Percentages (Grade 10 NSC Matric Mathematical Literacy): Revision Notes

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Percentages

What is a percentage?

Percentage is a number represented as a part of 100. The word "percent" literally means "per 100", so when we say 25%, we mean 25 out of every 100.

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Percentages help us compare different amounts and understand proportions in everyday situations like discounts, tax rates, exam scores, and statistical data.

How to calculate a percentage of an amount

There are two main methods to calculate a percentage of an amount:

Method 1: Using fractions

  1. Write the percentage as a fraction with denominator 100
    • For example: 20% = 20100\frac{20}{100}
  2. Multiply this fraction by the given amount

Method 2: Using decimals

  1. Convert the percentage to a decimal fraction
    • For example: 20% = 0.2
  2. Multiply the decimal by the given amount
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Both methods give the same result, so choose the one that feels easier for you.

Worked examples of percentage calculations

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Worked Example 1: Finding percentage of population

Question: There are 50 586 757 people in South Africa and 43% live in rural areas. How many people live in rural areas?

Solution: Method 1 (Fraction): 43% = 43100\frac{43}{100} 43100×50586757=21752305\frac{43}{100} \times 50 586 757 = 21 752 305 people live in rural areas.

Method 2 (Decimal): 43% = 0.43 0.43×50586757=217523050.43 \times 50 586 757 = 21 752 305 people live in rural areas.

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Worked Example 2: Medical statistics

Question: There are 1291 tuberculosis patients at the Chris Hani Baragwanath Hospital. 80% of them are H.I.V. positive. How many T.B. patients are H.I.V. positive?

Solution: 80% = 80100\frac{80}{100} 80100×1291=1032\frac{80}{100} \times 1291 = 1032 patients

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Worked Example 3: Voting statistics

Question: 21.7 million South Africans voted in the 1994 elections. 73% of them had never voted before. How many people had never voted before the 1994 election?

Solution: 73% = 73100\frac{73}{100} 73100×21700000=15841000\frac{73}{100} \times 21 700 000 = 15 841 000 people had never voted before.

Finding what percentage one amount is of another

Sometimes you need to find what percentage one number represents of another number.

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Worked Example: T-shirt sales

Question: Top Teenage T-shirts printed 120 T-shirts. They sold 72 T-shirts immediately. What percentage of the T-shirts were sold?

Solution: 72120×100=60%\frac{72}{120} \times 100 = 60\%

So 60% of the T-shirts were sold.

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Formula: PartWhole×100=Percentage\frac{\text{Part}}{\text{Whole}} \times 100 = \text{Percentage}

Percentage discounts and increases

Percentages are commonly used in business to show price changes, discounts, and increases.

Key business terms

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Key Business Definitions:

  • Cost price: The amount that the dealer, trader, or merchant pays for an article.

  • Marked price: The original price of the article before any discounts.

  • Selling price: The final price after discount has been applied.

  • Profit: The difference between selling price and cost price. Formula: Profit = Selling price - Cost price

Understanding discounts and increases

Discounts reduce the original price:

  • A dress was R239.96 with 25% discount
  • Roller skates were R299.50 with 15% discount

Increases add to the original price:

  • A salary was R9 875 with 8% increase
  • Furniture was R15 995 with 5% increase

Calculating discounts

To find the final price after a discount:

  1. Calculate the discount amount: Original price × discount percentage
  2. Subtract discount from original price: Final price = Original price - Discount amount
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Alternative method: If there's a 25% discount, you pay 75% of the original price. Final price = Original price × (100% - discount%)

Calculating increases

To find the final price after an increase:

  1. Calculate the increase amount: Original price × increase percentage
  2. Add increase to original price: Final price = Original price + Increase amount
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Alternative method: If there's a 10% increase, you pay 110% of the original price. Final price = Original price × (100% + increase%)

Exam tips

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Essential Exam Strategies:

  • Always read carefully whether you need to find the discount/increase amount or the final price
  • Check if the question asks for a percentage or an actual amount
  • Use your calculator for complex calculations, but show your working
  • Remember that "of" in mathematics usually means "multiply"
  • Double-check your answers - they should make sense in context

Remember!

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Key Points to Remember:

  • Percentage means "out of 100" - 50% = 50 out of 100 = 12\frac{1}{2}

  • Two methods for calculations: fraction method (percentage100\frac{\text{percentage}}{100}) or decimal method (percentage ÷ 100)

  • For discounts: Final price = Original price - (Original price × discount%)

  • For increases: Final price = Original price + (Original price × increase%)

  • Finding percentages: PartWhole×100=Percentage\frac{\text{Part}}{\text{Whole}} \times 100 = \text{Percentage}

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