Converting 50% to Its Equivalent Decimal Form: Basic Mathematics

Q: Why can't I just write 50% as 0.50?

You absolutely can! 50% = 0.50 = $ \frac{1}{2} $ are all equivalent. The question asks for the fraction form, so you need to convert the percentage to a simplified fraction.

Q: How do I know when a fraction is fully simplified?

A fraction is simplified when the numerator and denominator share no common factors except 1. For $ \frac{1}{2} $, the only common factor of 1 and 2 is 1, so it's fully simplified!

Q: Are there other ways to convert percentages to fractions?

Yes! You can also think: 50% means 50 out of every 100, which is half. So 50% = $ \frac{1}{2} $. Practice recognizing common percentages like 25% = $ \frac{1}{4} $, 75% = $ \frac{3}{4} $.

Q: What if the percentage doesn't simplify to a nice fraction?

Some percentages like 33% give $ \frac{33}{100} $ which doesn't simplify further. That's perfectly fine! Not all fractions can be reduced to simple forms.

Percentage Conversion with Fraction Simplification

The percentage 50% is equal to:

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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

00:24 Break down 100 into factors of 50 and 2

00:31 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 50% is equal to:

Step-by-step solution

Let's solve this problem by converting the given percentage into a fraction:

To convert 50% into a fraction, we follow these steps:

Step 1: Recognize that a percentage is simply a way of expressing a number as parts out of 100. So, 50% is equivalent to $\frac{50}{100}$ .
Step 2: Simplify the fraction $\frac{50}{100}$ . The greatest common divisor (GCD) of 50 and 100 is 50. Thus, we divide both the numerator and denominator by 50.
Step 3: Simplifying, we have:

\frac{50}{100} = \frac{50 \div 50}{100 \div 50} = \frac{1}{2}

Thus, the percentage 50% is equal to the fraction $\frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Percentage means parts out of 100, so 50% = 50/100
Technique: Find GCD of numerator and denominator: GCD(50,100) = 50
Check: Verify $\frac{1}{2} = 0.5 = 50\%$ works both ways ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction
Don't leave your answer as $\frac{50}{100}$ = unsimplified fraction! This makes it harder to recognize equivalent forms and compare with answer choices. Always reduce fractions to lowest terms by dividing by the GCD.

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 can't I just write 50% as 0.50?

You absolutely can! 50% = 0.50 = $\frac{1}{2}$ are all equivalent. The question asks for the fraction form, so you need to convert the percentage to a simplified fraction.

How do I know when a fraction is fully simplified?

A fraction is simplified when the numerator and denominator share no common factors except 1. For $\frac{1}{2}$ , the only common factor of 1 and 2 is 1, so it's fully simplified!

What if I can't find the GCD easily?

Try dividing both numbers by small primes like 2, 3, 5. For $\frac{50}{100}$ : both are even, so divide by 2 repeatedly. 50÷2=25, 100÷2=50, then 25÷5=5, 50÷5=10, then 5÷5=1, 10÷5=2.

Are there other ways to convert percentages to fractions?

Yes! You can also think: 50% means 50 out of every 100, which is half. So 50% = $\frac{1}{2}$ . Practice recognizing common percentages like 25% = $\frac{1}{4}$ , 75% = $\frac{3}{4}$ .

What if the percentage doesn't simplify to a nice fraction?

Some percentages like 33% give $\frac{33}{100}$ which doesn't simplify further. That's perfectly fine! Not all fractions can be reduced to simple forms.

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