Simplify 18/36: Finding the Reduction Factor to Denominator 18

Q: How do I know what factor to use when simplifying?

Look at what you need to divide the denominator by to get your target. Here, 36÷2 = 18, so the factor is 2. Then divide the numerator by the same factor: 18÷2 = 9.

Q: What if the target denominator doesn't work out evenly?

The target denominator must be a factor of the original denominator. Since 18 divides evenly into 36, it works. If it didn't divide evenly, the problem would be impossible.

Q: Why can't I just change the denominator to 18 directly?

Changing only the denominator would create a completely different fraction! You must maintain the same ratio by dividing both parts by the same number.

Q: How can I check if my simplified fraction is correct?

Use cross-multiplication: $ \frac{9}{18} $ should equal $ \frac{18}{36} $, so 9×36 should equal 18×18. Both equal 324, so it's correct!

Q: What does 'factor of 2' mean in this problem?

The simplification factor is the number you divide both numerator and denominator by. Here, we divided both 18 and 36 by 2, so the factor is 2.

Fraction Simplification with Target Denominators

Simplify the following fraction to the denominator 18 and specify the simplification factor:

$\frac{18}{36}$

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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 - 18

00:03 Divide the fraction by the appropriate factor

00:07 Make sure to divide both numerator and denominator

00:10 Calculate the quotients

00:14 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 to the denominator 18 and specify the simplification factor:

$\frac{18}{36}$

Step-by-step solution

Look at the denominator of the fraction. Try to find a number that, when divided by 36, gives you a result of 18:

$\frac{18:2}{36:2}=\frac{9}{18}$

Final Answer

$\frac{9}{18}$ , factor of 3

Key Points to Remember

Essential concepts to master this topic

Division Rule: Find common factor to divide both numerator and denominator
Technique: Divide 18÷2 = 9 and 36÷2 = 18 using factor 2
Check: Verify 9/18 equals original 18/36 by cross-multiplying: 9×36 = 18×18 ✓

Common Mistakes

Avoid these frequent errors

Dividing only the denominator to reach target
Don't divide just 36÷2 = 18 while keeping numerator as 18 = wrong fraction 18/18! This changes the fraction's value completely. Always divide both numerator and denominator by the same factor to maintain equivalence.

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 know what factor to use when simplifying?

Look at what you need to divide the denominator by to get your target. Here, 36÷2 = 18, so the factor is 2. Then divide the numerator by the same factor: 18÷2 = 9.

What if the target denominator doesn't work out evenly?

The target denominator must be a factor of the original denominator. Since 18 divides evenly into 36, it works. If it didn't divide evenly, the problem would be impossible.

Why can't I just change the denominator to 18 directly?

Changing only the denominator would create a completely different fraction! You must maintain the same ratio by dividing both parts by the same number.

How can I check if my simplified fraction is correct?

Use cross-multiplication: $\frac{9}{18}$ should equal $\frac{18}{36}$ , so 9×36 should equal 18×18. Both equal 324, so it's correct!

What does 'factor of 2' mean in this problem?

The simplification factor is the number you divide both numerator and denominator by. Here, we divided both 18 and 36 by 2, so the factor is 2.

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