Topic Details (Notes format)

Percentage to Fraction Table

Subject: Mathematics

Book: Basic Math Operations

Converting percentages to fractions is an essential arithmetic skill. A “percent” represents a certain number of parts per 100. By placing the percentage as the numerator over 100, you can then simplify the resulting fraction. Below is a commonly used reference for quickly converting key percentages into fraction form.

### Common Percentage-to-Fraction Conversions:
1. **1%** → 1/100
2. **5%** → 5/100 → 1/20
3. **10%** → 10/100 → 1/10
4. **12.5%** → 12.5/100 → 1/8
5. **20%** → 20/100 → 1/5
6. **25%** → 25/100 → 1/4
7. **33⅓%** (approx. 33.3%) → 1/3
8. **40%** → 40/100 → 2/5
9. **50%** → 50/100 → 1/2
10. **60%** → 60/100 → 3/5
11. **66⅔%** (approx. 66.7%) → 2/3
12. **75%** → 75/100 → 3/4
13. **80%** → 80/100 → 4/5
14. **90%** → 90/100 → 9/10
15. **100%** → 100/100 → 1

### Quick Tips for Converting:
- **General Formula**: (Percent) ÷ 100 = fraction. Simplify if possible.
- **Reduce**: For instance, 40% becomes 40/100, then dividing numerator and denominator by 20 gives 2/5.
- **Repeating Decimals**: Values like 33⅓% and 66⅔% are repeating decimals; writing them as fractions (1/3, 2/3) is often easier.
- **Familiarity**: Knowing a few key conversions—such as 25% = 1/4, 50% = 1/2—speeds up mental math.

By memorizing these typical conversions, you can effortlessly switch between percentages, fractions, and decimals—be it for shopping discounts, data analysis, or test preparations.

Practice Questions

What is the remainder when 5^100 is divided by 3?

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What is the sum of the first 10 positive even numbers?

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What is the cube of 4?

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If the radius of a circle is doubled, what happens to its area?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the HCF of 72 and 120?

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What is the sum of the interior angles of a hexagon?

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