Calculate the Whole: If 3 is 15 Percent, What is the Total?

Q: Why do I divide by the percentage instead of multiplying?

Think of it this way: if 3 is 15% of something, that something must be bigger than 3! Multiplying would make it smaller. Division gives you the larger whole that 3 represents just a piece of.

Q: How do I convert 15% to a decimal?

Simply divide by 100 or move the decimal point two places left. So 15% becomes $ \frac{15}{100} = 0.15 $.

Q: What if I get a really large answer - could that be right?

Yes! If the percentage is small, the whole will be much larger than the part. For example, if 3 is only 1% of something, that something would be 300!

Q: Can I use cross-multiplication for this type of problem?

Absolutely! Set up the proportion: $ \frac{3}{x} = \frac{15}{100} $. Cross-multiply to get $ 15x = 300 $, then divide both sides by 15 to get $ x = 20 $.

Q: How can I check my answer without doing the whole problem over?

Use the "of" method: calculate 15% of your answer. If you get back to 3, you're correct! So 15% of 20 = 0.15 × 20 = 3 ✓

Percentage Problems with Whole Value Calculation

Calculate the whole if 15 percent is equal to 3:

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Understand the problem

Calculate the whole if 15 percent is equal to 3:

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information.
Step 2: Apply the appropriate formula for finding the whole.
Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: We are given that 15 percent of some whole amount is equal to 3.
Step 2: We use the formula for calculating the whole:

\text{whole} = \frac{\text{part}}{\left(\frac{\text{percentage}}{100}\right)}

Substituting the given values into the formula:
The part is 3, and the percentage is 15%. Thus, we calculate:

\text{whole} = \frac{3}{\left(\frac{15}{100}\right)}

Step 3: Simplify the expression:
First, convert 15% to a decimal by dividing by 100, which gives 0.15.
Now calculate:

\text{whole} = \frac{3}{0.15}

Perform the division:

\text{whole} = 20

Therefore, the solution to the problem is $20$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Whole = Part ÷ (Percentage ÷ 100)
Technique: Convert 15% to 0.15, then divide: 3 ÷ 0.15 = 20
Check: Verify by calculating: 15% of 20 = 0.15 × 20 = 3 ✓

Common Mistakes

Avoid these frequent errors

Multiplying the part by the percentage instead of dividing
Don't calculate 3 × 15 = 45 or 3 × 0.15 = 0.45! This gives you more of the part, not the whole. When you know the part and percentage, always divide the part by the decimal percentage to find the whole.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why do I divide by the percentage instead of multiplying?

Think of it this way: if 3 is 15% of something, that something must be bigger than 3! Multiplying would make it smaller. Division gives you the larger whole that 3 represents just a piece of.

How do I convert 15% to a decimal?

Simply divide by 100 or move the decimal point two places left. So 15% becomes $\frac{15}{100} = 0.15$ .

What if I get a really large answer - could that be right?

Yes! If the percentage is small, the whole will be much larger than the part. For example, if 3 is only 1% of something, that something would be 300!

Can I use cross-multiplication for this type of problem?

Absolutely! Set up the proportion: $\frac{3}{x} = \frac{15}{100}$ . Cross-multiply to get $15x = 300$ , then divide both sides by 15 to get $x = 20$ .

How can I check my answer without doing the whole problem over?

Use the "of" method: calculate 15% of your answer. If you get back to 3, you're correct! So 15% of 20 = 0.15 × 20 = 3 ✓

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