Simplify the Fraction: Solving 25/250 Step by Step

Q: How do I find the GCD of 25 and 250?

List the factors of each number: 25 factors: 1, 5, 25 and 250 factors: 1, 2, 5, 10, 25, 50, 125, 250. The largest number that appears in both lists is 25, so GCD = 25.

Q: Why can't I just cancel the zeros?

You can only cancel common factors, not just matching digits! The zeros in 250 don't represent the same value as zeros you might see elsewhere. Always work with complete factors.

Q: Is 0.1 the same as 1/10?

Yes! $ \frac{1}{10} = 0.1 $ because when you divide 1 by 10, you get one-tenth, which is 0.1 in decimal form.

Q: What if the GCD is 1?

If the GCD is 1, the fraction is already in simplest form! This means the numerator and denominator share no common factors other than 1.

Q: How do I convert any fraction to a decimal?

Simply divide the numerator by the denominator. For $ \frac{1}{10} $, calculate 1 ÷ 10 = 0.1. Use long division if needed!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 We want the denominator to be some multiple of 10 and 10

00:07 We'll reduce the fraction, making sure to divide both numerator and denominator

00:14 Convert from fraction to decimal fraction

00:20 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

$\frac{25}{250}=$

2

Step-by-step solution

To convert the fraction $\frac{25}{250}$ to a decimal, follow these steps:

Step 1: Simplify the fraction. To simplify $\frac{25}{250}$ , find the greatest common divisor (GCD) of 25 and 250, which is 25.
Step 2: Divide both the numerator and denominator by their GCD.
$\frac{25}{250} = \frac{25 \div 25}{250 \div 25} = \frac{1}{10}$
Step 3: Convert the simplified fraction $\frac{1}{10}$ to a decimal. The decimal form of $\frac{1}{10}$ is 0.1.

Therefore, the decimal equivalent of the fraction $\frac{25}{250}$ is $0.1$ .

Among the choices provided, $0.1$ matches the computed answer.

3

Final Answer

$\text{0}.1$

Key Points to Remember

Essential concepts to master this topic

Rule: Find GCD of numerator and denominator to simplify fractions
Technique: Divide both terms by GCD: 25÷25 = 1, 250÷25 = 10
Check: Convert simplified fraction to decimal: 1÷10 = 0.1 ✓

Common Mistakes

Avoid these frequent errors

Canceling digits instead of finding GCD
Don't just cross out the same digits like canceling the '5' in 25 and 250 = wrong simplification! This ignores proper factoring and gives incorrect results. Always find the greatest common divisor of the entire numbers.

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 GCD of 25 and 250?

+

List the factors of each number: 25 factors: 1, 5, 25 and 250 factors: 1, 2, 5, 10, 25, 50, 125, 250. The largest number that appears in both lists is 25, so GCD = 25.

Why can't I just cancel the zeros?

+

You can only cancel common factors, not just matching digits! The zeros in 250 don't represent the same value as zeros you might see elsewhere. Always work with complete factors.

Is 0.1 the same as 1/10?

+

Yes! $\frac{1}{10} = 0.1$ because when you divide 1 by 10, you get one-tenth, which is 0.1 in decimal form.

What if the GCD is 1?

+

If the GCD is 1, the fraction is already in simplest form! This means the numerator and denominator share no common factors other than 1.

How do I convert any fraction to a decimal?

+

Simply divide the numerator by the denominator. For $\frac{1}{10}$ , calculate 1 ÷ 10 = 0.1. Use long division if needed!

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Simplify the Fraction: Solving 25/250 Step by Step

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