Convert 75% to a Fraction: Finding the Equivalent in 100ths

Q: Why is the denominator always 100 for percentages?

Because percent literally means "per hundred"! The word comes from Latin: 'per centum' = for every 100. So any percentage is automatically a fraction with 100 in the denominator.

Q: What if the percentage has a decimal, like 7.5%?

You'd write it as $ \frac{7.5}{100} $, but this creates a decimal in the numerator. To avoid decimals, multiply both parts by 10 to get $ \frac{75}{1000} $.

Q: Is there a shortcut for converting percentages to fractions?

Yes! Just drop the % sign and put the number over 100. So 25% → $ \frac{25}{100} $, 80% → $ \frac{80}{100} $, etc. It's that simple!

Percentage Conversion with Denominator 100

Write the percentage 75% as a fraction with a denominator of 100.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's convert percentages into fractions.

00:10 The percentage is a fraction where the top number is the percentage, and the bottom number is one hundred.

00:16 Now, let's use this formula for our exercise.

00:30 And there we have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the percentage 75% as a fraction with a denominator of 100.

Step-by-step solution

To express 75% as a fraction with a denominator of 100, follow these steps:

Step 1: Recall that a percentage is a fraction out of 100. This means that 75% represents 75 out of 100.
Step 2: Write the percentage as a fraction: Since 75% means 75 per hundred, this directly gives us the fraction $\frac{75}{100}$ .

Upon checking the given choices, the correct answer is $\frac{75}{100}$ , which matches option 4.

Therefore, the solution to the problem is $\frac{75}{100}$ .

Final Answer

$\frac{75}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Percentage means per hundred, so 75% = 75 out of 100
Technique: Write percentage as $\frac{\text{percentage number}}{100}$ , so 75% becomes $\frac{75}{100}$
Check: Does $\frac{75}{100} = 0.75 = 75\%$ ? Yes! ✓

Common Mistakes

Avoid these frequent errors

Putting the percentage in the wrong position
Don't write 75% as $\frac{75}{10}$ or $\frac{7.5}{100}$ = wrong fraction values! This happens when students misplace the number or add decimals unnecessarily. Always put the percentage number directly over 100: 75% = $\frac{75}{100}$ .

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 is the denominator always 100 for percentages?

Because percent literally means "per hundred"! The word comes from Latin: 'per centum' = for every 100. So any percentage is automatically a fraction with 100 in the denominator.

Do I need to simplify the fraction after converting?

The question specifically asks for a denominator of 100, so keep it as $\frac{75}{100}$ . If asked to simplify, then you'd reduce it to $\frac{3}{4}$ .

What if the percentage has a decimal, like 7.5%?

You'd write it as $\frac{7.5}{100}$ , but this creates a decimal in the numerator. To avoid decimals, multiply both parts by 10 to get $\frac{75}{1000}$ .

How can I check if my conversion is right?

Convert your fraction back to a percentage! Divide the numerator by denominator and multiply by 100. For $\frac{75}{100}$ : 75 ÷ 100 × 100 = 75% ✓

Is there a shortcut for converting percentages to fractions?

Yes! Just drop the % sign and put the number over 100. So 25% → $\frac{25}{100}$ , 80% → $\frac{80}{100}$ , etc. It's that simple!

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