what is 15% of 175
what is 15% of 175
The Correct Answer and Explanation is:
The correct answer is 26.25.
Explanation: Finding a Percentage of a Number
The problem asks for the value of 15% of 175. This common mathematical calculation involves understanding what a percentage represents and how to apply it to a whole number. There are several reliable methods to find the solution.
Understanding Percentages
The word “percent” originates from the Latin phrase per centum, meaning “per one hundred.” A percentage is simply a fraction where the denominator is 100. Therefore, 15 percent (written as 15%) is another way of expressing the fraction 15/100. To find a percentage of a number is to find a specific part of that number.
Method 1: The Decimal Conversion Method
A direct way to solve percentage problems is to convert the percentage into a decimal. Since a percentage is a part of 100, you can convert it to a decimal by dividing it by 100.
- Convert the percentage to a decimal:
15% = 15 ÷ 100 = 0.15 - Multiply the decimal by the total number: In mathematics, the word “of” typically indicates multiplication. So, the expression “15% of 175” becomes a multiplication problem.
0.15 × 175 = 26.25
Method 2: The Breakdown Method
An intuitive approach, often useful for mental calculation, is to break the percentage into simpler, more manageable parts. We can express 15% as the sum of 10% and 5%.
- Calculate 10% of the number: Finding 10% of any number is as simple as moving the decimal point one place to the left.
10% of 175 = 17.5 - Calculate 5% of the number: Since 5% is exactly half of 10%, we can find this value by taking half of the result from the previous step.
Half of 17.5 = 17.5 ÷ 2 = 8.75 - Add the parts together: To find the total for 15%, we add the value of 10% and the value of 5%.
17.5 + 8.75 = 26.25
Both methods confirm that 15% of 175 is 26.25.
