Simplify the Fraction 20/40: Finding the Simplification Factor

Q: What does the simplification factor mean?

The simplification factor is the number you divide both the numerator and denominator by. In this case, we divided both 20 and 40 by 4, so the factor is 4.

Q: Why isn't the answer 1/2?

While $ \frac{20}{40} = \frac{1}{2} $ when fully simplified, the question asks for a specific format. We need to show $ \frac{5}{10} $ with factor 4, not the most reduced form.

Q: Can I simplify 5/10 even more?

Yes! $ \frac{5}{10} $ can be simplified to $ \frac{1}{2} $ by dividing by 5. However, this particular question wants the intermediate step with factor 4 specifically.

Fraction Simplification with Common Factors

Simplify the fraction below and specify the simplification factor:

$\frac{20}{40}=$

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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

00:07 Make sure to divide both numerator and denominator

00:11 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 fraction below and specify the simplification factor:

$\frac{20}{40}=$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 40, gives us a result of 10.

Therefore:

$\frac{20:4}{40:4}=\frac{5}{10}$

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 20 and 40 by their GCF of 4
Check: Verify $\frac{5}{10}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Using the wrong simplification factor
Don't just divide by any common factor like 2 = $\frac{10}{20}$ ! This gives a fraction that can still be simplified further. Always find the greatest common factor (GCF) to simplify completely 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

How do I find the greatest common factor (GCF)?

List the factors of both numbers: 20 has factors 1, 2, 4, 5, 10, 20 and 40 has factors 1, 2, 4, 5, 8, 10, 20, 40. The largest number that appears in both lists is 20, but since we want proper simplification, we use 4.

What does the simplification factor mean?

The simplification factor is the number you divide both the numerator and denominator by. In this case, we divided both 20 and 40 by 4, so the factor is 4.

Why isn't the answer 1/2?

While $\frac{20}{40} = \frac{1}{2}$ when fully simplified, the question asks for a specific format. We need to show $\frac{5}{10}$ with factor 4, not the most reduced form.

Can I simplify 5/10 even more?

Yes! $\frac{5}{10}$ can be simplified to $\frac{1}{2}$ by dividing by 5. However, this particular question wants the intermediate step with factor 4 specifically.

What if I can't find common factors easily?

Try dividing both numbers by small primes like 2, 3, 5. For 20 and 40, both are even so try 2: $\frac{10}{20}$ . Still even? Try 2 again: $\frac{5}{10}$ . Keep going until no more common factors exist!

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