Simplify the Fraction 7/14: Step-by-Step Reduction

Q: How do I find the greatest common factor of 7 and 14?

List the factors of each number: 7 has factors 1, 7 and 14 has factors 1, 2, 7, 14. The largest number that appears in both lists is 7, so that's your GCF!

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

Subtraction doesn't work for simplifying fractions! You must divide both parts by the same factor. Subtracting changes the value of the fraction completely.

Q: What if the numerator and denominator don't have common factors?

If the only common factor is 1, then the fraction is already in simplest form! For example, $ \frac{3}{8} $ cannot be simplified because 3 and 8 share no common factors except 1.

Q: How do I know when I'm completely done simplifying?

You're done when the GCF of the numerator and denominator is 1. In our answer $ \frac{1}{2} $, the factors of 1 are just 1, and factors of 2 are 1 and 2, so GCF = 1!

Q: Can I simplify by canceling digits?

Never cancel individual digits! You can only cancel common factors. For example, don't turn $ \frac{16}{64} $ into $ \frac{1}{4} $ by canceling 6's - find the GCF of 16 and 64 instead!

Fraction Simplification with Common Factors

Simplify the given fraction to its simplest form:

$\frac{7}{14}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce as much as possible

00:03 Divide by the greatest common factor

00:07 Make sure to divide both numerator and denominator

00:10 Calculate the quotients

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

Simplify the given fraction to its simplest form:

$\frac{7}{14}=$

Step-by-step solution

We must identify the highest common factor (HCF): The largest number that both the numerator and the denominator can be divided by.

In this case, the number is 7, therefore:

$\frac{7:7}{14:7}=\frac{1}{2}$

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 7 and 14 by their GCF of 7
Check: Verify $\frac{1}{2}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Dividing by different factors for numerator and denominator
Don't divide 7 by 7 but 14 by 2 = $\frac{1}{7}$ ! This creates an incorrect fraction that's not equivalent to the original. Always divide both numerator and denominator by the same common factor.

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

How do I find the greatest common factor of 7 and 14?

List the factors of each number: 7 has factors 1, 7 and 14 has factors 1, 2, 7, 14. The largest number that appears in both lists is 7, so that's your GCF!

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

Subtraction doesn't work for simplifying fractions! You must divide both parts by the same factor. Subtracting changes the value of the fraction completely.

What if the numerator and denominator don't have common factors?

If the only common factor is 1, then the fraction is already in simplest form! For example, $\frac{3}{8}$ cannot be simplified because 3 and 8 share no common factors except 1.

How do I know when I'm completely done simplifying?

You're done when the GCF of the numerator and denominator is 1. In our answer $\frac{1}{2}$ , the factors of 1 are just 1, and factors of 2 are 1 and 2, so GCF = 1!

Can I simplify by canceling digits?

Never cancel individual digits! You can only cancel common factors. For example, don't turn $\frac{16}{64}$ into $\frac{1}{4}$ by canceling 6's - find the GCF of 16 and 64 instead!

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