Convert Fraction to Percentage: Finding 20/82 as a Percent

Q: Why do I multiply by 100 to get a percentage?

Percentage means 'per hundred'! When you have the decimal 0.24, multiplying by 100 converts it to 24 per hundred, which is 24%.

Q: What if my calculator gives me a long decimal like 0.243902?

That's normal! For multiple choice questions, round to the nearest option. Here, 0.2439 × 100 = 24.39%, which is closest to 25%.

Q: Can I simplify the fraction first before dividing?

Yes! $ \frac{20}{82} = \frac{10}{41} $ after dividing both by 2. However, the decimal result will be the same, so either method works fine.

Q: Is there a shortcut for common fractions?

Some fractions you can memorize: $ \frac{1}{4} = 25\% $, $ \frac{1}{2} = 50\% $. But for unusual fractions like $ \frac{20}{82} $, division is the most reliable method.

Fraction to Percentage with Division Method

Approximately what is $\frac{20}{82}$ written as a percentage?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert approximately to percentages

00:04 Convert to the closest fraction we can change to percentages

00:15 Break down 80 into factors 20 and 4

00:22 Reduce what we can

00:26 This is the simple fraction, now let's convert to percentages

00:31 Multiply the entire fraction by 100

00:36 Break down 100 into factors 25 and 4

00:40 Reduce what we can

00:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Approximately what is $\frac{20}{82}$ written as a percentage?

Step-by-step solution

To solve this problem, we'll convert the given fraction to a percentage using the following steps:

Step 1: Divide the numerator by the denominator to get a decimal value.
Step 2: Multiply the decimal by 100 to convert it to a percentage.
Step 3: Check the result with the provided multiple-choice options.

Now, let's work through each step:

Step 1: Divide $20$ by $82$ :

$\frac{20}{82} \approx 0.2439$

Step 2: Multiply the result by $100$ to convert to a percentage:

$0.2439 \times 100 \approx 24.39\%$

Step 3: Approximate the result to the nearest common percentage value, which is 25%.

Therefore, the solution to the problem is 25%.

Final Answer

25%

Key Points to Remember

Essential concepts to master this topic

Rule: Divide numerator by denominator, then multiply by 100
Technique: Calculate $\frac{20}{82} = 0.2439$ , then multiply by 100
Check: Verify 24.39% rounds to closest option: 25% ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100 after division
Don't just divide 20 ÷ 82 = 0.2439 and call it a percentage! This gives you a decimal, not a percent. The result would be 0.24% instead of 24%. Always multiply your decimal result by 100 to convert to percentage form.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is $\frac{11}{50}$ written as a percentage?

FAQ

Everything you need to know about this question

Why do I multiply by 100 to get a percentage?

Percentage means 'per hundred'! When you have the decimal 0.24, multiplying by 100 converts it to 24 per hundred, which is 24%.

What if my calculator gives me a long decimal like 0.243902?

That's normal! For multiple choice questions, round to the nearest option. Here, 0.2439 × 100 = 24.39%, which is closest to 25%.

Can I simplify the fraction first before dividing?

Yes! $\frac{20}{82} = \frac{10}{41}$ after dividing both by 2. However, the decimal result will be the same, so either method works fine.

How do I know which multiple choice answer to pick?

Calculate the exact percentage first: 24.39%. Then find the closest option. Since 24.39% is much closer to 25% than to 30%, choose 25%.

Is there a shortcut for common fractions?

Some fractions you can memorize: $\frac{1}{4} = 25\%$ , $\frac{1}{2} = 50\%$ . But for unusual fractions like $\frac{20}{82}$ , division is the most reliable method.

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