Simplify the Fraction: Reducing 250/500 to Lowest Terms

Q: How do I find the greatest common divisor of 250 and 500?

Look for the largest number that divides both evenly. Since 250 × 2 = 500, the GCD is 250. You can also list factors: 250 divides into both numbers perfectly!

Q: Why can't I just convert to decimal right away?

You absolutely can! $ \frac{250}{500} = 0.5 $ directly. However, simplifying first makes the math easier and shows you understand fraction relationships.

Q: What if the GCD is hard to find?

Start with obvious common factors like 10, 100, etc. For 250 and 500, both end in zeros, so try dividing by 10, then 100, then keep going until you find the largest one.

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

A fraction is fully 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.

Q: Is 0.5 the same as 50%?

Yes! $ \frac{1}{2} = 0.5 = 50\% $. They're three different ways to express the same value - fraction, decimal, and percentage.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:05 Reduce the fraction, make sure to divide both numerator and denominator

00:16 Convert from fraction to decimal fraction

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\frac{250}{500}=$

2

Step-by-step solution

To solve the problem of converting $\frac{250}{500}$ to a decimal, we will follow these steps:

Step 1: Simplify the fraction $\frac{250}{500}$ .
Step 2: Convert the resulting simplified fraction to a decimal.

Let's begin:

Step 1: Simplify the fraction $\frac{250}{500}$ .
To simplify, find the greatest common divisor (GCD) of 250 and 500. The GCD is 250.

Divide both the numerator and the denominator by their GCD:
$\frac{250 \div 250}{500 \div 250} = \frac{1}{2}$ .

Step 2: Convert the simplified fraction $\frac{1}{2}$ to a decimal.
To do this, divide 1 by 2 to get the decimal: $0.5$ .

Therefore, the decimal representation of $\frac{250}{500}$ is $\mathbf{0.5}$ .

3

Final Answer

$0.5$

Key Points to Remember

Essential concepts to master this topic

GCD Rule: Find greatest common divisor to reduce fractions completely
Division Method: Divide both 250 and 500 by GCD of 250
Verification: Convert $\frac{1}{2}$ to 0.5 to confirm simplification ✓

Common Mistakes

Avoid these frequent errors

Not finding the greatest common divisor properly
Don't just divide by any common factor like 10 or 50 = $\frac{25}{50}$ which isn't fully simplified! This leaves the fraction in a form that can be reduced further. Always find the GCD (250) to get the simplest form $\frac{1}{2}$ in one step.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

How do I find the greatest common divisor of 250 and 500?

+

Look for the largest number that divides both evenly. Since 250 × 2 = 500, the GCD is 250. You can also list factors: 250 divides into both numbers perfectly!

Why can't I just convert to decimal right away?

+

You absolutely can! $\frac{250}{500} = 0.5$ directly. However, simplifying first makes the math easier and shows you understand fraction relationships.

What if the GCD is hard to find?

+

Start with obvious common factors like 10, 100, etc. For 250 and 500, both end in zeros, so try dividing by 10, then 100, then keep going until you find the largest one.

How do I know when a fraction is fully simplified?

+

A fraction is fully 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.

Is 0.5 the same as 50%?

+

Yes! $\frac{1}{2} = 0.5 = 50\%$ . They're three different ways to express the same value - fraction, decimal, and percentage.

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Simplify the Fraction: Reducing 250/500 to Lowest Terms

Fraction Simplification with Greatest Common Divisor

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