Percentages Basic 6 Mathematics Lesson Note

What is Percentage?

Percentage means “out of 100” or “per hundred”. The symbol % represents percentage.

Examples:

• 50% = 50/100 = 1/2 = 0.5
• 25% = 25/100 = 1/4 = 0.25
• 75% = 75/100 = 3/4 = 0.75

Converting Between Fractions, Decimals and Percentages

Fraction to Percentage

Method: Multiply by 100

Examples:

• 1/2 = 1/2 × 100 = 50%
• 3/4 = 3/4 × 100 = 75%
• 1/5 = 1/5 × 100 = 20%

Decimal to Percentage

Method: Move decimal point 2 places right (or multiply by 100)

Examples:

• 0.45 = 45%
• 0.8 = 80%
• 0.125 = 12.5%

Percentage to Fraction

Method: Write over 100 and simplify

Examples:

• 60% = 60/100 = 3/5
• 25% = 25/100 = 1/4
• 80% = 80/100 = 4/5

Exercise A – Converting Percentages

Convert these fractions to percentages:

1. 1/4 = ______%
2. 3/5 = ______%
3. 7/10 = ______%
4. 2/3 = ______% (round to 1 decimal place)
5. 4/5 = ______%

Convert these decimals to percentages:

1. 0.35 = ______%
2. 0.9 = ______%
3. 0.125 = ______%
4. 0.65 = ______%
5. 1.25 = ______%

Convert these percentages to fractions (simplest form):

1. 30% = ______
2. 75% = ______
3. 40% = ______
4. 90% = ______
5. 15% = ______

Finding Percentage of a Number

Method 1: Using Fractions

Example: Find 25% of 80 25% = 25/100 = 1/4 25% of 80 = 1/4 × 80 = 20

Method 2: Using Decimals

Example: Find 15% of 200 15% = 0.15 15% of 200 = 0.15 × 200 = 30

Method 3: Using Division

Example: Find 20% of 150 20% of 150 = (20 × 150) ÷ 100 = 3000 ÷ 100 = 30

Exercise B – Finding Percentages

Calculate these percentages:

1. 50% of 120 = ______
2. 25% of 240 = ______
3. 10% of 450 = ______
4. 20% of 350 = ______
5. 75% of 160 = ______
6. 30% of 200 = ______
7. 5% of 800 = ______
8. 60% of 250 = ______
9. 15% of 300 = ______
10. 35% of 400 = ______

Finding What Percentage One Number is of Another

Formula: (Part/Whole) × 100 = Percentage

Example: What percentage is 15 out of 60? Percentage = (15/60) × 100 = 1/4 × 100 = 25%

Exercise C – Finding Percentages

Find what percentage:

1. 20 is of 80 = ______%
2. 45 is of 180 = ______%
3. 12 is of 48 = ______%
4. 75 is of 300 = ______%
5. 18 is of 72 = ______%
6. 35 is of 140 = ______%
7. 24 is of 96 = ______%
8. 50 is of 125 = ______%
9. 16 is of 64 = ______%
10. 90 is of 360 = ______%

Real Life Applications of Percentages

School and Test Scores

Example: Kemi scored 85 marks out of 100 in Mathematics Percentage = (85/100) × 100 = 85%

Money and Shopping

Example: A shirt costs ₦2,000. There is a 15% discount Discount = 15% of ₦2,000 = 15/100 × ₦2,000 = ₦300 Sale price = ₦2,000 – ₦300 = ₦1,700

Exercise D – School Problems

Solve these school-related problems:

1. Test Score: Tunde scored 72 marks out of 90 in English. What percentage did he score? Answer: ______%
2. Class Attendance: In a class of 40 students, 32 were present. What percentage attended? Answer: ______%
3. Exam Results: 60% of 150 students passed an exam. How many students passed? Answer: ______ students
4. Library Books: A school library has 800 books. 35% are Mathematics books. How many Mathematics books are there? Answer: ______ books
5. Sports Participation: In Primary 6, 75% of 120 students play football. How many students play football? Answer: ______ students

Exercise E – Money and Shopping Problems

Solve these money problems:

1. Discount Sale: A bag costs ₦4,500. If there is a 20% discount, what is the sale price? Answer: ₦______
2. Savings: Folake saves 25% of her monthly allowance of ₦2,400. How much does she save? Answer: ₦______
3. Price Increase: The price of rice increased from ₦15,000 to ₦18,000 per bag. What is the percentage increase? Answer: ______%
4. Commission: A sales agent earns 8% commission on sales. If he sells goods worth ₦50,000, how much commission does he earn? Answer: ₦______
5. Profit: A trader bought goods for ₦8,000 and sold them for ₦10,000. What is his percentage profit? Answer: ______%

Percentage Increase and Decrease

Percentage Increase

Formula: ((New Value – Old Value)/Old Value) × 100

Example: Price increased from ₦500 to ₦600 Increase = ₦600 – ₦500 = ₦100 Percentage increase = (100/500) × 100 = 20%

