Simplify the Fraction 2/13: Step-by-Step Reduction Guide

Fraction Simplification with Prime Denominators

Simplify the given fraction to its simplest form:

213= \frac{2}{13}=

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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
00:04 Divide by the greatest common factor
00:07 Make sure to divide both numerator and denominator
00:15 Calculate the quotients
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

Simplify the given fraction to its simplest form:

213= \frac{2}{13}=

2

Step-by-step solution

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

In this case, we can divide the numerator by 2, but we cannot divide 13 by 2.

Therefore, we cannot simplify further.

3

Final Answer

It is not possible to simplify

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the greatest common divisor (GCD) of numerator and denominator
  • Technique: Check if 2 and 13 share common factors: 2 = 2×1, 13 = 13×1
  • Check: Since GCD(2,13) = 1, the fraction is already in simplest form ✓

Common Mistakes

Avoid these frequent errors
  • Attempting to divide by any common factor without verification
    Don't divide numerator and denominator by 2 just because 2 appears in the numerator = incorrect simplification! Since 13 is not divisible by 2, this creates an invalid fraction. Always verify that both numerator and denominator are divisible by the same factor.

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

Why can't I simplify 2/13 even though 2 is in the numerator?

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To simplify a fraction, you need a common factor that divides both the numerator AND denominator. Since 13 is a prime number, it's only divisible by 1 and 13, but 2 isn't divisible by 13.

How do I know when a fraction is already in simplest form?

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A fraction is in simplest form when the GCD of the numerator and denominator is 1. This means they share no common factors except 1.

What makes 13 special in this fraction?

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13 is a prime number, meaning it only has factors 1 and 13. Since 2 doesn't equal 1 or 13, there's no way to simplify 213 \frac{2}{13} .

Could this fraction ever be simplified?

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Only if the numerator were a multiple of 13 (like 13, 26, 39, etc.) or if both numerator and denominator shared a common factor. Since 2 and 13 are relatively prime, simplification isn't possible.

How can I quickly check if two numbers are relatively prime?

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Use the Euclidean algorithm or check if they share any common prime factors. For small numbers like 2 and 13, you can see that 13 ÷ 2 = 6.5 (not a whole number), confirming no common factors.

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