Simplify the Fraction 4/16: Step-by-Step Reduction

Q: How do I find the greatest common factor of 4 and 16?

List the factors: 4 has factors 1, 2, 4 and 16 has factors 1, 2, 4, 8, 16. The largest number that appears in both lists is 4, so GCF = 4.

Q: Can I simplify this fraction in multiple steps?

Yes! You could divide by 2 first: $ \frac{4}{16} = \frac{2}{8} $, then divide by 2 again: $ \frac{2}{8} = \frac{1}{4} $. But using the GCF is faster!

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

A fraction is fully simplified when the numerator and denominator have no common factors except 1. Since 1 and 4 share no common factors, $ \frac{1}{4} $ is done!

Q: Why is simplifying fractions important?

Simplified fractions are easier to work with in calculations and comparisons. Plus, $ \frac{1}{4} $ is much clearer than $ \frac{4}{16} $ when describing parts of a whole!

Fraction Simplification with Greatest Common Factor

Simplify the following fraction:

$\frac{4}{16}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by 4

00:03 Divide the fraction by the given factor

00:06 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 following fraction:

$\frac{4}{16}=$

Step-by-step solution

We will reduce in the following way, divide the numerator by 4 and the denominator by 4:

$\frac{4:4}{16:4}=\frac{1}{4}$

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 4 and 16 by their GCF of 4
Check: Verify $\frac{1}{4}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by different numbers for numerator and denominator
Don't divide 4 by 2 and 16 by 8 = $\frac{2}{2}$ which is wrong! This changes the fraction's value completely. Always divide both numerator and denominator by the same number (their GCF).

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 greatest common factor of 4 and 16?

List the factors: 4 has factors 1, 2, 4 and 16 has factors 1, 2, 4, 8, 16. The largest number that appears in both lists is 4, so GCF = 4.

Can I simplify this fraction in multiple steps?

Yes! You could divide by 2 first: $\frac{4}{16} = \frac{2}{8}$ , then divide by 2 again: $\frac{2}{8} = \frac{1}{4}$ . But using the GCF is faster!

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator have no common factors except 1. Since 1 and 4 share no common factors, $\frac{1}{4}$ is done!

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

Start by dividing by small numbers like 2 or 3. Keep going until you can't divide both parts evenly anymore. You'll reach the same simplified answer eventually!

Why is simplifying fractions important?

Simplified fractions are easier to work with in calculations and comparisons. Plus, $\frac{1}{4}$ is much clearer than $\frac{4}{16}$ when describing parts of a whole!

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