Convert Fraction to Percentage: Solving 10/40 Step-by-Step

Q: Do I always need to simplify the fraction first?

Not always required, but it's highly recommended! Simplifying makes calculations easier and reduces errors. For example, $ \frac{1}{4} \times 100 $ is much simpler than $ \frac{10}{40} \times 100 $.

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

Yes! Divide 10 ÷ 40 = 0.25, then multiply by 100 to get 25%. Both methods work, but the fraction method helps you understand the relationship better.

Q: Why multiply by 100 to get a percentage?

Because percent means "per hundred"! When you multiply $ \frac{1}{4} \times 100 $, you're finding how many parts out of 100 equal your fraction.

Fraction to Percentage with Simplification

Convert the fraction into a percentage:

$\frac{10}{40}=\text{?}$

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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 A fraction with a denominator equal to 100 is equal to the numerator in percentage form (X)

00:14 Determine what to multiply the denominator by to obtain a denominator of 100

00:26 Multiply both the numerator and denominator by 2.5 to obtain a denominator equal to 100

00:39 Apply this formula to our exercise

00:44 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert the fraction into a percentage:

$\frac{10}{40}=\text{?}$

Step-by-step solution

To solve this problem, we will convert the fraction $\frac{10}{40}$ into a percentage by using the following steps:

Step 1: Simplify the fraction if possible. The fraction $\frac{10}{40}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 10. Hence, we have:
$\frac{10}{40} = \frac{1}{4}.$
Step 2: Convert the simplified fraction to a percentage by multiplying by 100:
$\frac{1}{4} \times 100 = 25.$
Step 3: Write the result as a percentage:

Thus, $\frac{1}{4} \equiv 25\%$ . This means $\frac{10}{40}$ is equivalent to 25%.

Therefore, the solution to the problem is 25%.

Final Answer

25%

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify fractions first by dividing by greatest common divisor
Technique: Multiply simplified fraction by 100: $\frac{1}{4} \times 100 = 25$
Check: Verify 25% equals original fraction: $\frac{25}{100} = \frac{1}{4} = \frac{10}{40}$ ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying first
Don't calculate $\frac{10}{40} \times 100 = 25$ directly = more complex arithmetic and error-prone! Working with larger numbers increases calculation mistakes. Always simplify to $\frac{1}{4}$ 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 the fraction first?

Not always required, but it's highly recommended! Simplifying makes calculations easier and reduces errors. For example, $\frac{1}{4} \times 100$ is much simpler than $\frac{10}{40} \times 100$ .

How do I find the greatest common divisor quickly?

List the factors of both numbers and find the largest one they share. For 10 and 40: factors of 10 are 1, 2, 5, 10 and factors of 40 include 1, 2, 4, 5, 8, 10, 20, 40. The GCD is 10!

Can I convert to decimal first, then percentage?

Yes! Divide 10 ÷ 40 = 0.25, then multiply by 100 to get 25%. Both methods work, but the fraction method helps you understand the relationship better.

What if I get a different percentage answer?

Double-check your arithmetic! Common errors include forgetting to multiply by 100 or making division mistakes. Always verify by converting your percentage back to a fraction.

Why multiply by 100 to get a percentage?

Because percent means "per hundred"! When you multiply $\frac{1}{4} \times 100$ , you're finding how many parts out of 100 equal your fraction.

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