The number is 300.
Understanding Percentage Calculations
Finding an unknown number when a specific percentage of it is given is a common mathematical problem. This involves using basic algebraic principles to reverse the percentage operation and determine the original whole.
The Problem Explained
The question asks: "What is the number if 15 percent of a number is 45?"
Here, we know a part (45) and the percentage that part represents (15%) of an unknown whole number. Our goal is to find that whole number.
Step-by-Step Calculation
To solve this, we can set up a simple equation. Let the unknown number be represented by 'x'.
-
Formulate the equation:
15% of x = 45 -
Convert the percentage to a decimal or fraction:
A percentage can be written as a decimal by dividing it by 100.
15% = 15/100 = 0.15 -
Rewrite the equation with the decimal:
0.15 * x = 45 -
Isolate 'x' by dividing both sides of the equation by 0.15:
x = 45 / 0.15 -
Perform the division:
x = 300
Therefore, the number is 300. This confirms that 15 percent of 300 is indeed 45, a fact consistently supported by various mathematical and educational resources.
Summary of Calculation Steps:
| Step | Description | Calculation | Result |
|---|---|---|---|
| 1. Define Variable | Let the unknown number be 'x'. | 15% of x = 45 | |
| 2. Convert Percentage | Convert 15% to its decimal equivalent. | 15 / 100 | 0.15 |
| 3. Set Up Equation | Formulate the equation using the decimal. | 0.15 * x = 45 | |
| 4. Solve for x | Divide 45 by 0.15 to find 'x'. | x = 45 / 0.15 | 300 |
Practical Applications of Percentage Calculations
Understanding how to find a number from its percentage is crucial in various real-world scenarios:
- Financial Planning: Calculating original income if you know the amount after a certain tax percentage is deducted.
- Retail and Sales: Determining the original price of an item when you only know the discounted price and the percentage off.
- Statistics and Data Analysis: Reconstructing total population figures from sample data and percentages.
- Academic Assessments: Understanding total marks achievable if you know the score on a particular section and its weightage.
These applications highlight the importance of mastering basic percentage calculations for everyday problem-solving and decision-making.
