Percentages basic rules and important formulas 

### Basic Rules of Percentages

1. **Definition of Percentage:**
   - A percentage is a fraction of 100. It is denoted using the percent symbol "%".
   - Example: 25% = 25/100 = 0.25.

2. **Converting Between Fractions, Decimals, and Percentages:**
   - **Fraction to Percentage:** Multiply the fraction by 100 and add the "%" symbol.
     - Example: \( \frac{1}{4} \) = \( \frac{1}{4} \times 100 \) = 25%
   - **Decimal to Percentage:** Multiply the decimal by 100 and add the "%" symbol.
     - Example: 0.75 = 0.75 × 100 = 75%
   - **Percentage to Decimal:** Divide the percentage by 100.
     - Example: 45% = 45/100 = 0.45
   - **Percentage to Fraction:** Write the percentage as a fraction with a denominator of 100 and simplify if necessary.
     - Example: 60% = \( \frac{60}{100} = \frac{3}{5} \)

3. **Finding a Percentage of a Number:**
   - Formula: \( \text{Percentage of a number} = \left(\frac{\text{Percentage}}{100}\right) \times \text{Number} \)
   - Example: 20% of 50 = \( \left(\frac{20}{100}\right) \times 50 = 10 \)

4. **Finding What Percentage One Number is of Another:**
   - Formula: \( \text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100 \)
   - Example: What percentage is 30 of 200? \( \left(\frac{30}{200}\right) \times 100 = 15\% \)

5. **Increasing/Decreasing a Number by a Percentage:**
   - **Increase:** Add the percentage of the number to the original number.
     - Formula: \( \text{Increased Number} = \text{Original Number} + \left(\frac{\text{Percentage}}{100} \times \text{Original Number}\right) \)
     - Example: Increase 100 by 20% = 100 + (0.20 × 100) = 120
   - **Decrease:** Subtract the percentage of the number from the original number.
     - Formula: \( \text{Decreased Number} = \text{Original Number} - \left(\frac{\text{Percentage}}{100} \times \text{Original Number}\right) \)
     - Example: Decrease 150 by 10% = 150 - (0.10 × 150) = 135

6. **Percentage Change:**
   - Formula: \( \text{Percentage Change} = \left(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}\right) \times 100 \)
   - Example: Original value = 50, New value = 75: \( \left(\frac{75 - 50}{50}\right) \times 100 = 50\% \) increase

### Important Formulas

1. **Percentage Formula:**
   \[ \text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100 \]

2. **Finding the Part:**
   \[ \text{Part} = \left(\frac{\text{Percentage}}{100}\right) \times \text{Whole} \]

3. **Finding the Whole:**
   \[ \text{Whole} = \left(\frac{\text{Part}}{\text{Percentage}}\right) \times 100 \]

4. **Increase by a Percentage:**
   \[ \text{New Value} = \text{Original Value} + \left(\frac{\text{Percentage}}{100} \times \text{Original Value}\right) \]

5. **Decrease by a Percentage:**
   \[ \text{New Value} = \text{Original Value} - \left(\frac{\text{Percentage}}{100} \times \text{Original Value}\right) \]

6. **Percentage Increase/Decrease:**
   \[ \text{Percentage Change} = \left(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}\right) \times 100 \]

7. **Percentage Difference:**
   \[ \text{Percentage Difference} = \left(\frac{\left| \text{Value 1} - \text{Value 2} \right|}{\text{Average of Value 1 and Value 2}}\right) \times 100 \]

### Relative Questions

1. How do you convert a fraction to a percentage?
2. What is the formula for finding a percentage of a number?
3. How can you find what percentage one number is of another?
4. What steps do you take to increase a number by a certain percentage?
5. How do you decrease a number by a certain percentage?
6. What is the formula for calculating percentage change?
7. How can you convert a decimal to a percentage?
8. How do you calculate the whole given a part and its percentage?

### Tip
When solving percentage problems, always double-check your calculations by converting back and forth between fractions, decimals, and percentages to ensure accuracy.

Explore the basic rules and important formulas for percentages. Learn how to convert between fractions, decimals, and percentages, find percentages of numbers, calculate increases and decreases, and determine percentage changes. Useful for anyone needing a comprehensive understanding of percentages.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation