A ratio is a comparison of two numbers. It can be written in three ways: using the word "to," using a colon, or as a fraction. For example, the ratio of boys to girls in a class of 20 students can be written as 4:6, 4 to 6, or 4/6.

A proportion is an equation that states that two ratios are equal. For example, if 2/3 is equal to 4/x, then it forms a proportion. Proportions can be solved using cross multiplication.

A percent is a ratio that compares a number to 100. It is often represented using the symbol "%". For example, 25% means 25 out of 100, or 0.25 as a decimal. Percentages are commonly used to express parts of a whole or to compare one quantity to another.

- Understand the concept of ratios and how to express them in different forms.
- Learn how to identify and solve proportions by using cross multiplication.
- Practice converting between fractions, decimals, and percents.
- Understand the relationship between fractions, decimals, and percents.
- Apply the concepts of ratios, proportions, and percents to real-world problems, such as discounts, taxes, and interest rates.

1. Calculate 30% of 80.

Answer: To calculate 30% of 80, you can use the formula: (30/100) * 80 = 24.

2. Solve the proportion: 2/5 = 4/x.

Answer: Cross multiplying gives you 2x = 20, so x = 10.

3. Express the ratio 3:5 as a fraction in simplest form.

Answer: The ratio 3:5 can be written as the fraction 3/5, which is already in its simplest form.

.Study GuideRatios, proportions and percents Worksheet/Answer key

Ratios, proportions and percents Worksheet/Answer key

Ratios, proportions and percents Worksheet/Answer key

Ratios, proportions and percents Worksheet/Answer keyRatios, proportions and percents

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

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.

Solve simple problems involving rates and derived measurements for such attributes as velocity and density.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.