Simplify the Fraction 12/18 to an Equivalent Fraction with Denominator 9

Q: What if the target denominator doesn't divide evenly into the original?

The target denominator must be a factor of the original denominator for this to work. If 9 doesn't divide evenly into 18, then you cannot simplify $ \frac{12}{18} $ to have denominator 9.

Q: Is there another way to think about this problem?

Yes! You can think of it as scaling down. Since 18 is twice as big as 9, the whole fraction gets scaled down by half: both 12 and 18 become half their size.

Q: How can I check if my answer is equivalent to the original fraction?

Convert both fractions to lowest terms or use cross-multiplication. For $ \frac{12}{18} $ and $ \frac{6}{9} $: both simplify to $ \frac{2}{3} $, so they're equivalent!

Q: What if I accidentally use the wrong factor?

You'll get a fraction that's not equivalent to the original. Always double-check by seeing if your new denominator matches the target (9 in this case).

Fraction Simplification with Target Denominators

Simplify the fraction below to the denominator 9:

$\frac{12}{18}$

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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 9

00:03 We'll reduce the fraction with the appropriate divisor so the denominator equals 9

00:07 Make sure to divide both numerator and denominator

00:10 Let's calculate the quotients

00:15 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 to the denominator 9:

$\frac{12}{18}$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 18, gives us a result of 9:

$\frac{12:2}{18:2}=\frac{6}{9}$

Final Answer

$\frac{6}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both numerator and denominator by the same factor
Technique: Find the common factor: 18 ÷ 2 = 9, so divide by 2
Check: Verify equivalent fractions: $\frac{12}{18} = \frac{6}{9}$ both equal $\frac{2}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing only the denominator to reach target
Don't just divide 18 by 2 to get 9 and keep 12 unchanged = $\frac{12}{9}$ ! This creates a different fraction with a different value. Always divide both the numerator and denominator by the same number.

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

How do I know what number to divide by?

Look at what changes the original denominator to your target denominator. Since 18 ÷ 2 = 9, you need to divide by 2. Then divide the numerator by the same number!

What if the target denominator doesn't divide evenly into the original?

The target denominator must be a factor of the original denominator for this to work. If 9 doesn't divide evenly into 18, then you cannot simplify $\frac{12}{18}$ to have denominator 9.

Is there another way to think about this problem?

Yes! You can think of it as scaling down. Since 18 is twice as big as 9, the whole fraction gets scaled down by half: both 12 and 18 become half their size.

How can I check if my answer is equivalent to the original fraction?

Convert both fractions to lowest terms or use cross-multiplication. For $\frac{12}{18}$ and $\frac{6}{9}$ : both simplify to $\frac{2}{3}$ , so they're equivalent!

What if I accidentally use the wrong factor?

You'll get a fraction that's not equivalent to the original. Always double-check by seeing if your new denominator matches the target (9 in this case).

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