What Percent is $30 of 135? A Step-by-Step Guide

Calculating what percent one number is of another can be a straightforward process once you understand how to set it up. In this example, we want to find out what percent $30 is of 135. Here’s how to approach this problem step-by-step:

1. **Identify the Components**: In the question, '$30 is what percent of 135?', we can break it down into parts. Here, $30 represents the 'part', while 135 is the 'whole'. The unknown percentage we want to find is denoted as 'x'.

2. **Setting Up the Equation**: The concept of percentage can be expressed mathematically. We can say that the percentage in decimal form times the whole equals the part. Therefore, we can write this as:


**x (as a decimal) × 135 = 30**

3. **Solving for x**: To find x, we need to isolate it in the equation. Start by dividing both sides by 135:


**x = 30 ÷ 135**

This can be simplified. First, we can divide both numbers by 5, as they share a common factor:


**30 ÷ 5 = 6** and **135 ÷ 5 = 27**, giving us:


**x = 6/27**

Now, we can simplify 6/27 further by dividing both the numerator and the denominator by 3:


**6 ÷ 3 = 2** and **27 ÷ 3 = 9**, so:


**x = 2/9**

4. **Converting to a Percentage**: Finally, to convert a fraction to a percentage, we multiply it by 100. First, convert 2/9 into a decimal:


**2 ÷ 9 ≈ 0.222...** (this is a repeating decimal).

Now, multiply this decimal by 100:


**0.222... × 100 ≈ 22.2%**

Thus, we conclude that $30 is approximately **22.2%** of 135.

### Real-World Applications:
Understanding percentages is crucial in everyday life. Whether you're budgeting, calculating discounts during shopping, or analyzing statistics in school projects, knowing how to compute percentages allows you to make informed decisions.

### Additional Examples:
For further practice, consider these similar problems:
- What percent is $50 of $200?
- If you scored 18 out of 60 on a test, what percent did you score?
- A jacket originally priced at $80 is on sale for $64. What percent discount is that?

Working through these types of problems will enhance your skills in calculating percentages and improve your overall math proficiency. Keep practicing, and soon you'll find this process becomes second nature!