Converting 20% to Its Decimal and Fractional Equivalents

Percentage Conversion with Simplification Steps

The percentage 20% is equal to:

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's turn percentages into fractions. It's easy!
00:08 Think of a percentage as a fraction. The top number, or numerator, is the percentage, and the bottom number is always 100.
00:17 Now, let's use this idea in our example step-by-step.
00:33 First, split 100 into the numbers 20 and 5.
00:39 Simplify the fraction whenever you can. Great job so far!
00:43 And that's how you solve it! Great work!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The percentage 20% is equal to:

2

Step-by-step solution

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

  • Step 1: Convert 20% to a fraction by dividing by 100.
  • Step 2: Simplify the resulting fraction, if necessary.

Now, let's work through each step:
Step 1: Convert 20% to a fraction:
The percentage 20% can be written as 20100\frac{20}{100}.

Step 2: Simplify the fraction:
To simplify 20100\frac{20}{100}, we find the greatest common divisor of 20 and 100, which is 20.
Divide both the numerator and the denominator by 20:
20÷20100÷20=15\frac{20 \div 20}{100 \div 20} = \frac{1}{5}.

Therefore, the fraction equivalent to 20% is 15\frac{1}{5}.

Thus, the correct answer is choice 2: 15 \frac{1}{5} .

3

Final Answer

15 \frac{1}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert percentage to fraction by placing over 100
  • Technique: Find GCD: 20 and 100 both divide by 20
  • Check: Verify 15=0.2=20% \frac{1}{5} = 0.2 = 20\%

Common Mistakes

Avoid these frequent errors
  • Not simplifying the fraction to lowest terms
    Don't leave your answer as 20100 \frac{20}{100} = unsimplified form! This makes calculations harder and isn't in standard form. Always find the GCD and divide both numerator and denominator to get the simplest fraction.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction \( \frac{75}{100} \)

to a percentage:

FAQ

Everything you need to know about this question

Why do I need to simplify 20100 \frac{20}{100} ?

+

Simplifying makes fractions easier to work with! 15 \frac{1}{5} is much cleaner than 20100 \frac{20}{100} and helps you recognize equivalent fractions faster.

How do I find the greatest common divisor quickly?

+

Look for common factors! Both 20 and 100 end in 0, so they're divisible by 10. Try larger factors: 20 divides into both 20 (gives 1) and 100 (gives 5).

Can I convert 20% to decimal instead?

+

Yes! 20%=20÷100=0.2 20\% = 20 \div 100 = 0.2 . But since the question asks for a fraction, you need to convert: 0.2=210=15 0.2 = \frac{2}{10} = \frac{1}{5} .

What if I get confused between numerator and denominator?

+

Remember: the percentage number goes on top (numerator), and 100 always goes on bottom (denominator). So 20% becomes 20100 \frac{20}{100} .

How can I check if 15 \frac{1}{5} really equals 20%?

+

Convert back! 15=1÷5=0.2=0.2×100%=20% \frac{1}{5} = 1 \div 5 = 0.2 = 0.2 \times 100\% = 20\% ✓. Or think: 1 out of 5 equal parts is the same as 20 out of 100 equal parts.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Percentage questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations