Convert 27/63 into a Percentage: A Practical Guide

Q: Why do I need to simplify the fraction first?

Simplifying makes calculations much easier! Working with $ \frac{3}{7} $ instead of $ \frac{27}{63} $ reduces computation errors and gives you the same exact answer.

Q: Should I round my final percentage answer?

Yes! Since $ \frac{3}{7} = 0.428571... $ repeats forever, round to two decimal places for practical use: 42.85%. Always check if your teacher wants a specific number of decimal places.

Q: What if I get a different decimal result?

Double-check your division! $ 3 ÷ 7 = 0.428571... $ exactly. If you're using a calculator, make sure you're dividing 3 by 7, then multiplying by 100 for the percentage.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's calculate 27 as a percentage of 63.

00:09 First, we'll use the formula to find percentages.

00:13 Divide 27 by 63. Then, multiply by 100.

00:17 Next, break down 27 into factors, which are 9 and 3.

00:22 Now, break down 63 into 9 and 7. Simplify where you can.

00:30 And that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Calculate 27 over 63 as a percentage:

2

Step-by-step solution

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

Step 1: Identify the given information
Step 2: Apply the percentage formula
Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: We are given that the "Part" is 27 and the "Whole" is 63.
Step 2: We'll use the formula for percentage calculation: $\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\%$ .
Step 3: Plugging in our values, we get:

\text{Percentage} = \left(\frac{27}{63}\right) \times 100\%

Simplifying the fraction $\frac{27}{63}$ , we find the greatest common divisor of both numbers, which is 9, thus:

\frac{27}{63} = \frac{27 \div 9}{63 \div 9} = \frac{3}{7}

Then, we multiply by 100 to convert to a percentage:

\text{Percentage} = \frac{3}{7} \times 100\% \approx 42.8571\%

Rounding to two decimal places, we get 42.85%.

Therefore, the solution to the problem is $42.85\%$ .

3

Final Answer

42.85%

Key Points to Remember

Essential concepts to master this topic

Formula: Percentage = (Part ÷ Whole) × 100%
Technique: Simplify $\frac{27}{63} = \frac{3}{7}$ by dividing by GCD of 9
Check: Verify 42.85% by calculating $\frac{3}{7} \times 100 = 42.857...$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction before converting
Don't calculate $\frac{27}{63} \times 100$ directly = harder computation and potential errors! Complex fractions make division more difficult and increase calculation mistakes. Always find the GCD and simplify to $\frac{3}{7}$ first for easier percentage conversion.

Practice Quiz

Test your knowledge with interactive questions

Calculate 15% of 100:

FAQ

Everything you need to know about this question

Why do I need to simplify the fraction first?

+

Simplifying makes calculations much easier! Working with $\frac{3}{7}$ instead of $\frac{27}{63}$ reduces computation errors and gives you the same exact answer.

How do I find the greatest common divisor (GCD)?

+

List the factors of both numbers: 27 (1, 3, 9, 27) and 63 (1, 3, 7, 9, 21, 63). The largest common factor is 9, so divide both numerator and denominator by 9.

Should I round my final percentage answer?

+

Yes! Since $\frac{3}{7} = 0.428571...$ repeats forever, round to two decimal places for practical use: 42.85%. Always check if your teacher wants a specific number of decimal places.

Can I convert to percentage without simplifying first?

+

Absolutely! You'll get the same answer either way. However, simplifying first makes the arithmetic easier and reduces chances of calculation errors, especially without a calculator.

What if I get a different decimal result?

+

Double-check your division! $3 ÷ 7 = 0.428571...$ exactly. If you're using a calculator, make sure you're dividing 3 by 7, then multiplying by 100 for the percentage.

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Convert 27/63 into a Percentage: A Practical Guide

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