Methods for Calculating Percentages of Numbers

May 5, 2024

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Lecture Notes: Calculating a Percent of a Number

Summary

Today’s lecture on Math Antics covered how to find a percent of a number. We learned that a percent represents a fraction of a total amount and can be found by using multiplication. Key methods include converting the percentage to both fraction and decimal forms before multiplying with the total amount.

Key Points

Understanding Percentages

  • Percentages as Fractions: A percentage represents a fraction of a total; for example, 25% represents 25/100.
  • Percentages and Multiplication: The term 'of' in percentage calculations is equivalent to multiplication (e.g., 25% of 20 is 25% x 20).

Methods to Calculate Percentages

Using the Fraction Form

  1. Convert the percentage to a fraction (e.g., 25% becomes 25/100).
  2. Write the total amount as a fraction (20 as 20/1).
  3. Multiply the numerators and denominators respectively.
  4. Simplify the resulting fraction to find the percentage of the number.
    • Example: ( \frac{25 \times 20}{100 \times 1} = \frac{500}{100} = 5 )
    • So, 25% of 20 is 5.

Using the Decimal Form

  1. Convert the percentage to a decimal (e.g., 25% becomes 0.25).
  2. Multiply the decimal by the total amount using a calculator or manually.
    • Example: ( 0.25 \times 20 = 5 )
    • Therefore, 25% of 20 is also 5.

Practice Examples

Example 1: Percentage with Money

  • Calculate 35% of $80 earned from walking dogs.
    1. Convert 35% to decimal (0.35).
    2. Multiply: ( 0.35 \times 80 = 28 )
    • Thus, 35% of $80 is $28.

Example 2: Percentage Exceeding 100%

  • Calculate 120% of a number, e.g., school students increasing from 400 to 120% of that.
    1. Convert 120% to decimal (1.20).
    2. Multiply: ( 1.20 \times 400 = 480 )
    • Hence, the school has 480 students this year, demonstrating an increase.

Conclusion

Finding a percent of a number involves converting the percentage to either a fraction or a decimal and multiplying it by the amount. This methodology accommodates both simple and complex real-life scenarios, such as financial calculations or analyzing increases. Regular practice with different examples is encouraged to gain proficiency in this mathematic skill.

For further learning and more examples, visit Math Antics.