A ratio is a comparison of two quantities. It is often written as a fraction or using the colon symbol (:). For example, the ratio of boys to girls in a class of 20 students can be written as 5:3 or 5/3. Ratios are used to compare the sizes of two or more quantities.

**Antecedent:**The first term in a ratio is called the antecedent. In the ratio a:b, 'a' is the antecedent.**Consequent:**The second term in a ratio is called the consequent. In the ratio a:b, 'b' is the consequent.

Ratios can be expressed in the following ways:

**As a fraction:**For example, the ratio 3:5 can be expressed as 3/5.**Using the colon symbol:**For example, the ratio of 2:7.**As a verbal statement:**For example, "The ratio of boys to girls is 2 to 3."

Equivalent ratios are ratios that express the same comparison. For example, the ratios 2:3 and 4:6 are equivalent because they both compare the same relationship, which is 2 to 3.

Ratios can be used to solve various types of problems, such as mixing different quantities of ingredients to create a recipe, determining the proportion of different colors used in a painting, or sharing a sum of money in a specific ratio among a group of people.

- Express the ratio 6:9 as a fraction in simplest form.
- Determine if the ratios 4:6 and 6:9 are equivalent.
- If a recipe calls for a ratio of 2 cups of flour to 3 cups of sugar, how much sugar would you need if you used 4 cups of flour?

Study GuideGeometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key Numerical & Geometric Proportions

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.