Expressing One Number as a Percentage of Another

In this lecture, we cover how to express one number as a percentage of another number. The process involves expressing the numbers as a fraction and then converting that fraction to a percentage by multiplying by 100.

Steps to Convert Number to a Percentage

1. Express as a Fraction:
   • Example: To express 15 as a percentage of 25, set it as 15/25.
2. Convert Fraction to Percentage:
   • Multiply the fraction by 100.
   • Simplify the fraction if necessary.

Example Calculations

• 15 as a percentage of 25:

  • Fraction: 15/25 = 3/5
  • Percentage: (3/5) * 100 = 60%

• 240 grams as a percentage of 320 grams:

  • Fraction: 240/320
  • Percentage: (240/320) * 100 = 75%

Handling Decimals

• Example: 0.3 as a percentage of 1.5:
  • Fraction: 0.3/1.5
  • Use a calculator or simplify by multiplying top and bottom by 10.
  • Simplified: 3/15 = 1/5
  • Percentage: (1/5) * 100 = 20%

Different Units

• Example: 1.2 kilos as a percentage of 800 grams:
  • Convert 1.2 kilos to 1200 grams.
  • Fraction: 1200/800
  • Since 1200 > 800, expect percentage > 100.
  • Percentage: (1200/800) * 100 = 150%

Percentage Change Example

• Scenario: Price of a car decreases by 4,000 pounds from an original price of 32,000 pounds.
  • Calculation: 4,000 / 32,000
  • Percentage decrease: (4,000/32,000) * 100 = 12.5%

Key Points

• Simplify fractions before multiplying by 100 for easier calculation.
• Ensure units are consistent when calculating percentages.
• If numerators are greater than denominators, percentages will be above 100%.

Conclusion

• The method applies to various scenarios, including those with different units or within word problems.
• Practice with a calculator or manual simplification for more efficiency.

Remember, practice with different examples to master these conversions. Share this knowledge with others to help them understand. Cheers!