12 Is 48 Of What Number

12 is 48% of What Number? Solving Percentage Problems

This article will guide you through solving the percentage problem: "12 is 48% of what number?" We'll break down the process step-by-step, explain the underlying concepts, and provide a formula you can use to solve similar problems. Understanding percentages is crucial in many areas, from calculating discounts and taxes to analyzing financial data and understanding statistics. This article will equip you with the knowledge to tackle these types of problems with confidence.

Understanding the Problem

The question "12 is 48% of what number?" essentially asks us to find the whole number, given a part of that number (12) and the percentage that part represents (48%). We can approach this problem using a simple formula.

The Formula

The fundamental formula for solving percentage problems is:

(Part / Percentage) * 100 = Whole

However, in this specific scenario, we know the part and the percentage, and we need to find the whole. We can rearrange the formula to solve for the unknown "whole" number:

Whole = (Part / Percentage) * 100

Solving the Problem: Step-by-Step

1. Identify the known values:

   • Part = 12
   • Percentage = 48%

2. Convert the percentage to a decimal: To use the percentage in our calculation, we need to convert it to a decimal by dividing by 100.

   • 48% = 48 / 100 = 0.48

3. Apply the formula: Substitute the known values into our rearranged formula:

   • Whole = (12 / 0.48) * 100

4. Perform the calculation:

   • Whole = 25 * 100 = 2500

Therefore, 12 is 48% of 25.

Alternative Method: Using Proportions

Another way to solve this type of problem is using proportions. We can set up a proportion:

12/x = 48/100

Where 'x' represents the whole number we're trying to find. To solve for 'x', we can cross-multiply:

12 * 100 = 48 * x

1200 = 48x

x = 1200 / 48 = 25

This method confirms our previous result.

Practical Applications

Understanding how to solve percentage problems is invaluable in everyday life and various professional fields. Here are some practical applications:

• Calculating discounts: Finding the original price of an item after a discount.
• Determining tax amounts: Calculating the total cost of an item including sales tax.
• Analyzing financial statements: Understanding profit margins, growth rates, and other financial ratios.
• Interpreting survey data: Analyzing the percentage of respondents who chose a specific answer.

Mastering percentage calculations empowers you to handle these situations with ease and accuracy.

Conclusion

Solving the problem "12 is 48% of what number?" requires understanding the relationship between parts, percentages, and the whole. By applying the appropriate formula or using proportions, we've determined that 12 represents 48% of 25. This knowledge is transferable to many real-world situations, making it a valuable skill to possess. Remember to always convert percentages to decimals before using them in calculations to avoid errors.