Percent

Percentages are used to express a portion out of 100. Understanding percentages is important in many areas, including finance, science, and everyday life. In mathematics, percentages are often used to compare quantities and to solve problems involving ratios and proportions.

Key Concepts

Percent: A percent is a ratio that compares a number to 100. It is denoted by the symbol "%". For example, 50% means 50 out of 100.
Converting between Percentages and Decimals: To convert a percentage to a decimal, divide by 100. For example, 25% is equivalent to 0.25 as a decimal. To convert a decimal to a percentage, multiply by 100. For example, 0.6 is equivalent to 60% as a percentage.
Converting between Percentages and Fractions: To convert a percentage to a fraction, write the percentage as a fraction with a denominator of 100. For example, 75% is equivalent to 75/100, which simplifies to 3/4. To convert a fraction to a percentage, multiply the fraction by 100 and add a percent sign. For example, 2/5 is equivalent to 40% as a percentage.
Percent Increase and Decrease: To calculate a percent increase, use the formula: ((New Value - Original Value) / Original Value) * 100. To calculate a percent decrease, use the formula: ((Original Value - New Value) / Original Value) * 100.

Practice Problems

1. Convert 0.6 to a percentage.

Answer: 0.6 * 100 = 60%

2. Convert 3/4 to a percentage.

Answer: (3/4) * 100 = 75%

3. Calculate the percent increase if a $50 item is now selling for $65.

Answer: ((65 - 50) / 50) * 100 = 30%

4. Calculate the percent decrease if the temperature drops from 80°F to 68°F.

Answer: ((80 - 68) / 80) * 100 = 15%

Summary

Understanding percentages is an essential skill in mathematics. By mastering the conversion between percentages, decimals, and fractions, as well as the calculation of percent increase and decrease, you will be able to apply this knowledge to a wide range of real-world problems.