Percentages

Lesson Objectives

Understand the concept of percentages and their applications.
Convert between fractions, decimals, and percentages.
Calculate percentage increase, decrease, and percentage of quantities.
Solve real-life problems involving percentages.

Lesson Introduction

A percentage is a way of expressing a number as a part of 100. The symbol for percent is \(\%\). For example, 45% means 45 out of 100, or \(\frac{45}{100}\). Percentages are used widely in finance, sales, statistics, and many daily situations.

Lesson Content

Meaning of Percentage

Percentage means "per hundred." So:

\(25\% = \frac{25}{100} = 0.25\)

Conversion Between Forms

Fraction to percentage: Multiply by 100
\(\frac{1}{4} \times 100\% = 25\%\)
Decimal to percentage: Multiply by 100
\(0.6 \times 100\% = 60\%\)
Percentage to decimal: Divide by 100
\(75\% = \frac{75}{100} = 0.75\)

Finding Percentage of a Quantity

To find \(x\%\) of a number, multiply the number by \(\frac{x}{100}\).
E.g., 20% of 60 = \(\frac{20}{100} \times 60 = 12\)

Percentage Increase and Decrease

Increase: \(\text{Increase} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%\)
Decrease: \(\text{Decrease} = \frac{\text{Old} - \text{New}}{\text{Old}} \times 100\%\)

Applications of Percentage

Profit and loss
Discounts and interest
Statistics and data interpretation

Examples

Example: Convert \(\frac{3}{5}\) to a percentage.

\(\frac{3}{5} \times 100 = 60\%\)

Example: Find 25% of 80.

\(\frac{25}{100} \times 80 = 20\)

Example: Increase 120 by 10%.

\(\frac{10}{100} \times 120 = 12\),
New value = \(120 + 12 = 132\)

Example: A number is reduced from 200 to 160. Find the percentage decrease.

\(\frac{200 - 160}{200} \times 100 = \frac{40}{200} \times 100 = 20\%\)

Example: A trader bought goods for ₦5000 and sold them for ₦6000. What is the percentage profit?

Profit = \(6000 - 5000 = 1000\)
\(\frac{1000}{5000} \times 100 = 20\%\)

Exercises

Convert \(0.85\) to a percentage.
[WAEC] Find 12% of 250. (Past Question)
Convert 36% to a decimal.
[NECO] Express \(\frac{7}{8}\) as a percentage. (Past Question)
What is the percentage increase from 50 to 70?
[JAMB] A dress was ₦4000 but is now ₦3000. What is the percentage decrease? (Past Question)
Find 40% of ₦1,200.
[NABTEB] A trader gained ₦150 on a sale of ₦750. Find the gain percentage. (Past Question)
Write \(\frac{9}{10}\) as a percentage.
Increase 250 by 20%.

Conclusion/Recap

This lesson has explained how to work with percentages, convert between formats, and apply percentage calculations in real-world problems. Mastery of this topic is essential for commerce, finance, data interpretation, and everyday decision-making.