⚖️ Ratios & Proportional Relationships
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Solving Percentage Problems

Part, whole, and percent — know two, find the third.

Percent means "per hundred." Percentage problems always involve three quantities: the part, the whole, and the percent. Knowing any two of these lets you find the third. The relationship is captured in one key equation.

Part=Percent100×Whole\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}

Three Types of Percent Problems

1Find the part: Part = (Percent ÷ 100) × Whole
2Find the whole: Whole = Part ÷ (Percent ÷ 100)
3Find the percent: Percent = (Part ÷ Whole) × 100
🏬All Three Types
TYPE 1: 30% of 80 = 0.30 × 80 = 24
TYPE 2: 24 is 30% of what? → 24 ÷ 0.30 = 80
TYPE 3: 24 is what % of 80? → (24 ÷ 80) × 100 = 30%

Convert percent to decimal before computing: move the decimal two places left. 45% = 0.45, 8% = 0.08, 120% = 1.20.

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Remember This!

Use the "is over of equals percent over 100" proportion: (part/whole) = (percent/100). Cross-multiply to solve for any unknown.

✏️ Try It!

A shirt originally costs $40. It is on sale for 25% off. What is the sale price?

Practice with CalcVerse
🔄Fraction ↔ Decimal ↔ %%Percent Calculator🍽️Tip & Bill Splitter
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