How to Calculate Percentages: Four Common Problems Solved

1. What Percent of a Number

The most common percentage question: "What is X% of Y?"

Example: What is 35% of 240?

(35 ÷ 100) × 240 = 0.35 × 240 = 84

2. What Percentage Is One Number of Another

"X is what percent of Y?"

Example: 45 is what percent of 180?

(45 ÷ 180) × 100 = 0.25 × 100 = 25%

3. Percentage Change

"By what percentage did a value increase or decrease?" This is used for price changes, salary increases, test score comparisons, and similar situations.

Example: A product price increased from $80 to $96.

[(96 − 80) ÷ 80] × 100 = [16 ÷ 80] × 100 = 0.20 × 100 = +20%

A negative result indicates a decrease. If the price dropped from $96 to $80: [(80 − 96) ÷ 96] × 100 = −16.67%

4. Finding the Original Value (Working Backward)

"If X is Y% of some number, what is that number?" This comes up when a sale price is known and the original price is needed.

Example: A jacket is on sale for $68, which is 85% of the original price. What was the original price?

$68 ÷ 0.85 = $80.00

Common Percentage Mistakes

• Percentage points vs. percent change: If an interest rate rises from 4% to 6%, it increased by 2 percentage points, but by 50% in relative terms. These are different statements.
• A 50% increase followed by a 50% decrease does not return to the original: $100 + 50% = $150. $150 − 50% = $75. The result is 25% below the starting point.
• Percent of a percent: "20% off, then an additional 10% off" is not 30% off. It is 28% off: 100% × 0.80 × 0.90 = 72% of original price.