Percentages: – Understanding and calculating percentage values.

PERCENTAGES Understanding and calculating percentage values. Grade 7 Mathematics: Percentages – Understanding and Calculating Percentage Values Subtopic Navigator Introduction Concept of Percentages Converting Between Fractions, Decimals, and Percentages Calculating Percentages of Quantities Percentage Increase and Decrease Applications and Mixed Problems Cumulative Exercises Conclusion Lesson Objectives Understand the meaning of percentage as "per hundred". Convert between percentages, decimals, and fractions. Calculate percentages of numbers and quantities. Apply percentages in real-life problems such as discounts and profit/loss. Lesson Introduction The term percentage comes from "per cent," meaning "out of 100". It is a way of expressing a fraction with a denominator of 100. For example, [latex]25% = tfrac{25}{100} = 0.25[/latex]. Percentages are widely used in daily life: discounts in shops, exam scores, bank interest rates, and data statistics. This lesson will guide you on how to calculate, compare, and apply percentages effectively. Concept of Percentages A percentage represents a portion of 100. The symbol "%" denotes percent. For example: [latex]60% = tfrac{60}{100} = 0.6[/latex]. Example 1: Express 45% as a fraction and as a decimal. Solution: [latex]45% = tfrac{45}{100} = tfrac{9}{20} = 0.45[/latex] Example 2: Write 0.72 as a percentage. Solution: [latex]0.72 times 100 = 72%[/latex] Exercises (Concept of Percentages) Write 85% as a fraction in its simplest form. Express 0.36 as a percentage. Converting Between Fractions, Decimals, and Percentages Conversion between percentages, fractions, and decimals requires simple multiplication or division by 100. - To convert a fraction to a percentage: multiply by 100. - To convert a decimal to a percentage: multiply by 100. - To convert a percentage to a decimal: divide by 100. Example 3: Convert [latex]tfrac{3}{4}[/latex] to a percentage. Solution: [latex]tfrac{3}{4} times 100% = 75%[/latex] Example 4: Convert 120% to a decimal. Solution: [latex]120% = tfrac{120}{100} = 1.2[/latex] Exercises (Conversions) Convert 0.18 to a percentage. Write 150% as a fraction in its simplest form. Calculating Percentages of Quantities To calculate a percentage of a number, multiply the number by the percentage (in decimal or fraction form). Formula: [latex]text{Percentage of a number} = tfrac{text{Percentage}}{100} times text{Number}[/latex] Example 5: Find 25% of 200. Solution: [latex]tfrac{25}{100} times 200 = 50[/latex] Example 6: A student scored 72% of 150 marks. How many marks did he score? Solution: [latex]tfrac{72}{100} times 150 = 108[/latex] Exercises (Calculating Percentages) Find 40% of 350. A girl scored 65% of 200 marks. How many marks did she get? Percentage Increase and Decrease Percentage increase or decrease shows the relative change in value. Formula: [latex]tfrac{text{Change}}{text{Original Value}} times 100%[/latex] Example 7: A price increases from $80 to $100. Find the percentage increase. Solution: Change = 20. [latex]tfrac{20}{80} times 100 = 25%[/latex] Example 8: A shirt was $60 but is now sold for $45. Find the percentage decrease. Solution: Change = 15. [latex]tfrac{15}{60} times 100 = 25%[/latex] Exercises (Percentage Increase/Decrease) The population of a town increased from 40,000 to 50,000. Find the percentage increase. The value of a car decreased from $25,000 to $20,000. Find the percentage decrease. Applications and Mixed Problems Example 9: A shop gives a 10% discount on a $500 TV. How much is the discount and the new price? Solution: Discount = [latex]tfrac{10}{100} times 500 = 50[/latex]. New price = [latex]500 - 50 = 450[/latex]. Example 10: A man invests $2000 in a bank that pays 5% interest per year. How much interest does he earn in a year? Solution: Interest = [latex]tfrac{5}{100} times 2000 = 100[/latex]. Exercises (Applications) A trader bought a phone for $800 and sold it for $1000. Find his profit percentage. A bag costs $250. A discount of 8% is given. Find the discount and selling price. Cumulative Exercises Express 0.57 as a percentage. Write 135% as a fraction in its simplest form. Find 12% of 450. Convert 72% to a decimal. The cost of a laptop increased from $600 to $750. Find the percentage increase. A student got 45 marks out of 60. Express his score as a percentage. A machine valued at $5000 depreciates to $4000. Find the percentage decrease. A store offers 15% discount on a $200 item. What is the new price? A man earns $3500 per month and spends 40% of it on rent. How much does he spend on rent? The price of a commodity increased from $120 to $150. Find the percentage increase. Conclusion/Recap Percentages allow us to compare quantities easily since they are based on 100. We have learned how to convert between percentages, fractions, and decimals, calculate percentages of numbers, and solve real-life problems involving percentage increase, decrease, profit, and discounts. Mastery of percentages is essential for handling financial literacy, examinations, and daily life. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c