Convert Fraction to Percentage: Solving 5/20 Step by Step

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

Simplifying makes calculations easier and helps you recognize common fractions like $ \frac{1}{4} $. Once you know $ \frac{1}{4} = 25\% $, you'll spot it instantly!

Q: Can I just multiply by 100 without converting to decimal?

Yes! You can multiply the fraction directly: $ \frac{5}{20} \times 100 = \frac{500}{20} = 25\% $. Both methods work, but converting to decimal first is often clearer.

Q: What's the fastest way to convert this fraction?

Recognize the pattern! $ \frac{5}{20} $ is the same as 5 out of 20, which is $ \frac{1}{4} $. Memorize that $ \frac{1}{4} = 25\% $!

Q: How do I check if my percentage is correct?

Convert back: 25% = 0.25 = $ \frac{25}{100} = \frac{1}{4} $. Since $ \frac{1}{4} = \frac{5}{20} $, your answer is correct!

Fraction to Percentage with Simplification

Convert the fraction into a percentage:

$\frac{5}{20}=\text{?}$

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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 equals the numerator in percentage form (X)

00:12 Determine which number to multiply the fraction by

00:22 Multiply both the numerator and denominator by 5 to obtain the denominator 100

00:35 Apply this formula to our exercise

00:40 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:

$\frac{5}{20}=\text{?}$

Step-by-step solution

To solve the problem of converting the fraction $\frac{5}{20}$ into a percentage, follow these steps:

Step 1: Simplify the Fraction (if necessary).
For $\frac{5}{20}$ , we can simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 5.
This simplifies to $\frac{1}{4}$ .
Step 2: Convert the Fraction to a Decimal.
Divide the numerator of the simplified fraction by its denominator: $\frac{1}{4} = 0.25$ .
Step 3: Convert the Decimal to a Percentage.
Multiply the decimal by 100 to change it to a percentage: $0.25 \times 100 = 25$ .

Therefore, the fraction $\frac{5}{20}$ , when converted to a percentage, is $25\%$ .

Final Answer

25%

Key Points to Remember

Essential concepts to master this topic

Simplification: Divide numerator and denominator by greatest common divisor
Technique: Convert $\frac{5}{20}$ to $\frac{1}{4}$ by dividing by 5
Check: $\frac{1}{4} = 0.25 = 25\%$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying first
Don't divide 5 ÷ 20 directly getting 0.25 = 25%! While this gives the right answer, you miss learning fraction simplification. Always simplify the fraction first, then convert to build stronger number sense.

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

Why do I need to simplify the fraction first?

Simplifying makes calculations easier and helps you recognize common fractions like $\frac{1}{4}$ . Once you know $\frac{1}{4} = 25\%$ , you'll spot it instantly!

What if I can't find the greatest common divisor?

Start by listing factors of both numbers. For 5 and 20: factors of 5 are {1, 5}, factors of 20 are {1, 2, 4, 5, 10, 20}. The largest common factor is 5.

Can I just multiply by 100 without converting to decimal?

Yes! You can multiply the fraction directly: $\frac{5}{20} \times 100 = \frac{500}{20} = 25\%$ . Both methods work, but converting to decimal first is often clearer.

What's the fastest way to convert this fraction?

Recognize the pattern! $\frac{5}{20}$ is the same as 5 out of 20, which is $\frac{1}{4}$ . Memorize that $\frac{1}{4} = 25\%$ !

How do I check if my percentage is correct?

Convert back: 25% = 0.25 = $\frac{25}{100} = \frac{1}{4}$ . Since $\frac{1}{4} = \frac{5}{20}$ , your answer is correct!

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