P6 Mathematics - Term II

Topic 5: Fractions

Lesson 4: Percentages and Conversions

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

• Define percentage and explain it means "per hundred"
• Convert fractions to percentages and vice versa
• Convert decimals to percentages and vice versa
• Solve simple word problems involving percentages
• Apply percentage calculations to real-life situations

Breaking Down the Word

PER CENT

PER = for each
CENT = 100

PER CENT = PER 100

(Like century = 100 years!)

The Percent Symbol: %

The symbol: %

Means: "out of 100" or "per hundred"

Examples:

• 25% means 25 out of 100
• 50% means 50 out of 100
• 80% means 80 out of 100

Visualizing Percentages

Imagine 100 small squares:

• Shade 25 squares = 25%
• Shade 50 squares = 50%
• Shade 75 squares = 75%

The whole grid = 100%

Real-Life Percentages

Where have you seen percentages?

• Test scores: "You scored 80%"
• Shop discounts: "10% off!"
• Phone battery: "75% remaining"
• Survey results: "60% of people agree"

Converting Fractions to Percentages

Goal: Make the denominator 100!

Method 1: Convert to denominator 100
Method 2: Divide and multiply by 100

Let's learn both methods!

Method 1: Make Denominator 100

Example: 1/2 = ?%

Step 1: Make denominator 100
1/2 = 50/100

Step 2: Write as percentage
50/100 = 50%

Answer: 1/2 = 50%

Another Example: Method 1

Example: 3/4 = ?%

Step 1: 3/4 = ?/100
(Multiply by 25)

Step 2: 3/4 = 75/100 = 75%

Answer: 3/4 = 75%

Method 2: Divide and Multiply

Example: 2/5 = ?%

Step 1: Divide 2 ÷ 5 = 0.4

Step 2: Multiply 0.4 × 100 = 40%

Answer: 2/5 = 40%

Method 2: Another Example

Example: 3/8 = ?%

Step 1: 3 ÷ 8 = 0.375

Step 2: 0.375 × 100 = 37.5%

Answer: 3/8 = 37.5%

Common Fractions to Memorize

Know these by heart:

1/2 = 50% 1/4 = 25% 3/4 = 75%
1/5 = 20% 1/10 = 10% 1/100 = 1%

These are used all the time!

Your Turn: Fraction to Percentage

Convert in your exercise book:

a) 2/5 to percentage
b) 7/10 to percentage
c) 1/4 to percentage

Use whichever method you prefer!

Converting Percentages to Fractions

Method: Write over 100, then simplify

Example: 25% = ?

Step 1: Write as fraction: 25/100

Step 2: Simplify: 25/100 = 1/4

Answer: 25% = 1/4

More Examples: Percentage to Fraction

Example 1: 60% = 60/100 = 3/5

Example 2: 75% = 75/100 = 3/4

Example 3: 35% = 35/100 = 7/20

Always simplify to lowest terms!

Decimals to Percentages

Rule: Multiply by 100 and add %

Or: Move decimal point 2 places right

Examples:
0.5 × 100 = 50%
0.25 × 100 = 25%
0.08 × 100 = 8%

More Than 100%?

Yes, percentages can be over 100%!

Example: 1.5 = 150%

This means one and a half, or 150 out of 100!

Examples:

• 1.25 = 125%
• 2.0 = 200%

Percentages to Decimals

Rule: Divide by 100

Or: Move decimal point 2 places left

Examples:
50% = 50 ÷ 100 = 0.5
25% = 25 ÷ 100 = 0.25
8% = 8 ÷ 100 = 0.08

Your Turn: Decimal Conversions

Convert in your exercise book:

a) 0.6 to percentage
b) 45% to decimal
c) 0.75 to percentage
d) 12% to decimal

Remember: Move decimal 2 places!

Finding Percentage of a Number

Question: What is 20% of 50?

Method 1: Convert to fraction
20% = 1/5, so 1/5 of 50 = 10

Method 2: Convert to decimal
20% = 0.2, so 0.2 × 50 = 10

Real-Life Example: Classroom

Problem:
In a class of 40 learners, 25% are absent.
How many are absent?

Solution:
25% = 1/4
1/4 of 40 = 10 learners

Real-Life Example: Test Scores

Problem:
Akello scored 36 out of 40 in a test.
What percentage did she score?

Solution:
Fraction: 36/40 = 9/10
Percentage: 9/10 = 90/100 = 90%

The Conversion Triangle

Remember these connections:

     FRACTION
      /    \
     /      \
DECIMAL — PERCENTAGE

All three forms represent the same thing!

Quick Assessment

Answer in your exercise book:

1. Convert 3/5 to percentage
2. Convert 45% to a fraction
3. Convert 0.8 to percentage
4. Convert 65% to a decimal
5. What is 25% of 60?

Challenge: Working Backwards

Problem:
10% of a number is 15.
What is the number?

Think: If 10% = 15, then 100% = ?

Solution: 15 × 10 = 150

Real-Life Applications

Shopping: "20% off means save 20 per 100 shillings"
School: "Scoring 80% means 80 out of 100 questions"
Sports: "Team won 75% of games"
Health: "90% of children vaccinated"

Why Percentages Matter

Percentages help us:

• Compare things fairly
• Understand discounts and deals
• Track progress and achievement
• Make informed decisions
• Communicate clearly

Mental Math Shortcuts

Quick calculations:

• 10% of any number? Divide by 10
• 50% of any number? Divide by 2
• 25% of any number? Divide by 4
• 1% of any number? Divide by 100

Practice: Quick Calculations

Try these mentally:

• 10% of 80 = ?
• 50% of 120 = ?
• 25% of 60 = ?

Use your shortcuts!

Homework: Parts A and B

Part A: Fraction to Percentage

1. 1/4 2. 3/5 3. 7/10 4. 4/5

Part B: Percentage to Fraction
5. 30% 6. 70% 7. 85% 8. 12%

Simplify all fractions!

Homework: Parts C and D

Part C: Decimal to Percentage
9. 0.3 10. 0.65 11. 0.09

Part D: Percentage to Decimal
12. 55% 13. 8% 14. 95%

Remember: Move decimal 2 places!

Homework: Part E

Part E: Percentage Problems
15. What is 20% of 80?
16. What is 50% of 140?
17. Shopkeeper has 200 oranges, sells 75%. How many sold?
18. Akello scored 45 out of 50. What percentage?

Looking Ahead

Next Lesson:
We will learn about loss and profit in business

Connection:
Profit and loss are calculated as percentages!
Everything you learned today will be used!

Key Takeaways

Percentage: Per hundred (out of 100)

Fractions Percentages: Over 100, or divide and multiply

Decimals Percentages: Move decimal 2 places

Finding %: Convert and multiply

Always: Think - does it make sense?