Fraction Reduction Practice: Converting 20/50 to Lowest Terms

Q: What's the difference between a common factor and the greatest common factor?

A common factor divides both numbers evenly, but the greatest common factor (GCF) is the largest one. For 20 and 50, common factors are 2, 5, and 10, but 10 is the greatest.

Q: Why does the problem ask for the highest common factor when I simplified by 2?

The problem wants the complete simplification process. While dividing by 2 gives $ \frac{10}{25} $, this isn't fully simplified since 10 and 25 share a factor of 5!

Q: What's the fully simplified form of 20/50?

First find GCF(20,50) = 10. Then $ \frac{20 ÷ 10}{50 ÷ 10} = \frac{2}{5} $. Since GCF(2,5) = 1, this is the simplest form.

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

20 = 2² × 550 = 2 × 5²GCF = 2¹ × 5¹ = 10This method works great for larger numbers!

Fraction Simplification with Greatest Common Factor

Simplify the fraction below and specify the highest common factor:

$\frac{20}{50}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction to denominator 25

00:03 We'll reduce the fraction with the appropriate divisor so the denominator equals 25

00:07 Make sure to divide both numerator and denominator

00:10 Let's calculate the quotients

00:18 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 fraction below and specify the highest common factor:

$\frac{20}{50}=$

Step-by-step solution

First look at the denominator of the fraction. We must try to find a number that, when divided by 50, gives us a result of 25.

Therefore:

$\frac{20:2}{50:2}=\frac{10}{25}$

Final Answer

$\frac{10}{25}$ , 2

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor (GCF) of numerator and denominator
Technique: Divide both 20 and 50 by their GCF of 10
Check: Verify $\frac{10}{25}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't just divide 20/50 by 2 to get 10/25 and stop there = fraction not fully simplified! The GCF is 10, not 2, so 10/25 can be reduced further to 2/5. Always find the greatest common factor to get the simplest form in one step.

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

What's the difference between a common factor and the greatest common factor?

A common factor divides both numbers evenly, but the greatest common factor (GCF) is the largest one. For 20 and 50, common factors are 2, 5, and 10, but 10 is the greatest.

How do I find the GCF of two numbers?

List all factors of each number, then find the largest one they share. For 20: 1, 2, 4, 5, 10, 20. For 50: 1, 2, 5, 10, 25, 50. The GCF is 10.

Why does the problem ask for the highest common factor when I simplified by 2?

The problem wants the complete simplification process. While dividing by 2 gives $\frac{10}{25}$ , this isn't fully simplified since 10 and 25 share a factor of 5!

What's the fully simplified form of 20/50?

First find GCF(20,50) = 10. Then $\frac{20 ÷ 10}{50 ÷ 10} = \frac{2}{5}$ . Since GCF(2,5) = 1, this is the simplest form.

Can I use prime factorization to find the GCF?

20 = 2² × 5
50 = 2 × 5²
GCF = 2¹ × 5¹ = 10

This method works great for larger numbers!

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