4.2 Fractions, Decimals & Percentages

Fractions, Decimals & Percentages

Government clerical work is full of everyday math: computing discounts, splitting shared costs, calculating percentage completion of a task, or converting a fraction of a budget into pesos. The CSE-PPT tests exactly these skills. This section covers converting between fractions, decimals, and percentages; performing the four basic operations on fractions; and solving percentage, discount, and markup problems.

Converting Between Fractions, Decimals, and Percentages

These three forms represent the same value in different ways, and you must be able to move fluidly between them.

• Fraction → Decimal: divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75.
• Decimal → Percentage: multiply by 100 (move the decimal point two places right) and add a % sign. 0.75 → 75%.
• Percentage → Decimal: divide by 100 (move the decimal point two places left). 62.5% → 0.625.
• Decimal → Fraction: write the decimal over a power of 10 and simplify. 0.75 = 75/100 = 3/4.

Operations on Fractions

• Adding/Subtracting: the denominators must match. Find the least common denominator (LCD), convert each fraction, then add or subtract the numerators. 1/4 + 1/6: the LCD of 4 and 6 is 12, so 1/4 = 3/12 and 1/6 = 2/12; 3/12 + 2/12 = 5/12.
• Multiplying: multiply numerators together and denominators together, then simplify. 2/3 × 3/5 = 6/15 = 2/5.
• Dividing: multiply by the reciprocal (flip the second fraction) of the divisor. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.

Worked Example 1: Adding Unlike Fractions

A clerk finishes 2/5 of a report in the morning and 1/3 of the report in the afternoon. What fraction of the report is finished?

• Step 1: Find the LCD of 5 and 3, which is 15.
• Step 2: Convert: 2/5 = 6/15 and 1/3 = 5/15.
• Step 3: Add: 6/15 + 5/15 = 11/15.

Answer: 11/15 of the report is finished.

Worked Example 2: Dividing Fractions

A budget officer has 7/8 of a liter of correction fluid left in a supply cabinet. Each employee requisition uses 1/4 of a liter. How many full requisitions can be filled?

• Step 1: Divide by multiplying by the reciprocal: 7/8 ÷ 1/4 = 7/8 × 4/1.
• Step 2: Multiply: 7 × 4 = 28 and 8 × 1 = 8, giving 28/8.
• Step 3: Simplify: 28/8 = 3 4/8 = 3 1/2.

Answer: 3 full requisitions can be filled, with 1/2 liter left over.

Percentage of a Number

To find a percentage of a number, convert the percentage to a decimal and multiply. "What is 15% of 800?" becomes 0.15 × 800 = 120.

Worked Example 3: Simple Discount

A government office charges ₱800 for processing a document, and offers a 15% senior citizen discount. How much will the discounted fee be?

• Step 1: Find the discount amount: 15% × 800 = 0.15 × 800 = 120.
• Step 2: Subtract the discount from the original price: 800 − 120 = 680.

Answer: ₱680.

Percent Increase and Percent Decrease

The general formula is:

Percent change = (Amount of change ÷ Original amount) × 100

Use the original (starting) value as the base — this is the most common error on this topic.

Worked Example 4: Percent Increase (Markup)

A stationery item originally priced at ₱250 is marked up to ₱300. What is the percent increase?

• Step 1: Find the amount of change: 300 − 250 = 50.
• Step 2: Divide by the original amount: 50 ÷ 250 = 0.2.
• Step 3: Convert to a percentage: 0.2 × 100 = 20%.

Answer: The price increased by 20%.

If instead the price had dropped from ₱250 to ₱200, the amount of change would still be 50, and the percent decrease would still be 50 ÷ 250 = 20% — always divide by the original value, not the new one.

Markup and Discount in Practice

• Markup increases a cost to set a selling price: Selling price = Cost + (Markup % × Cost).
• Discount reduces a listed price: Sale price = Listed price − (Discount % × Listed price), which can also be written as Sale price = Listed price × (1 − Discount rate).

For instance, a 20% discount on a ₱500 item can be computed directly as 500 × (1 − 0.20) = 500 × 0.80 = 400, which matches subtracting the discount amount (500 × 0.20 = 100; 500 − 100 = 400) — both methods give the same answer, so use whichever is faster for you under time pressure.

Common Pitfalls

• Forgetting to find a common denominator before adding or subtracting fractions — you cannot add or subtract numerators when the denominators differ.
• Using the new value instead of the original value as the base when calculating percent change.
• Confusing the discount amount with the discounted price — the discount amount must be subtracted from the original price to get the final answer.

Exam Strategy

Percentage word problems on the CSE-PPT almost always hinge on correctly identifying the base — the original amount the percentage applies to. Read carefully to see whether the question is asking for a percentage of the original price, the new price, or the difference between them; mixing these up is the most common error examinees make on this topic.