Convert Fraction to Percentage: Solving 8/35 Step by Step

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

Percentage means "per hundred"! When you multiply by 100, you're finding how many parts out of 100. So $ \frac{8}{35} \times 100 $ tells you how many parts out of 100.

Q: How do I know when to round my answer?

For percentages, two decimal places is usually perfect! Since 800 ÷ 35 = 22.857..., we round to 22.85%. This gives a precise but clean answer.

Q: Can I convert to decimal first?

Absolutely! You can do $ \frac{8}{35} = 0.2286... $ then multiply by 100. Both methods give the same answer: 22.85%.

Q: What if I get a percentage over 100%?

That's totally normal! If your fraction is improper (numerator bigger than denominator), you'll get a percentage over 100%. For example, $ \frac{3}{2} = 150\% $.

Fraction to Percentage with Division

Write the fraction $\frac{8}{35}$ 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

00:11 Factor 35 into 7 and 5, and 100 into 20 and 5

00:17 Simplify wherever possible

00:32 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the fraction $\frac{8}{35}$ as a percentage

Step-by-step solution

To solve this problem, we'll convert the fraction $\frac{8}{35}$ into a percentage by multiplying it by 100.

Step 1: Multiply the fraction by 100 to convert it to a percentage.
This gives us:

$\frac{8}{35} \times 100\%$

We now perform the actual multiplication:

Calculate $\frac{8 \times 100}{35}$ .
This equals $\frac{800}{35}$ .
Divide 800 by 35 to simplify the result:

$800 \div 35 \approx 22.8571$

We round this to two decimal places to get an approximate percentage:

The result is approximately $22.85\%$ .

Thus, the fraction $\frac{8}{35}$ as a percentage is 22.85%.

Final Answer

22.85%

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply the fraction by 100 to convert to percentage
Technique: Calculate $\frac{8 \times 100}{35} = \frac{800}{35}$
Check: Verify that 22.85% ÷ 100 returns $\frac{8}{35}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by 100 instead of multiplying
Don't divide 8/35 by 100 = 0.0023%! This makes the percentage extremely small because you're going backwards. Always multiply by 100 to convert fractions to percentages.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{24}{100}=\text{?}$

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 multiply by 100, you're finding how many parts out of 100. So $\frac{8}{35} \times 100$ tells you how many parts out of 100.

How do I know when to round my answer?

For percentages, two decimal places is usually perfect! Since 800 ÷ 35 = 22.857..., we round to 22.85%. This gives a precise but clean answer.

Can I convert to decimal first?

Absolutely! You can do $\frac{8}{35} = 0.2286...$ then multiply by 100. Both methods give the same answer: 22.85%.

What if I get a percentage over 100%?

That's totally normal! If your fraction is improper (numerator bigger than denominator), you'll get a percentage over 100%. For example, $\frac{3}{2} = 150\%$ .

How can I check if 22.85% is correct?

Convert back! Take 22.85% ÷ 100 = 0.2285, which should equal $\frac{8}{35}$ . Since 8 ÷ 35 ≈ 0.2286, you're very close!

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