Reduce the Fraction 2/14 to Its Simplest Form: Step-by-Step Solution

Q: How do I find the highest common factor quickly?

List the factors of both numbers: 2 has factors 1, 2 and 14 has factors 1, 2, 7, 14. The largest number that appears in both lists is your HCF!

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

A fraction is in simplest form when the numerator and denominator share no common factors except 1. If you can't divide both by the same number, you're done!

Q: Can I reduce fractions by canceling digits?

Never cancel individual digits! For example, don't cross out the 1's in $ \frac{16}{64} $ to get $ \frac{6}{4} $. Always divide the entire numerator and denominator by their common factors.

Fraction Simplification with Common Factor Division

Reduce the given fraction into its simplest form:

$\frac{2}{14}=$

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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

00:14 And that's 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:

$\frac{2}{14}=$

Step-by-step solution

We need to 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 2, therefore:

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

Final Answer

$\frac{1}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the highest common factor (HCF) of numerator and denominator
Technique: Divide both parts by HCF: $\frac{2÷2}{14÷2} = \frac{1}{7}$
Check: Verify 1 and 7 have no common factors except 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the highest one
Don't just divide by the first common factor you find like 1 = still $\frac{2}{14}$ ! This leaves the fraction unreduced. Always find the highest (greatest) common factor to get the simplest form in one step.

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 highest common factor quickly?

List the factors of both numbers: 2 has factors 1, 2 and 14 has factors 1, 2, 7, 14. The largest number that appears in both lists is your HCF!

What if I can't see the HCF right away?

Start by dividing both numbers by small primes like 2, 3, 5. For $\frac{2}{14}$ , both are even, so try dividing by 2 first!

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator share no common factors except 1. If you can't divide both by the same number, you're done!

Can I reduce fractions by canceling digits?

Never cancel individual digits! For example, don't cross out the 1's in $\frac{16}{64}$ to get $\frac{6}{4}$ . Always divide the entire numerator and denominator by their common factors.

What if the numerator is larger than the denominator?

The same rules apply! Find the HCF and divide both parts by it. The process works exactly the same whether you have a proper or improper fraction.

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