Percentages are a way of expressing a number as a fraction of 100. The term "percent" means "per hundred," so when we say "10 percent," we mean "10 out of 100." Percentages are used in many real-life situations, such as calculating discounts, expressing proportions, and understanding interest rates.

To convert a percentage to a decimal, divide the percentage by 100. To convert a decimal to a percentage, multiply the decimal by 100.

For example:

- 25% as a decimal is 0.25 (25 ÷ 100)
- 0.6 as a percentage is 60% (0.6 × 100)

To calculate a percentage of a number, multiply the number by the percentage as a decimal. To find the percentage increase or decrease between two numbers, use the formula:

Percentage Change = ((New Value - Old Value) / Old Value) × 100

Percentages can also be used to express proportions. For example, if 40% of a group of students are girls, it means 40 out of every 100 students are girls. To calculate the actual number of students, you can use proportions and cross-multiplication.

- Convert 0.75 to a percentage.
- If a shirt originally costs $40 and is on sale for 20% off, what is the sale price?
- A population of 5000 people increases to 6000 people. What is the percentage increase?
- If 30% of a number is 45, what is the number?

- 0.75 as a percentage is 75% (0.75 × 100 = 75%)
- The sale price of the shirt is $32 ($40 - (20% of $40))
- The percentage increase is 20% ((6000 - 5000) / 5000 × 100 = 20%)
- The number is 150 (45 ÷ 0.3 = 150)

By understanding percentages and practicing these types of problems, you can become more comfortable with this important concept in mathematics.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

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.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

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

Solve problems involving scale factors, using ratio and proportion.

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.