Converting 84% to Its Equivalent Decimal and Fraction Forms

Q: How do I find the GCD of 84 and 100?

List the factors: 84 = 2² × 3 × 7 and 100 = 2² × 5². The common factors are 2², so GCD = 4. You can also use the Euclidean algorithm for larger numbers!

Q: Why can't I just write 84% as 0.84?

The question asks for the fraction form, not decimal! While 84% = 0.84 is correct, you need to express it as a simplified fraction: $ \frac{21}{25} $.

Q: What if I can't find the GCD easily?

Try dividing both numbers by small primes like 2, 3, 5. For 84 and 100: both divide by 2 twice (giving 21 and 25), and 21 and 25 share no common factors.

Q: How do I check if my fraction is fully simplified?

A fraction is simplified when the GCD of numerator and denominator equals 1. For $ \frac{21}{25} $: 21 = 3 × 7, and 25 = 5², so GCD = 1. ✓

Q: Can I convert back to check my answer?

Absolutely! Divide 21 ÷ 25 = 0.84, then multiply by 100 to get 84%. This confirms $ \frac{21}{25} $ is correct!

Percentage Conversion with Fraction Simplification

The percentage 84% 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

00:04 Let's change percentages into fractions step by step.

00:09 Remember, a percentage is like a fraction. The top number, or numerator, is the percentage value or X, and the bottom number, or denominator, is always one hundred.

00:20 Next, we'll use this idea in our example. Follow along as we transform the percentage into a fraction.

00:29 Let's factor eighty-four into twenty-one times four, and one hundred into twenty-five times four.

00:36 Now, reduce the fractions wherever you can.

00:40 And there you have it, your solution is complete!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The percentage 84% is equal to:

Step-by-step solution

To solve this problem effectively, follow these steps:

Step 1: Convert the percentage to a fraction.
To express 84% as a fraction, write it as $\frac{84}{100}$ since percent means per hundred.
Step 2: Simplify the fraction.
We need to simplify $\frac{84}{100}$ by finding the greatest common divisor (GCD) of 84 and 100. The GCD of 84 and 100 is 4.
Step 3: Divide both numerator and denominator by their GCD.
Divide 84 by 4 to get 21, and divide 100 by 4 to get 25.
Thus, $\frac{84}{100} = \frac{21}{25}$ .
Step 4: Identify the correct choice.
Among the provided options, $\frac{21}{25}$ corresponds to choice 2.

Thus, the percentage 84% is equal to $\frac{21}{25}$ .

Final Answer

$\frac{21}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percent to fraction by placing over 100
Technique: Find GCD of 84 and 100, which is 4
Check: Verify $\frac{21}{25} = 0.84 = 84%$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction
Don't leave your answer as $\frac{84}{100}$ = incomplete solution! This fraction isn't in lowest terms and won't match answer choices. Always find the GCD and divide both numerator and denominator by it.

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

How do I find the GCD of 84 and 100?

List the factors: 84 = 2² × 3 × 7 and 100 = 2² × 5². The common factors are 2², so GCD = 4. You can also use the Euclidean algorithm for larger numbers!

Why can't I just write 84% as 0.84?

The question asks for the fraction form, not decimal! While 84% = 0.84 is correct, you need to express it as a simplified fraction: $\frac{21}{25}$ .

What if I can't find the GCD easily?

Try dividing both numbers by small primes like 2, 3, 5. For 84 and 100: both divide by 2 twice (giving 21 and 25), and 21 and 25 share no common factors.

How do I check if my fraction is fully simplified?

A fraction is simplified when the GCD of numerator and denominator equals 1. For $\frac{21}{25}$ : 21 = 3 × 7, and 25 = 5², so GCD = 1. ✓

Can I convert back to check my answer?

Absolutely! Divide 21 ÷ 25 = 0.84, then multiply by 100 to get 84%. This confirms $\frac{21}{25}$ 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