Simplify the Fraction 8/16: Step-by-Step Reduction

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

They mean the same thing! Both terms refer to dividing the numerator and denominator by their greatest common factor to get the simplest form of the fraction.

Q: Why can't I just divide by any common factor?

You can, but it's more efficient to use the greatest common factor. Using smaller factors means you'll need multiple steps to reach the simplest form.

Q: Is 2/4 the final answer for 8/16?

No! The fraction $ \frac{2}{4} $ can be reduced further. Both 2 and 4 are divisible by 2, so the simplest form is $ \frac{1}{2} $.

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

A fraction is fully simplified when the GCF of the numerator and denominator is 1. This means they share no common factors except 1.

Fraction Simplification with Common Factor Division

Simplify the following fraction:

$\frac{8}{16}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by dividing by 4

00:04 Divide the fraction by the appropriate factor

00:07 Make sure to divide both numerator and denominator

00:10 Calculate the numerators

00:15 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following fraction:

$\frac{8}{16}$

Step-by-step solution

First look at the denominator of the fraction. Try to find a number that, when divided by 16, gives you a result of 4:

$\frac{8:4}{16:4}=\frac{2}{4}$

Final Answer

$\frac{2}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 8 and 16 by their GCF of 8
Check: Verify $\frac{2}{4}$ cannot be reduced further by finding GCF(2,4) = 2 ✓

Common Mistakes

Avoid these frequent errors

Stopping at the first reduction without checking for further simplification
Don't stop at $\frac{2}{4}$ = incomplete answer! This fraction can still be reduced since 2 and 4 share a common factor of 2. Always check if your result can be simplified further to get $\frac{1}{2}$ .

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

What's the difference between reducing and simplifying a fraction?

They mean the same thing! Both terms refer to dividing the numerator and denominator by their greatest common factor to get the simplest form of the fraction.

How do I find the greatest common factor quickly?

List the factors of both numbers and find the largest one they share. For 8 and 16: factors of 8 are 1, 2, 4, 8; factors of 16 are 1, 2, 4, 8, 16. The GCF is 8!

Why can't I just divide by any common factor?

You can, but it's more efficient to use the greatest common factor. Using smaller factors means you'll need multiple steps to reach the simplest form.

Is 2/4 the final answer for 8/16?

No! The fraction $\frac{2}{4}$ can be reduced further. Both 2 and 4 are divisible by 2, so the simplest form is $\frac{1}{2}$ .

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the GCF of the numerator and denominator is 1. This means they share no common factors except 1.

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