Ratios & Percentages Cheat Sheet

Understand and simplify ratios, and solve word problems involving percentages, including increases and decreases.

Core Principles

A ratio compares two or more numbers.
Ratios can be simplified like fractions by dividing all parts by a common factor.
For comparison, quantities must have the same units.
Percentages relate a part to a whole (100).
The formula Part/Base = Percent/100 is key for all percentage problems.
Increases add to 100%; decreases subtract from 100%.

For ratios, ensure units are the same before simplifying.
Divide all parts of a ratio by the greatest common divisor.
To simplify decimals in ratios, multiply by powers of 10.
To simplify fractions in ratios, find a common denominator.
Identify 'Part', 'Base', and 'Percent' in word problems.
Substitute knowns into \frac{Part}{Base} = \frac{Percent}{100} and solve for the unknown.
For increases, add the percentage to 100% before using the formula.
For decreases, subtract the percentage from 100% before using the formula.

Ratio: A comparison of two or more numbers, often expressed in the form a:b:c.
Simplify Ratio: Reducing a ratio to its lowest terms by dividing all parts by a common factor.
Percentage: A rate or proportion per hundred.
Part: A portion of the whole or base amount.
Base: The total or original amount to which the part is compared.
Markup: An increase in price or value.
Markdown: A decrease in price or value.

A student scores 96 out of 120 on a test.: Calculate the percentage score: (96/120) * 100 = 80%.
A product priced at $550 has a 6% sales tax.: Calculate the sales tax amount: $550 * 0.06 = $33.
A salary increases by 5%.: New Salary = Original Salary * (1 + 0.05).
A price is marked down by 15%.: Sale Price = Original Price * (1 - 0.15).