Simplify the Fraction: Reducing 1/15 to Lowest Terms

Fraction Simplification with Prime Numerators

Reduce the given fraction into its simplest form:

115= \frac{1}{15}=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's start by simplifying the fraction as much as possible.
00:09 Find the greatest common factor, or G C F, of the numerator and denominator.
00:14 Now, divide both the top, and the bottom by this number.
00:18 Calculate what each of those divisions equals.
00:22 And there you have it! That's the solution to our fraction problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Reduce the given fraction into its simplest form:

115= \frac{1}{15}=

2

Step-by-step solution

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

In this case, that number is 1, so:

1:115:1=115 \frac{1:1}{15:1}=\frac{1}{15}

Therefore, it cannot be simplified further

3

Final Answer

It is not possible to simplify

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find GCD of numerator and denominator to simplify fractions
  • Technique: Since 1 and 15 share only GCD of 1, 115 \frac{1}{15} cannot be reduced
  • Check: Verify no common factors exist between 1 and 15 ✓

Common Mistakes

Avoid these frequent errors
  • Trying to cancel digits that aren't factors
    Don't cancel the 1 in 15 with the numerator 1 = 15 \frac{1}{5} ! This confuses digit cancellation with factor division. Always find the GCD of the entire numerator and denominator first.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

\( \frac{4}{8}= \)

FAQ

Everything you need to know about this question

Why can't I simplify 115 \frac{1}{15} ?

+

Because the numerator is 1, and 1 only has itself as a factor. Since 15 is not divisible by 1 in a way that reduces the fraction, 115 \frac{1}{15} is already in simplest form.

What does GCD mean and how do I find it?

+

GCD (Greatest Common Divisor) is the largest number that divides both the numerator and denominator. For 1 and 15: factors of 1 are just {1}, factors of 15 are {1, 3, 5, 15}, so GCD = 1.

Can I cancel the 1 in 15 with the numerator 1?

+

No! You can only cancel common factors, not individual digits. The 1 in 15 is just a digit, not a separate factor. Always work with the entire numbers.

How do I know when a fraction is fully simplified?

+

A fraction is fully simplified when the GCD of numerator and denominator equals 1. This means they share no common factors other than 1.

What if the numerator is always 1?

+

When the numerator is 1, the fraction is called a unit fraction. These can only be simplified if the denominator has 1 as a factor multiple times, which never happens with whole numbers.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations