Converting 65% to Its Fractional Equivalents

Q: Can I convert 65% to a decimal first?

Yes! 65% = 0.65 = $ \frac{65}{100} $. Both paths lead to the same fraction, but going straight from percentage is often faster.

Q: What if the percentage doesn't divide evenly?

No problem! For example, 33% = $ \frac{33}{100} $. Since 33 and 100 share no common factors, this fraction is already in simplest form.

Q: How can I check if my simplified fraction is correct?

Convert your fraction back to a decimal by dividing: $ \frac{13}{20} = 13 ÷ 20 = 0.65 $. Then multiply by 100 to get 65%!

Q: Why do some percentages have simpler fractions than others?

It depends on the factors involved! Percentages like 25%, 50%, 75% have many common factors with 100, so they simplify nicely. Others like 17% don't share factors with 100.

Percentage Conversion with Fraction Simplification

The percentage 65% 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

00:00 Convert from percentages to fractions

00:05 The percentage equals a fraction where the numerator is the percentage (X) and the denominator is 100

00:10 Apply this formula to our exercise

00:25 Factor 65 into 13 and 5, and 100 into 5 and 20

00:30 Reduce wherever possible

00:36 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The percentage 65% is equal to:

Step-by-step solution

To solve this problem, we need to convert 65% into a fraction and simplify it. Let's walk through this process:

Step 1: Convert the percentage to a fraction

Percentages can be easily converted to fractions by writing them over 100. For 65%, we write:

65\% = \frac{65}{100}

Step 2: Simplify the fraction

To simplify $\frac{65}{100}$ , we find the greatest common divisor (GCD) of 65 and 100. The GCD is 5. Therefore, divide both the numerator and the denominator by 5:

\frac{65 \div 5}{100 \div 5} = \frac{13}{20}

Thus, 65% as a simplified fraction is $\frac{13}{20}$ .

Upon reviewing the multiple-choice options, we see that choice 3: $\frac{13}{20}$ matches our simplified result.

Therefore, the percentage 65% is equal to $\frac{13}{20}$ .

Final Answer

$\frac{13}{20}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentage to fraction by placing over 100
Technique: Find GCD to simplify: $\frac{65}{100} = \frac{13}{20}$ using GCD of 5
Check: Verify by converting back: $\frac{13}{20} = 0.65 = 65\%$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction to lowest terms
Don't leave your answer as $\frac{65}{100}$ = still has common factors! This makes your fraction unnecessarily complex and won't match multiple choice answers. Always find the GCD and divide both numerator and denominator by it.

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

How do I find the GCD of 65 and 100?

List the factors of each number: 65 = 1, 5, 13, 65 and 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common factor they share is 5!

Can I convert 65% to a decimal first?

Yes! 65% = 0.65 = $\frac{65}{100}$ . Both paths lead to the same fraction, but going straight from percentage is often faster.

What if the percentage doesn't divide evenly?

No problem! For example, 33% = $\frac{33}{100}$ . Since 33 and 100 share no common factors, this fraction is already in simplest form.

How can I check if my simplified fraction is correct?

Convert your fraction back to a decimal by dividing: $\frac{13}{20} = 13 ÷ 20 = 0.65$ . Then multiply by 100 to get 65%!

Why do some percentages have simpler fractions than others?

It depends on the factors involved! Percentages like 25%, 50%, 75% have many common factors with 100, so they simplify nicely. Others like 17% don't share factors with 100.

🌟 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