Lesson 4: Percentages, Rates, and Taxes

📥 Introduction

Every day, you see percentages: “50% discount!” “Interest rate is 12%!” “5% tax on goods!”
Percentages, rates, and taxes help us understand parts of a whole, compare values, and calculate real-world costs.

In this lesson, you’ll learn how to work with percentages, solve problems involving rates, and understand simple taxes — skills that will help you in shopping, banking, and everyday decision-making!

🧠 Key Concepts and Explanations

1. What is a Percentage?

A percentage (%) is a way of expressing a number as a part of 100.
It means “per hundred.”

Example: 25% means 25 out of 100, or .

2. Converting Between Fractions, Decimals, and Percentages

• Fraction to Percentage: Multiply the fraction by 100.
• Decimal to Percentage: Multiply the decimal by 100.
• Percentage to Fraction or Decimal: Divide by 100.

Examples:

• (Fraction to percentage)
• 0.75 × 100 = 75% (Decimal to percentage)
• 25% = 0.25 or

3. Finding Percentage of a Quantity

To find a percentage of a number, multiply the number by the percentage divided by 100.

Formula:

Example: Find 20% of 250.

• 20% × 250 ÷ 100 = 50

4. Rates

A rate compares two quantities with different units, often “per” something (like kilometers per hour, cedis per kilogram, etc.).

5. Simple Taxes

Tax is a percentage added to the price of goods or income. In shops, you might pay VAT (Value Added Tax).

Formula:

Example: Find the tax on GHS 200 if tax rate is 5%.

• 5% × 200 ÷ 100 = GHS 10
• Total price = GHS 200 + GHS 10 = GHS 210

📝 Step-by-Step Sample Walkthroughs

Example 1: Convert 0.65 to a percentage

• 0.65 × 100 = 65%

Example 2: Find 15% of 320

• 15 × 320 ÷ 100 = 48

Example 3: A car travels 180 km in 3 hours. Find the speed.

• Speed = Distance ÷ Time = 180 ÷ 3 = 60 km/h

Example 4: Calculate the total cost of an item priced at GHS 400 with a 7.5% VAT.

• VAT = 7.5% × 400 ÷ 100 = GHS 30
• Total = GHS 400 + GHS 30 = GHS 430

✅ Practice Exercises

A. Convert Between Forms

• = ? %
• 0.4 = ? %
• 90% = ? as a decimal

B. Find the Percentage

• Find 25% of 600.
• Find 35% of 480.

C. Solve Rate Problems

• A machine produces 150 items in 5 hours. What is its rate per hour?
• A car covers 240 km in 4 hours. Find its speed.

D. Calculate Simple Taxes

• Find the tax on GHS 500 at 6% VAT.
• A laptop costs GHS 1200. How much is the total cost if VAT is 5%?

E. True or False?

• 50% of 300 is 150.
• 0.2 is the same as 2%.

🔁 Recap

• Percentages express parts out of 100.
• Rates compare different quantities per unit.
• Taxes are extra amounts paid based on percentage rates.
• Real-life skills: shopping, banking, travel, and business!

🪞Reflection Prompt

Think about your last purchase. Did you pay tax? Could you calculate the tax and final price yourself? Try it!