Ratio

Definition

A ratio is a quantitative relationship between two or more values, quantities, or measures. It is used to express how one number or quantity relates to another, often in the form of a fraction or a comparison.

5 Must Know Facts For Your Next Test

1. Ratios can be used to solve percent applications by expressing the relationship between a part and the whole.
2. Proportions are used to solve similar figure applications by setting up a ratio between corresponding sides of the figures.
3. Direct variation is a relationship where two quantities are proportional, meaning their ratio remains constant.
4. Inverse variation is a relationship where two quantities are inversely proportional, meaning their product is constant.
5. Ratios are fundamental to understanding and solving a variety of mathematical problems, from everyday applications to advanced concepts.

Review Questions

• Explain how ratios can be used to solve percent applications.
  • Ratios can be used to solve percent applications by expressing the relationship between a part and the whole. For example, if a student scored 18 out of 25 points on a test, the ratio of the student's score to the total points would be 18:25. This ratio can then be used to calculate the student's percentage score by setting up a proportion and solving for the unknown value.
• Describe how ratios are used to solve proportion and similar figure applications.
  • Proportions, which are equations that state two ratios are equal, are used to solve for unknown values in similar figure applications. By setting up a proportion between the corresponding sides of two similar figures, you can use the known ratios to determine the lengths of the unknown sides. This is a powerful tool for solving problems involving scale, scale drawings, and other geometric applications that rely on the properties of similar figures.
• Analyze how the concept of ratio is fundamental to understanding direct and inverse variation.
  • $$Direct variation$$ is a relationship where two quantities are proportional, meaning their ratio remains constant. This can be expressed as a ratio equation, such as $\frac{y}{x} = k$, where $k$ is the constant of proportionality. $$Inverse variation$$ is a relationship where two quantities are inversely proportional, meaning their product is constant. This can be expressed as a ratio equation, such as $\frac{x}{y} = k$, where $k$ is the constant of variation. Understanding the ratio relationships between the variables is crucial for identifying, modeling, and solving problems involving direct and inverse variation.

Related terms

Proportion: A proportion is an equation that states that two ratios are equal, often used to solve for an unknown value.

Rate: A rate is a ratio that compares two different quantities, such as miles per hour or dollars per pound.

Unit Rate: A unit rate is a ratio that compares a quantity to a single unit of another quantity, such as cost per item or miles per gallon.