CAPS Mathematical Literacy Grade 12: Percentages Revision Notes

Introduction

Understanding percentages is crucial for many aspects of mathematical literacy. They are used to express how large or small one quantity is relative to another. Percentages are essential in finance, data analysis, and everyday life such as discounts, interest rates, and population statistics.

Essential Learning Objectives:

• Calculate percentages of given quantities.
• Understand percentage increase and decrease.
• Apply percentages to real-world problems.

Key Points

1. Definition:

   • A percentage is a way of expressing a number as a fraction of 100.
   • Formula: [ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 ]

2. Calculating Percentages:

   • To find what percentage one number is of another, use: [ \text{percentage} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100 ]
   • Example: What percentage is 20 of 50?
     [ \left( \frac{20}{50} \right) \times 100 = 40\% ]

3. Percentage Increase and Decrease:

   • Increase: [ \text{Percentage Increase} = \left( \frac{\text{New Value – Original Value}}{\text{Original Value}} \right) \times 100 ]
   • Decrease: [ \text{Percentage Decrease} = \left( \frac{\text{Original Value – New Value}}{\text{Original Value}} \right) \times 100 ]

4. Percentage of a Quantity:

   • Finding a specific percentage of a quantity: [ \text{Result} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Quantity} ]
   • Example: What is 25% of 200?
     [ \left( \frac{25}{100} \right) \times 200 = 50 ]

Real-World Applications

• Discounts: If a jacket costs R200 and there is a 15% discount, the discount amount is:
  [ \text{Discount Amount} = \left( \frac{15}{100} \right) \times 200 = R30 ]
  [ \text{Sale Price} = 200 – 30 = R170 ]

• Interest Rates: If you invest R1000 at an annual interest rate of 5%, the interest earned in one year is:
  [ \text{Interest} = \left( \frac{5}{100} \right) \times 1000 = R50 ]

Common Misconceptions and Errors

• Misunderstanding the Base: Confusing the part and whole in percentage calculations.
  • Solution: Always identify which number is the part and which is the whole.
• Percentage Over 100: Assuming percentages cannot exceed 100.
  • Note: Percentages over 100 are possible, indicating that the part is greater than the whole.

Practice and Review

Basic Practice Questions

1. What is 10% of 250?
2. A shirt worth R450 is on sale for 20% off. What is the new price?

Advanced Practice Questions

1. If the population of a town increases by 12% to 5600, what was the original population?
2. Solution: [ \text{Original Population} = \frac{5600}{1 + \frac{12}{100}} = 5000 ]
3. A car depreciates by 15% each year. If its current value is R200,000, what was its value one year ago?
4. Solution: [ \text{Original Value} = \frac{200,000}{1 – \frac{15}{100}} = 235,294.12 ]

Examination Tips

• Keywords: Look for terms like “increase,” “discount,” “off,” and “rate.”
• Time Management: Allocate more time for complex percentage problems involving multiple steps.

Connections and Extensions

• Understanding percentages can help in other subjects such as economics, business studies, and health sciences.
• Explore how percentages relate to fractions and decimals for a broader comprehension.

Summary and Quick Review

• Percentages express ratios out of 100.
• Calculate percentages using part/whole formulas.
• Apply percentage calculations to increases, decreases, and finding parts of quantities.
• Avoid common errors by understanding part/whole contexts.

Additional Resources

• Khan Academy: Offers video tutorials on percentage calculations.
• YouTube Channels: Look for channels dedicated to math tutorials, such as “Math Antics.”
• Educational Websites: Websites like BBC Bitesize and IXL provide interactive percentage problems.

By grasping these basic skills, students can confidently approach a wide range of mathematical problems and practical situations involving percentages【4:10†source】【4:12†source】【4:17†source】【4:19†source】.