Convert 75% to Its Decimal and Fractional Equivalents

Q: Why do I need to simplify the fraction?

Simplifying gives you the standard form that matches answer choices. $ \frac{75}{100} $ and $ \frac{3}{4} $ are equal, but only the simplified version appears in multiple choice options!

Q: How do I find the greatest common divisor quickly?

List factors of both numbers: 75 = 3×25, 100 = 4×25. The largest shared factor is 25, so divide both numerator and denominator by 25.

Q: Can I convert to decimal first instead?

Yes! 75% = 0.75, then convert 0.75 to $ \frac{75}{100} $ and simplify. Both methods work, but direct fraction conversion is usually faster.

Q: How can I double-check my answer?

Convert your fraction back: $ \frac{3}{4} = 3 ÷ 4 = 0.75 = 75\% $. If you get back to the original percentage, your answer is correct!

Percentage Conversion with Fraction Simplification

The percentage 75% 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 75 into 25 and 3, and 100 into 25 and 4

00:30 Reduce wherever possible

00:35 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The percentage 75% is equal to:

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Convert the percentage to a fraction
Step 2: Simplify the fraction
Step 3: Compare with the available choices

Let's perform these steps:

Step 1: Percentages can be expressed as fractions by dividing by 100. So, we write 75% as $\frac{75}{100}$ .

Step 2: Now, simplify the fraction. Find the greatest common divisor (GCD) of 75 and 100. The GCD is 25, so we divide both the numerator and the denominator by 25:

$\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}$ .

Step 3: Compare our simplified fraction $\frac{3}{4}$ to the given choices. The correct choice is:

$\frac{3}{4}$

Thus, 75% is equal to $\frac{3}{4}$ .

Final Answer

$\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentage to fraction by placing over 100
Technique: Find GCD of 75 and 100, which is 25
Check: Verify $\frac{3}{4} = 0.75 = 75\%$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction completely
Don't leave $\frac{75}{100}$ unsimplified = wrong answer choice! This fraction can be reduced further by dividing both parts by their GCD. Always find the greatest common divisor and simplify to lowest terms.

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 the fraction?

Simplifying gives you the standard form that matches answer choices. $\frac{75}{100}$ and $\frac{3}{4}$ are equal, but only the simplified version appears in multiple choice options!

How do I find the greatest common divisor quickly?

List factors of both numbers: 75 = 3×25, 100 = 4×25. The largest shared factor is 25, so divide both numerator and denominator by 25.

Can I convert to decimal first instead?

Yes! 75% = 0.75, then convert 0.75 to $\frac{75}{100}$ and simplify. Both methods work, but direct fraction conversion is usually faster.

What if the percentage doesn't simplify nicely?

Some percentages like 33.33% create repeating decimals or complex fractions. For this problem, 75% simplifies perfectly to $\frac{3}{4}$ because 75 and 100 share a common factor.

How can I double-check my answer?

Convert your fraction back: $\frac{3}{4} = 3 ÷ 4 = 0.75 = 75\%$ . If you get back to the original percentage, your answer is correct!

🌟 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