drill runs ten or twenty items with full explanations and tracks which traps you fall for most often. Included with a paid plan.
Study tactics that actually move the score
- 01
Memorize the eight percentage-fraction conversions cold. They come up constantly in percentage items, and recognition is much faster than computation.
- 02
On percentage change items, always multiply the factors instead of adding the percentages. 20% up then 20% down is 1.20 × 0.80 = 0.96, not 0%.
- 03
On reverse-percentage items, divide by the factor. "What was the original before a 25% increase?" Divide the new value by 1.25, don't subtract 25%.
- 04
When you encounter mixed operations, write the expression out and circle the multiplication and division before computing. Catches MDAS errors before they happen.
- 05
Drill without a calculator from day one. Phone calculators feel harmless but they hide which steps are slowing you down. The exam is paper-only.
Frequently asked questions
How many basic-operations items appear on the exam?
The CSC does not publish a per-topic item count, so nobody can give you an exact number. What is official: the Professional paper has 170 items total and the Subprofessional paper has 165 items total, and basic operations is one of the three Numerical Ability topics. Treat any specific count you see online as an estimate, and prepare so that arithmetic is automatic rather than betting on a fixed number of items.
Are exponents tested?
Rarely. Most order-of-operations items on the CSC use MDAS (no exponents). When exponents do appear, they're usually small squares or cubes that you can compute directly without a calculator.
What about scientific notation?
Not tested. CSC arithmetic items use regular decimal notation. If you see numbers with many decimal places, the question is testing your ability to round or to count decimal places in multiplication.
Is there a shortcut for converting fractions to percentages?
Yes. Divide the numerator by the denominator, then move the decimal two places right. 3/8 = 0.375 = 37.5%. The eight memorized conversions cover the most common fractions; for unfamiliar fractions, fall back to long division.
What's the most common trap on percentage items?
Adding or subtracting percentages instead of multiplying them. A 20% increase followed by a 20% decrease does not return you to the original. It gives you 96% of the original. Always convert to factors and multiply.
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