Simplify the Fraction 4/20: Step-by-Step Reduction

Q: How do I find the greatest common factor of 4 and 20?

List the factors of each number: 4: 1, 2, 4 and 20: 1, 2, 4, 5, 10, 20. The largest number that appears in both lists is 4, so that's your GCF!

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

Start by dividing both numbers by small factors like 2. Keep going until you can't divide both by the same number anymore. The product of all these factors is your GCF.

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

A fraction is in simplest form when the only common factor of the numerator and denominator is 1. If you can't find any number (except 1) that divides both parts, you're done!

Q: Can I use prime factorization to find the GCF?

Yes! Find the prime factors: $ 4 = 2^2 $ and $ 20 = 2^2 \times 5 $. The GCF uses the lowest power of each common prime: $ 2^2 = 4 $.

Q: What if my answer doesn't match any of the choices?

Double-check your work! Make sure you divided both the numerator and denominator by the same number, and verify that your fraction is fully reduced.

Fraction Simplification with Greatest Common Factor

Simplify the given fraction to its simplest form:

$\frac{4}{20}=$

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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

00:09 Calculate the quotients

00:12 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:

$\frac{4}{20}=$

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 4, therefore:

$\frac{4:4}{20:4}=\frac{1}{5}$

Final Answer

$\frac{1}{5}$

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 20 by their GCF of 4
Check: Verify $\frac{1}{5}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by a common factor that isn't the greatest
Don't divide by 2 to get $\frac{2}{10}$ = still not simplified! This leaves the fraction partially reduced and requires more steps. Always find the greatest common factor (GCF) first and divide by that number.

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 20?

List the factors of each number: 4: 1, 2, 4 and 20: 1, 2, 4, 5, 10, 20. The largest number that appears in both lists is 4, so that's your GCF!

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

Start by dividing both numbers by small factors like 2. Keep going until you can't divide both by the same number anymore. The product of all these factors is your GCF.

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the only common factor of the numerator and denominator is 1. If you can't find any number (except 1) that divides both parts, you're done!

Can I use prime factorization to find the GCF?

Yes! Find the prime factors: $4 = 2^2$ and $20 = 2^2 \times 5$ . The GCF uses the lowest power of each common prime: $2^2 = 4$ .

What if my answer doesn't match any of the choices?

Double-check your work! Make sure you divided both the numerator and denominator by the same number, and verify that your fraction is fully reduced.

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