Math
Master the quantitative skills used in science and healthcare: significant figures, unit conversions, proportions, functions, exponents, logarithms, statistics, and introductory calculus.
Ratios, Proportions & Percentages
Sign in to track progressRatios, proportions, and percentages are used constantly in science, engineering, and everyday calculations involving concentrations and scaling.
Percent to Decimal Conversion To convert a percentage to a decimal, divide by 100 (or move the decimal two places left).
Examples:
- 75% = 0.75
- 12.5% = 0.125
- 0.5% = 0.005
Ratios A ratio compares two quantities. A ratio of 1:4 means 1 part of one thing for every 4 parts of another.
Fractions from Ratios The ratio a:b can be written as the fraction a/b or a/(a+b) depending on the context.
Example: A 1:4 mixture has 1 part solute in 5 total parts, so the fraction of solute is 1/5.
Solving Proportions A proportion states that two ratios are equal: a/b = c/d. Cross-multiply to solve: a·d = b·c.
Example: x/5 = 8/10 → 10x = 40 → x = 4
Finding Percentages of Numbers Convert the percent to a decimal, then multiply by the number.
Example: 20% of 150 = 0.20 × 150 = 30
Basic Proportional Reasoning Proportions are used for scaling concentrations, recipes, and mixtures. If you know the relationship for one case, you can extend it to another by keeping the ratio constant.
Key Points
- Convert percent to decimal by dividing by 100
- A ratio a:b compares two quantities directly
- Solve proportions by cross-multiplying
- To find a percentage of a number, multiply the decimal form by the number
- Proportional reasoning scales concentrations and mixtures consistently