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 GuideNumbers and percents Worksheet/Answer key

Numbers and percents Worksheet/Answer key

Numbers and percents Worksheet/Answer key

Numbers and percents

Number and Operations (NCTM)

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

Work flexibly with fractions, decimals, and percents to solve problems.

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.