Simplify the Fraction 20/50: Find the Simplification Factor

Q: What exactly is a simplification factor?

The simplification factor is the number you divide both the numerator and denominator by. For $ \frac{20}{50} $, we divide both by 10, so the factor is 10, not 5!

Q: Why isn't the answer 2/5 instead of 4/10?

Great observation! $ \frac{4}{10} $ can be simplified further to $ \frac{2}{5} $, but this question asks for a specific target denominator of 10. The factor that gets us from 50 to 10 is 5.

Q: How do I find the GCD quickly?

List the factors of both numbers: 20: 1, 2, 4, 5, 10, 2050: 1, 2, 5, 10, 25, 50The largest number that appears in both lists is 10!

Q: Can I use prime factorization instead?

Absolutely! $ 20 = 2^2 \times 5 $ and $ 50 = 2 \times 5^2 $. The GCD uses the lowest power of each common prime: $ 2^1 \times 5^1 = 10 $.

Q: What if the fraction can't be simplified?

If the GCD is 1, the fraction is already in lowest terms! For example, $ \frac{3}{7} $ cannot be simplified because 3 and 7 share no common factors except 1.

Fraction Simplification with Factor Identification

Simplify the following fraction and specify the simplification 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 10

00:03 We'll reduce the fraction with the appropriate divisor so the denominator equals 10

00:06 Make sure to divide both numerator and denominator

00:11 Let's calculate the quotients

00:16 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 and specify the simplification factor:

$\frac{20}{50}$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 50, gives us a result of 10.

Therefore:

$\frac{20:5}{50:5}=\frac{4}{10}$

Final Answer

$\frac{4}{10}$ , factor of 5

Key Points to Remember

Essential concepts to master this topic

GCD Rule: Find greatest common divisor of numerator and denominator
Division Method: Divide both 20 and 50 by their GCD of 10
Verification: Check that $\frac{4}{10}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't divide 20/50 by 2 to get 10/25 and stop there! This leaves the fraction partially simplified with factor 2 instead of the complete factor 10. Always find the GCD first, then divide both parts by it 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

What exactly is a simplification factor?

The simplification factor is the number you divide both the numerator and denominator by. For $\frac{20}{50}$ , we divide both by 10, so the factor is 10, not 5!

Why isn't the answer 2/5 instead of 4/10?

Great observation! $\frac{4}{10}$ can be simplified further to $\frac{2}{5}$ , but this question asks for a specific target denominator of 10. The factor that gets us from 50 to 10 is 5.

How do I find the GCD quickly?

List the factors of both numbers:

20: 1, 2, 4, 5, 10, 20
50: 1, 2, 5, 10, 25, 50

The largest number that appears in both lists is 10!

Can I use prime factorization instead?

Absolutely! $20 = 2^2 \times 5$ and $50 = 2 \times 5^2$ . The GCD uses the lowest power of each common prime: $2^1 \times 5^1 = 10$ .

What if the fraction can't be simplified?

If the GCD is 1, the fraction is already in lowest terms! For example, $\frac{3}{7}$ cannot be simplified because 3 and 7 share no common factors except 1.

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