Percentages - BBC Bitesize Lecture Notes

What are Percentages?

• Percent or % means 'out of one hundred'.
• Example: In a diagram, 30 out of 100 squares shaded = 30% shaded.

Examples of Percentages

• Various diagrams illustrate different percentages shaded:
  • 72%, 60%, 50%, 25% shaded, etc.

Writing One Number as a Percentage of Another

• Key Formula: Divide the first number by the second number, then multiply by 100 to find the percentage.
• Example Problems:
  • Dress reduced by £10 on £80 cost = 12.5% reduction.
  • 12 boys in 20-member swim team = 60% boys.

Finding the Percentage of a Quantity

• Useful for calculating increases such as fare hikes.
• Method 1:
  • Find 1% by dividing quantity by 100.
  • Multiply 1% by desired percentage.
• Method 2:
  • Multiply quantity by percentage as a fraction.
• Example: 20% of 60 pens = 12 red pens.

How to Work Out the Percentage of an Amount

• Illustrated Steps:
  1. Draw bars to visualize problem (e.g., 20% of 70g chocolate).
  2. Convert percentage to decimal (e.g., 20% = 0.20).
  3. Multiply by decimal to find the amount.
  4. Calculate and visualize using context.

Bargain Calculations

• Example: Calculating 35% of £48 reduces it by £16.80.
• Comparing discounts: Fraction to percentage conversion to determine best bargain.

Test Section (Practice Questions)

• Examples:
  • 40 squares out of 100 shaded = 40%.
  • Calculate 70% of grid shaded for different configurations.
  • Calculate percentage of quantities like number of people, weight, or price reductions.

Conclusion

• Understanding percentages involves converting between fractions, decimals, and percentages.
• Practical applications include financial calculations, exam scores, and everyday discounts.

Further Learning

• Explore more on percentage change, simple and compound interest to deepen understanding.