A proportion is a statement that two ratios are equal. In other words, it expresses the equality of two ratios. The general form of a proportion is:

*a/b = c/d*

Where *a, b, c,* and *d* are numbers or algebraic expressions, and *b* and *d* are not zero.

**Ratios:**A ratio is a comparison of two quantities. For example, if there are 3 boys and 5 girls in a class, the ratio of boys to girls is 3:5.**Proportional Relationships:**When two ratios are equal, they form a proportional relationship. If*a/b = c/d*, then*a*is directly proportional to*b*and*c*is directly proportional to*d*.**Cross Products Property:**In a proportion*a/b = c/d*, the cross products*ad*and*bc*are equal. This property can be used to solve proportions.

**Cross Multiplication:**To solve a proportion*a/b = c/d*, you can cross multiply by multiplying*a*by*d*and*b*by*c*. Set the resulting products equal to each other and solve for the unknown.**Equivalent Fractions:**You can also solve proportions by finding an equivalent fraction. Multiply or divide both parts of the ratio by the same number to find a new ratio that is equivalent to the given one.

Find the value of *x* in the proportion *3/5 = x/15*.

**Solution:** Using cross multiplication, we get *3 * 15 = 5x*. Simplifying, we have *45 = 5x*. Dividing both sides by 5, we find that *x = 9*.

- Understand the concept of ratios and how they are used to compare quantities.
- Learn to recognize proportional relationships and how to express them in the form of a proportion.
- Practice solving proportions using cross multiplication and finding equivalent fractions.
- Work on real-world problems that involve proportional reasoning, such as scaling and map problems.
- Review the cross products property and how it can be used to solve proportions.

Proportions are an important concept in mathematics and have many applications in everyday life. Understanding how to work with proportions will help you solve various types of problems involving comparisons and scaling.

.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.