By what number must a given number be multiplied to increase it by `20%`

Answer

To solve the problem of determining by what number a given number must be multiplied to increase it by 20%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Percentage Increase**:
- When we say we want to increase a number by 20%, it means we want to find a new value that is 120% of the original number.

2. **Express the Increase Mathematically**:
- If the original number is represented as \( x \), then increasing it by 20% can be expressed as:
\[ x + 0.20x = 1.20x \]
- This shows that the new value after the increase is \( 1.20 \) times the original number.

3. **Set Up the Equation**:
- We need to find a number \( n \) such that:
\[ x \times n = 1.20x \]

4. **Isolate \( n \)**:
- To find \( n \), we can divide both sides of the equation by \( x \) (assuming \( x \neq 0 \)):
\[ n = \frac{1.20x}{x} = 1.20 \]

5. **Convert to Fraction**:
- The decimal \( 1.20 \) can be expressed as a fraction:
\[ 1.20 = \frac{120}{100} = \frac{6}{5} \]

6. **Conclusion**:
- Therefore, the number by which the original number must be multiplied to increase it by 20% is:
\[ n = \frac{6}{5} \]

### Final Answer:
To increase a number by 20%, it must be multiplied by \( \frac{6}{5} \).

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