TACHS Math

Comprehensive study of tachs math covering fundamental concepts and advanced applications.

Numbers and OperationsFractions, Decimals, and PercentsRatios, Proportions, and Rates
Algebraic Expressions and EquationsGeometry: Shapes, Area, and VolumeData Analysis and Probability
Budgeting and Money MathMeasuring and EstimatingPlanning and Scheduling
Time Management on the TestUsing Estimation and Elimination
Numbers and Operatio...Fractions, Decimals,...Ratios, Proportions,...Algebraic Expression...Geometry: Shapes, Ar...Data Analysis and Pr...Budgeting and Money ...Measuring and Estima...Planning and Schedul...Time Management on t...Using Estimation and...
Basic Concepts

Ratios, Proportions, and Rates

Making Comparisons

Ratios, proportions, and rates help you compare amounts and solve real-life math problems.

Ratios

A ratio compares two quantities. If there are 4 apples and 6 oranges, the ratio is 4:6 (or simplified, 2:3).

Proportions

A proportion is when two ratios are equal. If 2 out of 3 students like pizza, and 8 out of 12 students in another class like pizza, that’s a proportion because \( \frac{2}{3} = \frac{8}{12} \).

Rates

A rate is a special ratio where the two things being compared have different units, like miles per hour.

Real-World Example

Ratios and rates help with recipes, travel, and comparing prices at the store!

Examples

  • If a car travels 60 miles in 2 hours, its rate is 30 miles per hour.

  • Doubling a recipe by keeping ingredient ratios the same.

In a Nutshell

Ratios, proportions, and rates are tools for comparing quantities in real life.

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Algebraic Expressions and Equations