If you’ve ever wondered what 15% of 65 is, you’ve come to the right place. Using the “What is X Percent of Y Calculator,” we can easily determine that 15% of 65 equals 9.75.
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Step-by-Step Solution: What is 15% of 65?
Now, let’s explore two different ways to solve this percentage problem step-by-step. Each approach leads to the same conclusion, but mastering different methods of mathematical thinking will deepen your understanding.
Method 1: Convert the Percent to a Decimal and Multiply
One way to find 15% of 65 is by converting the percentage to a decimal and multiplying. Here are the steps:
Step 1: Identify the part and whole
The part is the amount we want as a percentage, which in this case is 15%.
The whole is the total amount, which in this case is 65.
Step 2: Write the percentage as a decimal by dividing it by 100:
15% = 15/100 = 0.15
Step 3: Multiply the decimal form of the percentage by the whole amount:
0.15 * 65 = 9.75
Therefore, 15% of 65 is 9.75.
Let’s visualize it:
15% 65 = 15/100 65 = 0.15 * 65 = 9.75
This approach of converting the percentage to a decimal and multiplying is straightforward and applicable to any “percent of number” problem. The key is to correctly convert the percentage to a decimal by dividing it by 100.
Method 2: Finding Percentages Using Algebraic Equations
Another way to find 15% of 65 is by setting up an algebraic equation and solving it. Here are the steps:
A proportion is an equation that states two ratios are equivalent. The formula for a proportion is:
Part/Whole = Percentage/100
Step 1: Define the Unknown Variable
To represent 15% of 65, let’s define an unknown variable, x.
Step 2: Set Up the Equation
Using the variable x, we can set up an equation with the given information:
The unknown variable x (Part) is the value we want to find, which is 15% of 65.
The Whole is 65.
The Percentage is 15.
Substitute into the equation:
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65 x/65 = 15/100 65
x = 15/100 * 65 = 975/100 = 9.75
Therefore, 15% of 65 is 9.75.
Comparing the Methods
Both methods yield the same solution:
- Method 1 converts 15% to 0.15 and multiplies it by 65.
- Method 2 sets up an equation, defines a variable, and solves it algebraically.
The decimal conversion method is straightforward as it avoids any algebra. However, the algebraic method is more flexible and useful for complex problems that benefit from defining variables and setting up equations.
Common Percentage Scenarios
Here are some common percentage scenarios and how to solve them:
Finding the Percentage Given the Part and Whole
The proportion formula is:
Part/Whole = Percentage/100
Let’s demonstrate how to use the proportion formula to calculate the percentage given a part and whole amount. For example, let’s determine what percent of 65 is 9.75.
Step 1: Define the Unknown Variable
Let the unknown variable x represent the percent we want to find.
Step 2: Set Up the Equation
Using the variable x, we can set up an equation with the given information:
- The unknown variable x (Percentage) is the number we want to find.
- The Part is 9.75.
- The Whole is 65.
Substitute into the equation:
9.75/65 = x/100
Step 3: Solve the Equation
To isolate x, we can cross-multiply:
(9.75 100) = (x 65)
9.75 100 = x 65
x = 15
Therefore, the answer is that 15% of 65 is 9.75.
Finding the Whole Given the Percentage and Part
The proportion formula is:
Part/Whole = Percentage/100
Let’s demonstrate how to use the proportion formula to calculate the whole given the percentage and part. For example, let’s determine what number is 9.75 when it represents 15% of the whole.
Step 1: Define the Unknown Variable
Let the unknown variable x represent the number we want to find.
Step 2: Set Up the Equation
Using the variable x, we can set up an equation with the given information:
- The unknown variable x (Whole) is the number we want to find.
- The Part is 9.75.
- The Percentage is 15.
Substitute into the equation:
9.75/x = 15/100
Step 3: Solve the Equation
To isolate x, we can cross-multiply:
(9.75 100) = (15 x)
9.75 100 = 15 x
x = 65
Therefore, the answer is that 9.75 is 15% of 65.
Common Percentage Calculations
Here is a quick reference table for some typical percentage calculations:
| Calculation | Formula | Example |
|---|---|---|
| Find what percentage a part is of a whole | Part/Whole x 100% | 9.75 / 65 x 100% |
| Find what percentage a part is of a whole | Part/Percentage | 9.75 / 15% |
| Find the part given the whole and percentage | Whole x Percentage | 65 * 15% = 9.75 |
Having these common formulas memorized can make solving various percentage problems quicker. When in doubt, break down the steps into smaller pieces to simplify the process.
Standard Percentage of 65 Calculation Examples
Here are some examples of calculating percentages of 65:
- 5 Percent of 65 = 5/100 65 = 0.05 65 = 3.25
- 10 Percent of 65 = 10/100 65 = 0.1 65 = 6.5
- 15 Percent of 65 = 15/100 65 = 0.15 65 = 9.75
- 20 Percent of 65 = 20/100 65 = 0.2 65 = 13
- 25 Percent of 65 = 25/100 65 = 0.25 65 = 16.25
- 30 Percent of 65 = 30/100 65 = 0.3 65 = 19.5
- 35 Percent of 65 = 35/100 65 = 0.35 65 = 22.75
- 40 Percent of 65 = 40/100 65 = 0.4 65 = 26
- 45 Percent of 65 = 45/100 65 = 0.45 65 = 29.25
- 50 Percent of 65 = 50/100 65 = 0.5 65 = 32.5
- 55 Percent of 65 = 55/100 65 = 0.55 65 = 35.75
- 60 Percent of 65 = 60/100 65 = 0.6 65 = 39
- 65 Percent of 65 = 65/100 65 = 0.65 65 = 42.25
- 70 Percent of 65 = 70/100 65 = 0.7 65 = 45.5
- 75 Percent of 65 = 75/100 65 = 0.75 65 = 48.75
- 80 Percent of 65 = 80/100 65 = 0.8 65 = 52
- 85 Percent of 65 = 85/100 65 = 0.85 65 = 55.25
- 90 Percent of 65 = 90/100 65 = 0.9 65 = 58.5
- 95 Percent of 65 = 95/100 65 = 0.95 65 = 61.75
- 100 Percent of 65 = 100/100 65 = 1 65 = 65
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