Converting 20/50 to a Percentage: A Step-by-Step Guide

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

Simplifying makes the calculation much easier! Working with $ \frac{2}{5} $ instead of $ \frac{20}{50} $ gives you smaller, cleaner numbers to multiply by 100.

Q: Can I just divide 20 by 50 and multiply by 100?

Yes, that works too! $ 20 ÷ 50 = 0.4 $, then $ 0.4 × 100 = 40\% $. But simplifying first helps you avoid decimals and understand the relationship better.

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

Some fractions can't be simplified further, like $ \frac{7}{11} $. That's okay! Just multiply by 100 and you'll get a decimal percentage like 63.64%.

Q: How do I know if my percentage is reasonable?

Think about it logically: $ \frac{20}{50} $ means 20 out of 50 parts. Since 25 out of 50 would be half (50%), and 20 less than 50%. 40% makes sense!

Fraction to Percentage with Simplification

Convert the fraction into a percentage:

$\frac{20}{50}=\text{?}$

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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 We need a fraction with a denominator of 100, in order to convert to a percentage

00:10 Therefore we multiply both the numerator and denominator by 2

00:17 A fraction with a denominator equal to 100 equals the numerator in percentages (X)

00:21 Apply this formula to our exercise

00:26 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:

$\frac{20}{50}=\text{?}$

Step-by-step solution

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

Step 1: Simplify the fraction $\frac{20}{50}$ .
Step 2: Convert the simplified fraction into a percentage by multiplying it by 100.

Now, let's work through each step:

Step 1: Simplify the fraction $\frac{20}{50}$ :
Divide both the numerator and the denominator by their greatest common divisor, which is 10:

$\frac{20 \div 10}{50 \div 10} = \frac{2}{5}$ .

Step 2: Convert the simplified fraction to a percentage:
We multiply $\frac{2}{5}$ by 100 to convert it to a percentage:

$\frac{2}{5} \times 100\% = 40\%$ .

Therefore, the fraction $\frac{20}{50}$ as a percentage is 40\%.

Final Answer

40%

Key Points to Remember

Essential concepts to master this topic

Simplification Rule: Always find GCD first to reduce fraction
Conversion Method: Multiply simplified fraction by 100: $\frac{2}{5} \times 100 = 40\%$
Verification Check: Convert back: 40% = 0.4 = $\frac{2}{5}$ = $\frac{20}{50}$ ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying first
Don't convert $\frac{20}{50}$ directly by doing 20 ÷ 50 × 100 = wrong steps! This creates unnecessary decimals and confusion. Always simplify to $\frac{2}{5}$ first, then multiply by 100.

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 need to simplify the fraction first?

Simplifying makes the calculation much easier! Working with $\frac{2}{5}$ instead of $\frac{20}{50}$ gives you smaller, cleaner numbers to multiply by 100.

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

List the factors of both numbers: 20 has factors 1, 2, 4, 5, 10, 20 and 50 has factors 1, 2, 5, 10, 25, 50. The largest shared factor is 10, so GCD = 10.

Can I just divide 20 by 50 and multiply by 100?

Yes, that works too! $20 ÷ 50 = 0.4$ , then $0.4 × 100 = 40\%$ . But simplifying first helps you avoid decimals and understand the relationship better.

What if the fraction doesn't simplify evenly?

Some fractions can't be simplified further, like $\frac{7}{11}$ . That's okay! Just multiply by 100 and you'll get a decimal percentage like 63.64%.

How do I know if my percentage is reasonable?

Think about it logically: $\frac{20}{50}$ means 20 out of 50 parts. Since 25 out of 50 would be half (50%), and 20 < 25, your answer should be less than 50%. 40% makes sense!

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