Percentage Decrease

Formula: ((Old Value – New Value)/Old Value) × 100

Example: Price decreased from ₦800 to ₦640 Decrease = ₦800 – ₦640 = ₦160 Percentage decrease = (160/800) × 100 = 20%

Exercise F – Increase and Decrease

Calculate these percentage changes:

1. Population Growth: A town’s population increased from 50,000 to 60,000. What is the percentage increase? Answer: ______%
2. Weight Loss: Tunde’s weight decreased from 60 kg to 54 kg. What is the percentage decrease? Answer: ______%
3. School Enrollment: Enrollment increased from 1,200 to 1,440 students. What is the percentage increase? Answer: ______%
4. Price Reduction: A phone price dropped from ₦25,000 to ₦20,000. What is the percentage decrease? Answer: ______%
5. Crop Yield: Harvest increased from 800 kg to 960 kg. What is the percentage increase? Answer: ______%

Simple Interest

Formula: Simple Interest = (Principal × Rate × Time) / 100

Example: Find simple interest on ₦5,000 at 8% per year for 3 years Simple Interest = (5,000 × 8 × 3) / 100 = 120,000 / 100 = ₦1,200

Exercise G – Simple Interest

Calculate simple interest:

1. Principal: ₦2,000, Rate: 5% per year, Time: 4 years Simple Interest: ₦______
2. Principal: ₦10,000, Rate: 6% per year, Time: 2 years Simple Interest: ₦______
3. Principal: ₦1,500, Rate: 10% per year, Time: 5 years Simple Interest: ₦______
4. Principal: ₦8,000, Rate: 7.5% per year, Time: 3 years Simple Interest: ₦______
5. Principal: ₦12,000, Rate: 4% per year, Time: 6 years Simple Interest: ₦______

Mixed Percentage Problems

Exercise H – Problem Solving

Solve these challenging problems:

1. Class Statistics: In a class, 40% are boys and there are 24 girls. How many students are in the class? Answer: ______ students
2. Budget Planning: A family spends 30% of their income on food, 25% on rent, and saves the rest. If they save ₦45,000 monthly, what is their total income? Answer: ₦______
3. Election Results: In a school election, the winning candidate got 65% of 400 votes. The runner-up got 25% of the votes. How many more votes did the winner get? Answer: ______ votes
4. Production Analysis: A factory increased production by 25%. If they now produce 750 items, how many did they produce before? Answer: ______ items
5. Mixture Problem: A solution is 40% water and 60% chemical. If there are 120 liters of chemical, how much water is there? Answer: ______ liters

Exercise I – Mental Calculations

Calculate these percentages quickly:

1. 10% of 340 = ______
2. 50% of 86 = ______
3. 25% of 120 = ______
4. 20% of 150 = ______
5. 1% of 2,500 = ______
6. 5% of 400 = ______
7. 75% of 80 = ______
8. 30% of 200 = ______
9. 2% of 450 = ______
10. 60% of 250 = ______

Exercise J – Real World Applications

Apply percentage skills:

1. Sports Statistics: A basketball player makes 80% of his free throws. If he attempts 25 free throws, how many will he likely make? Answer: ______ free throws
2. Farming: A farmer plants 60% of his 50-hectare farm with maize. How many hectares are planted with maize? Answer: ______ hectares
3. Technology: A phone battery is at 85% charge. If the full capacity is 4,000 mAh, how much charge is currently stored? Answer: ______ mAh
4. Transportation: A bus is 70% full with 42 passengers. What is the bus capacity? Answer: ______ passengers
5. Academic Performance: 85% of 200 students passed the promotion exam. How many students need to retake the exam? Answer: ______ students

Answer Key

Exercise A: 1-5: 25%, 60%, 70%, 66.7%, 80% 6-10: 35%, 90%, 12.5%, 65%, 125% 11-15: 3/10, 3/4, 2/5, 9/10, 3/20

Exercise B: 1-10: 60, 60, 45, 70, 120, 60, 40, 150, 45, 140

Exercise C: 1-10: 25%, 25%, 25%, 25%, 25%, 25%, 25%, 40%, 25%, 25%

Exercise D:

1. 80%
2. 80%
3. 90 students
4. 280 books
5. 90 students

Exercise E:

1. ₦3,600
2. ₦600
3. 20%
4. ₦4,000
5. 25%

Exercise F:

1. 20%
2. 10%
3. 20%
4. 20%
5. 20%

Exercise G:

1. ₦400
2. ₦1,200
3. ₦750
4. ₦1,800
5. ₦2,880

Exercise H:

1. 40 students
2. ₦100,000
3. 160 votes
4. 600 items
5. 80 liters

Exercise I: 1-10: 34, 43, 30, 30, 25, 20, 60, 60, 9, 150

Exercise J:

1. 20 free throws
2. 30 hectares
3. 3,400 mAh
4. 60 passengers
5. 30 students