Percentage II

Grade 12 Math - Percentage

Lesson Objectives

Understand the concept of percentage and its real-life applications.
Calculate percentages of quantities.
Solve problems on percentage increase and decrease.
Interpret results in context-based scenarios such as profit, discount, and inflation.

Lesson Introduction

Percentages are used to express proportions, compare changes, and describe relationships in finance, business, and everyday life. This lesson explores how to calculate percentages and understand the impact of percentage increase and decrease in various scenarios.

Core Lesson Content

Key Concepts

\( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \)
\( \text{Percentage Increase} = \frac{\text{Increase}}{\text{Original}} \times 100 \)
\( \text{Percentage Decrease} = \frac{\text{Decrease}}{\text{Original}} \times 100 \)

Worked Example

Example 1: Find 25% of ₦4,000.
\( \frac{25}{100} \times 4000 = ₦1000 \)

Example 2: What is 60% of 850?
\( \frac{60}{100} \times 850 = 510 \)

Example 3: Increase ₦2,000 by 10%.
Increase = \( \frac{10}{100} \times 2000 = ₦200 \)
New amount = ₦2,000 + ₦200 = ₦2,200

Example 4: Decrease ₦5,000 by 12%.
Decrease = \( \frac{12}{100} \times 5000 = ₦600 \)
New amount = ₦5,000 - ₦600 = ₦4,400

Example 5: A TV that cost ₦40,000 is now sold at ₦36,000. Find the percentage decrease.
Decrease = ₦40,000 - ₦36,000 = ₦4,000
Percentage decrease = \( \frac{4000}{40000} \times 100 = 10\% \)

Example 6: A product’s price increased from ₦25,000 to ₦30,000. Find the percentage increase.
Increase = ₦30,000 - ₦25,000 = ₦5,000
Percentage increase = \( \frac{5000}{25000} \times 100 = 20\% \)

Example 7: [WAEC] If 15% of a number is 75, find the number.
\( \frac{15}{100} \times x = 75 \Rightarrow x = \frac{75 \times 100}{15} = 500 \)

Example 8: What percentage of ₦2,500 is ₦375?
\( \frac{375}{2500} \times 100 = 15\% \)

Example 9: A trader made a profit of ₦600 on goods worth ₦2,400. Find the percentage profit.
\( \frac{600}{2400} \times 100 = 25\% \)

Example 10: A student scored 45 out of 60 in a test. What percentage did the student score?
\( \frac{45}{60} \times 100 = 75\% \)

Exercises

Find 18% of ₦3,600.
Decrease ₦2,400 by 8%.
[JAMB] Increase ₦12,000 by 25%. (Past Question)
What is the percentage decrease if a price drops from ₦2,500 to ₦2,000?
[WAEC] A product was ₦1,500 but is now ₦1,800. Find the percentage increase. (Past Question)
[NECO] 30% of a number is 120. Find the number. (Past Question)
What percentage of 200 is 40?
If a trader makes a ₦750 profit on ₦3,000 goods, what is the percentage profit?
[WAEC] A test has 80 marks. A student scored 60 marks. Find the percentage score. (Past Question)
What is 5% of ₦50,000?

Conclusion/Recap

Calculating percentages is useful in understanding increases and decreases in quantities, discounts, profits, test scores, and other real-life applications. Mastery of these calculations helps students in everyday decision-making and exams.