Calculate the Whole Number When 27% Equals 4: Percentage Problem

Q: Why do I divide by 0.27 instead of 27?

You need to convert the percentage to a decimal first! 27% means 27 out of 100, which equals $ \frac{27}{100} = 0.27 $. Always divide percentages by 100 before using them in calculations.

Q: How can 4 be 27% of something smaller than 4?

Great question! When the percentage is less than 100%, the whole number is actually larger than the part. Think of it this way: if 4 is only 27% of something, that something must be much bigger than 4!

Q: Can I use the formula Whole = Part ÷ Percentage × 100?

Yes! That's the same as dividing by the decimal. $ \frac{4}{27} \times 100 = \frac{400}{27} = 14.81 $. Both methods work - choose whichever feels easier!

Q: What if my calculator shows more decimal places?

Round to a reasonable number of decimal places based on the context. For this problem, 14.81 is appropriate. If you got 14.814814..., rounding to 2-3 decimal places is usually fine.

Q: How do I check if 14.81 is really correct?

Multiply your answer by the percentage: $ 14.81 \times 0.27 = 3.9987 $ which rounds to 4. Since this matches the given part, your answer is correct!

Percentage Problems with Unknown Whole Values

Calculate the whole if 27 percent is equal to 4:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 First, let's find the whole number.

00:07 Next, we'll use a formula to change the percentage into a fraction.

00:14 This fraction represents 27 percent.

00:22 Multiply this fraction with the whole number to get 4, as given.

00:28 Then, multiply by the reciprocal to find the whole number.

00:34 Simplify the steps wherever you can.

01:00 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the whole if 27 percent is equal to 4:

Step-by-step solution

To solve this problem, we need to find the whole value when 27% of it equals 4. We'll use the percentage formula:

$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$

We know the percentage is 27%, and the part is 4. Substituting these values, we have:

$27 = \left(\frac{4}{\text{Whole}}\right) \times 100$

To find the whole, rearrange the equation:

$27 = \frac{4}{\text{Whole}} \times 100$

Now, solve for the whole:

$\text{Whole} = \frac{4 \times 100}{27}$

$\text{Whole} = \frac{400}{27}$

By calculating the division:

$\text{Whole} \approx 14.81$

Therefore, the solution to the problem is $14.81$ .

Final Answer

14.81

Key Points to Remember

Essential concepts to master this topic

Formula: Use Part ÷ Percentage × 100 to find whole
Technique: Convert 27% to decimal: 4 ÷ 0.27 = 14.81
Check: Verify by calculating 14.81 × 0.27 = 4 ✓

Common Mistakes

Avoid these frequent errors

Multiplying instead of dividing by the percentage
Don't multiply 4 × 27 = 108! This gives you the wrong operation and makes the whole much too large. The part must be smaller than the whole when dealing with percentages less than 100%. Always divide the part by the percentage (as a decimal) 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 0.27 instead of 27?

You need to convert the percentage to a decimal first! 27% means 27 out of 100, which equals $\frac{27}{100} = 0.27$ . Always divide percentages by 100 before using them in calculations.

How can 4 be 27% of something smaller than 4?

Great question! When the percentage is less than 100%, the whole number is actually larger than the part. Think of it this way: if 4 is only 27% of something, that something must be much bigger than 4!

Can I use the formula Whole = Part ÷ Percentage × 100?

Yes! That's the same as dividing by the decimal. $\frac{4}{27} \times 100 = \frac{400}{27} = 14.81$ . Both methods work - choose whichever feels easier!

What if my calculator shows more decimal places?

Round to a reasonable number of decimal places based on the context. For this problem, 14.81 is appropriate. If you got 14.814814..., rounding to 2-3 decimal places is usually fine.

How do I check if 14.81 is really correct?

Multiply your answer by the percentage: $14.81 \times 0.27 = 3.9987$ which rounds to 4. Since this matches the given part, your answer is correct!

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