Percentages

Grade 7 Mathematics - Percentages

Lesson Objectives

Understand the meaning of percentage.
Convert between fractions, decimals, and percentages.
Calculate a percentage of a quantity.
Solve problems involving increases, decreases, discounts, and interest.

Lesson Introduction

Percentages are used daily — in shopping, banking, profit, and statistics. A percentage is a way of expressing a number as a part of 100. For example, 25% means 25 out of 100. In this lesson, we’ll explore how to calculate percentages and apply them to real-life problems.

Core Lesson Content

Definition of Percentage

Percentage means "per hundred". It is represented using the symbol %.
For example: $50\% = \frac{50}{100} = 0.5$

Converting Between Forms

To convert a percentage to a decimal, divide by 100: $25\% = \frac{25}{100} = 0.25$
To convert a fraction to a percentage, multiply by 100: $\frac{3}{4} \times 100\% = 75\%$

Worked Examples

Example 1: What is 20% of 150?

\frac{20}{100} \times 150 = 30

Explanation: Multiply the percentage fraction by the number.

Example 2: Convert 0.75 to a percentage.

0.75 \times 100\% = 75\%

Explanation: Multiply the decimal by 100 and add the % sign.

Example 3: Express

\frac{1}{5}

as a percentage.

\frac{1}{5} \times 100\% = 20\%

Explanation: Multiply the fraction by 100.

Example 4: A student scored 18 out of 20 in a test. What percentage did the student score?

\frac{18}{20} \times 100\% = 90\%

Explanation: Divide the score by the total and multiply by 100.

Example 5: Increase ₦500 by 10%.

\frac{10}{100} \times 500 = 50

500 + 50 = 550

Explanation: Find 10% of 500 and add it.

Example 6: Decrease ₦800 by 25%.

\frac{25}{100} \times 800 = 200

800 - 200 = 600

Explanation: Find 25% of 800 and subtract it.

Example 7: A shop gives a 15% discount on a ₦1200 bag. What is the new price?

\frac{15}{100} \times 1200 = 180

1200 - 180 = 1020

Explanation: Calculate discount and subtract from original price.

Example 8: Find the percentage increase from 200 to 260.

\frac{260 - 200}{200} \times 100 = \frac{60}{200} \times 100 = 30\%

Explanation: Use the percentage change formula.

Example 9: What percent of 250 is 50?

\frac{50}{250} \times 100 = 20\%

Explanation: Divide the part by the whole and multiply by 100.

Example 10: A ₦1500 item is sold at 10% loss. What is the selling price?

\frac{10}{100} \times 1500 = 150

1500 - 150 = 1350

Explanation: Calculate 10% loss and subtract it.

Exercises

Find 35% of 400.
Convert $\frac{7}{10}$ to percentage.
Express 0.2 as a percentage.
[NABTEC] Increase ₦320 by 25%. [Past Question]
Decrease ₦500 by 12%.
[NECO] A student scored 36 out of 60. What percentage is this? [Past Question]
[JAMB] Find the new price after 20% discount on ₦2500. [Past Question]
[WAEC] What is the percentage increase from 80 to 100? [Past Question]
A jacket costs ₦1800 and was sold for ₦1620. What is the percentage loss?
What percent of 480 is 96?

Conclusion/Recap

In this lesson, we learned how to calculate and apply percentages in various ways including price changes, scores, discounts, and increases. In the next lesson, we will study Ratio and Proportion.