Percentages

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.

Converting between Percentages and Decimals

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)

Calculating Percentages

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 and Proportions

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.

Practice Problems

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

Answers

1. 0.75 as a percentage is 75% (0.75 × 100 = 75%)
2. The sale price of the shirt is $32 ($40 - (20% of $40))
3. The percentage increase is 20% ((6000 - 5000) / 5000 × 100 = 20%)
4. 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.

[Percentages] Related Worksheets and Study Guides:

• Introduction to PercentMathematics • Seventh Grade
• PercentageMathematics • Sixth Grade
• PercentsMathematics • Fourth Grade
• PercentsMathematics • Fifth Grade