Determine the Percentage Value of 100/500: Step-by-Step Calculation

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

Simplifying makes the calculation much easier! Working with $ \frac{1}{5} $ instead of $ \frac{100}{500} $ reduces errors and saves time.

Q: How do I find the GCD of 100 and 500?

Look for common factors: Both numbers are divisible by 100. Since 100 goes into 500 exactly 5 times, the GCD is 100.

Q: Can I just divide 100 by 500 and multiply by 100?

Yes! That works too: $ 100 \div 500 = 0.2 $, then $ 0.2 \times 100 = 20\% $. But simplifying first often makes mental math easier.

Q: How can I verify my percentage is correct?

Work backwards: Calculate 20% of 500. If you get 100, your answer is right! $ 0.20 \times 500 = 100 $ ✓

Fraction to Percentage with Simplification

Calculate 100 over 500 as a percentage:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate 100 as a percentage of 500

00:04 Apply the formula to calculate percentages

00:10 Divide the first number by the second number and proceed to multiply by 100

00:19 Break down into factors and simplify wherever possible

00:30 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate 100 over 500 as a percentage:

Step-by-step solution

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

Step 1: Simplify the given fraction, if possible.
Step 2: Convert the simplified fraction to a percentage.

Now, let's work through each step:

Step 1: Simplifying the fraction $\frac{100}{500}$ involves finding the greatest common divisor (GCD) of 100 and 500. The GCD is 100, so we divide both the numerator and denominator by 100:
$\frac{100 \div 100}{500 \div 100} = \frac{1}{5}$

Step 2: Convert the fraction $\frac{1}{5}$ to a percentage by multiplying by 100:
$\left( \frac{1}{5} \right) \times 100 = 20\%$

Therefore, the fraction $\frac{100}{500}$ expressed as a percentage is $20\%$ .

Final Answer

20%

Key Points to Remember

Essential concepts to master this topic

Simplification: Find GCD first to reduce fraction to lowest terms
Technique: Multiply simplified fraction by 100: $\frac{1}{5} \times 100 = 20\%$
Check: Verify 20% of 500 equals 100: 0.20 × 500 = 100 ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying first
Don't calculate $\frac{100}{500} \times 100$ directly = messy arithmetic and potential errors! This makes calculations harder and increases mistake chances. Always simplify the fraction first by finding the GCD, then convert to percentage.

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 need to simplify the fraction first?

Simplifying makes the calculation much easier! Working with $\frac{1}{5}$ instead of $\frac{100}{500}$ reduces errors and saves time.

How do I find the GCD of 100 and 500?

Look for common factors: Both numbers are divisible by 100. Since 100 goes into 500 exactly 5 times, the GCD is 100.

Can I just divide 100 by 500 and multiply by 100?

Yes! That works too: $100 \div 500 = 0.2$ , then $0.2 \times 100 = 20\%$ . But simplifying first often makes mental math easier.

What if I get a different GCD?

Double-check your work! For 100 and 500, the GCD must be 100 because 100 is a factor of both numbers and it's the largest such factor.

How can I verify my percentage is correct?

Work backwards: Calculate 20% of 500. If you get 100, your answer is right! $0.20 \times 500 = 100$ ✓

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