Simplify the Fraction 2/10: Step-by-Step Reduction Guide

Q: How do I find the greatest common divisor (GCD) of 2 and 10?

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

Q: Why can't I just subtract the same number from top and bottom?

Never subtract! Subtraction changes the fraction's value. For example, $ \frac{2-1}{10-1} = \frac{1}{9} $ is completely different from $ \frac{2}{10} $. Only divide by the same number.

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

A fraction is fully simplified when the GCD of the numerator and denominator equals 1. For $ \frac{1}{5} $, since GCD(1,5) = 1, it cannot be simplified further.

Q: What if the GCD is 1 from the start?

If GCD = 1, the fraction is already in simplest form! For example, $ \frac{3}{7} $ cannot be simplified because GCD(3,7) = 1.

Q: Can I simplify by dividing by any common factor?

Yes, but it's more efficient to use the greatest common divisor. You could divide $ \frac{2}{10} $ by 1 first, but using GCD = 2 gets you to the answer in one step!

Fraction Simplification with Common Factors

Simplify the following fraction:

$\frac{2}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by 2

00:03 Divide the fraction by the given factor

00:07 Make sure to divide both numerator and denominator

00:10 Calculate the quotients

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following fraction:

$\frac{2}{10}=$

Step-by-step solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

$\frac{2:2}{10:2}=\frac{1}{5}$

Final Answer

$\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common divisor of numerator and denominator
Technique: Divide both 2 and 10 by their GCD of 2
Check: Verify $\frac{1}{5}$ cannot be reduced further since GCD(1,5) = 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by different numbers for numerator and denominator
Don't divide 2 by 1 and 10 by 5 = $\frac{2}{2}$ ! This changes the fraction's value completely. Always divide both numerator and denominator by the same number (their GCD).

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I find the greatest common divisor (GCD) of 2 and 10?

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

Why can't I just subtract the same number from top and bottom?

Never subtract! Subtraction changes the fraction's value. For example, $\frac{2-1}{10-1} = \frac{1}{9}$ is completely different from $\frac{2}{10}$ . Only divide by the same number.

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the GCD of the numerator and denominator equals 1. For $\frac{1}{5}$ , since GCD(1,5) = 1, it cannot be simplified further.

What if the GCD is 1 from the start?

If GCD = 1, the fraction is already in simplest form! For example, $\frac{3}{7}$ cannot be simplified because GCD(3,7) = 1.

Can I simplify by dividing by any common factor?

Yes, but it's more efficient to use the greatest common divisor. You could divide $\frac{2}{10}$ by 1 first, but using GCD = 2 gets you to the answer in one step!

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