Convert Fraction to Percentage: Finding the Percentage Value of 2/8

Q: Do I always need to simplify fractions before converting to percentages?

While not absolutely required, simplifying first makes calculations much easier! Compare: $ \frac{1}{4} \times 100 = 25 $ versus $ \frac{2}{8} \times 100 = \frac{200}{8} = 25 $. The simplified version is cleaner!

Q: Can I convert to decimal first, then percentage?

Absolutely! $ \frac{2}{8} = 0.25 $, then multiply by 100 to get 25%. This method works great, especially with a calculator.

Q: What if my fraction doesn't simplify evenly?

That's fine! Some fractions like $ \frac{1}{3} $ give repeating decimals (33.33...%). Just round to the nearest reasonable place value for your answer.

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

Percent means "per hundred"! When you multiply a decimal by 100, you're expressing it as parts out of 100. For example, 0.25 becomes 25 parts out of 100, or 25%.

Fraction to Percentage with Simplification

Write the fraction $\frac{2}{8}$ as a percentage

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert fractions to percentages

00:05 Multiply the fraction by 100 in order to convert to a percentage

00:19 Factor 8 into 2 and 4

00:24 Simplify wherever possible

00:29 Factor 100 into 25 and 4

00:32 Simplify wherever possible

00:37 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the fraction $\frac{2}{8}$ as a percentage

Step-by-step solution

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

Step 1: Simplify the fraction $\frac{2}{8}$ if necessary.
Step 2: Convert the simplified fraction to a percentage by multiplying by 100.

Now, let's work through each step:
Step 1: Simplify the fraction $\frac{2}{8}$ . The greatest common divisor of 2 and 8 is 2. So, we divide the numerator and the denominator by 2:
$\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$
Step 2: To convert the fraction $\frac{1}{4}$ to a percentage, multiply it by 100:
$\frac{1}{4} \times 100 = 25$
Therefore, the fraction $\frac{2}{8}$ is equivalent to $25\%$ .

The correct answer is $\boxed{25\%}$ .

Final Answer

25%

Key Points to Remember

Essential concepts to master this topic

Simplify First: Find GCD to reduce fractions before converting to percentages
Multiply by 100: Convert $\frac{1}{4}$ to percentage: $\frac{1}{4} \times 100 = 25\%$
Verify: Check that $\frac{2}{8} = \frac{1}{4} = 0.25 = 25\%$ ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying the fraction first
Don't calculate $\frac{2}{8} \times 100 = 25$ directly without simplifying = harder calculations and more chance for errors! Working with unsimplified fractions makes the math unnecessarily complex. Always simplify to lowest terms first, then multiply by 100.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Do I always need to simplify fractions before converting to percentages?

While not absolutely required, simplifying first makes calculations much easier! Compare: $\frac{1}{4} \times 100 = 25$ versus $\frac{2}{8} \times 100 = \frac{200}{8} = 25$ . The simplified version is cleaner!

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

List the factors of both numbers and find the largest one they share. For 2 and 8: factors of 2 are {1, 2}, factors of 8 are {1, 2, 4, 8}. The GCD is 2.

Can I convert to decimal first, then percentage?

Absolutely! $\frac{2}{8} = 0.25$ , then multiply by 100 to get 25%. This method works great, especially with a calculator.

What if my fraction doesn't simplify evenly?

That's fine! Some fractions like $\frac{1}{3}$ give repeating decimals (33.33...%). Just round to the nearest reasonable place value for your answer.

Why do we multiply by 100 to get a percentage?

Percent means "per hundred"! When you multiply a decimal by 100, you're expressing it as parts out of 100. For example, 0.25 becomes 25 parts out of 100, or 25%.

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