Reduce the Fraction 2/5 to Its Simplest Form: Step-by-Step Solution

Q: How do I know when a fraction can't be simplified?

A fraction is already in simplest form when the numerator and denominator share no common factors except 1. For $ \frac{2}{5} $, the factors of 2 are {1, 2} and factors of 5 are {1, 5} - they only share 1!

Q: What's the difference between reducing and simplifying?

Reducing and simplifying mean the same thing! Both involve dividing the numerator and denominator by their greatest common factor to get the simplest form.

Q: Why can't I just divide 2 by something to make it smaller?

You can only divide both the numerator and denominator by the same number. Since 2 doesn't divide evenly into 5, there's no common factor to use for simplifying $ \frac{2}{5} $.

Q: Are there other fractions like 2/5 that can't be simplified?

Yes! Any fraction where the numerator and denominator are relatively prime (share no common factors) cannot be simplified. Examples: $ \frac{3}{7} $, $ \frac{4}{9} $, $ \frac{5}{8} $.

Q: Should I always check if a fraction can be simplified?

Always check first! Start by finding the GCF of the numerator and denominator. If the GCF is 1, the fraction is already in simplest form. This saves time and prevents unnecessary work.

Fraction Simplification with Prime Numerators

Reduce the given fraction into its simplest form:

$\frac{2}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction as much as possible

00:03 Divide by the greatest common factor

00:06 Make sure to divide both numerator and denominator

00:09 Calculate the portions

00:13 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

Reduce the given fraction into its simplest form:

$\frac{2}{5}=$

Step-by-step solution

Let's find the highest number that divides both the numerator and the denominator.

In this case, the number is 2 but it doesn't divide the denominator.

Therefore, it cannot be simplified.

Final Answer

It is not possible to simplify

Key Points to Remember

Essential concepts to master this topic

Rule: Find greatest common factor (GCF) of numerator and denominator
Technique: Check if any factor divides both 2 and 5
Check: Verify no common factors exist: 2 and 5 share no divisors ✓

Common Mistakes

Avoid these frequent errors

Assuming all fractions can be simplified
Don't automatically try to reduce every fraction = wasted time and confusion! When numerator and denominator share no common factors, the fraction is already in simplest form. Always check for common factors first before attempting to simplify.

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 know when a fraction can't be simplified?

A fraction is already in simplest form when the numerator and denominator share no common factors except 1. For $\frac{2}{5}$ , the factors of 2 are {1, 2} and factors of 5 are {1, 5} - they only share 1!

What's the difference between reducing and simplifying?

Reducing and simplifying mean the same thing! Both involve dividing the numerator and denominator by their greatest common factor to get the simplest form.

Why can't I just divide 2 by something to make it smaller?

You can only divide both the numerator and denominator by the same number. Since 2 doesn't divide evenly into 5, there's no common factor to use for simplifying $\frac{2}{5}$ .

Are there other fractions like 2/5 that can't be simplified?

Yes! Any fraction where the numerator and denominator are relatively prime (share no common factors) cannot be simplified. Examples: $\frac{3}{7}$ , $\frac{4}{9}$ , $\frac{5}{8}$ .

Should I always check if a fraction can be simplified?

Always check first! Start by finding the GCF of the numerator and denominator. If the GCF is 1, the fraction is already in simplest form. This saves time and prevents unnecessary work.

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