Ratios vs. Percentages

A clear guide with examples, conversions, and common mistakes.

1) What is a Ratio?

A ratio compares two quantities using division.

Common forms:

a : b
a to b
a / b

Example: Ratio of boys to girls = 3 : 2

This means for every 3 boys, there are 2 girls.

Key idea: Ratios can compare part-to-part or part-to-whole.

2) What is a Percentage?

A percentage is a ratio out of 100.

Formula:

Percent = (part / whole) × 100

Example: 25% means 25 out of 100.

3) Converting a Ratio to a Percentage

Example 1: Part-to-Whole Ratio

Ratio of red balls to total balls = 3 : 12

Write as a fraction: 3/12
Simplify (optional): 1/4
Convert to percent: (1/4) × 100 = 25%

Answer: 25% of the balls are red.

Example 2: Boys to Girls → Percentage of Boys

Ratio of boys to girls = 3 : 2

Find total parts: 3 + 2 = 5
Boys as a fraction of total: 3/5
Convert to percent: (3/5) × 100 = 60%

Answer: 60% of the class are boys.

4) Converting a Percentage to a Ratio

Example 1: Simple Percentage

Convert 40% to a ratio.

Write as a fraction: 40/100
Simplify: 2/5
Write as a ratio: 2 : 5

Answer: 40% = 2 : 5

Example 2: Percent to Part-to-Part Ratio

60% boys and 40% girls

Write as a ratio: 60 : 40
Simplify: 3 : 2

Answer: Boys : Girls = 3 : 2

5) Solving Real-World Problems

Example: Discounts

A $50 shirt is 20% off.

Find the discount: 0.20 × 50 = 10
Subtract: 50 − 10 = 40

Final price: $40

Example: Finding the Whole

15 is 30% of what number?

Set up equation: 0.30x = 15
Solve: x = 15 / 0.30 = 50

Whole = 50

6) Common Student Mistakes

Mistake: Using the wrong whole when converting to percent
Mistake: Forgetting to add ratio parts (like 3 + 2)
Mistake: Forgetting to multiply by 100
Mistake: Mixing up part-to-part and part-to-whole comparisons

7) Quick Comparison Chart

Concept	Ratio	Percentage
Compares	Any two quantities	Part out of 100
Format	3:2	60%
Needs a whole?	Not always	Always
Common use	Comparisons	Discounts, statistics

8) Teacher Tip

Ratios tell how things compare.

Percentages tell how much out of 100.