Simplify 6/24: Converting to an Equivalent Fraction with Denominator 12

Q: How do I know what number to divide by?

Look at your target denominator! Ask yourself: "What do I divide 24 by to get 12?" Since 24 ÷ 2 = 12, you divide both parts by 2.

Q: Why can't I just change the bottom number to 12?

Changing only the denominator creates a completely different fraction! $ \frac{6}{12} $ is not equal to $ \frac{6}{24} $. You must change both parts proportionally.

Q: How can I check if my answer is right?

Use cross-multiplication! For $ \frac{3}{12} = \frac{6}{24} $, multiply diagonally: 3 × 24 = 72 and 6 × 12 = 72. If both products are equal, you're correct!

Q: Is there a faster way to do this?

Yes! Find the greatest common factor (GCF) of the numerator and denominator first. For $ \frac{6}{24} $, the GCF is 6, so divide both by 6 to get $ \frac{1}{4} $, then convert to twelfths.

Fraction Simplification with Specific Denominators

Simplify the fraction below to the denominator 12:

$\frac{6}{24}$

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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 12

00:03 Let's reduce the fraction with the appropriate divisor so the denominator equals 12

00:06 Make sure to divide both numerator and denominator

00:09 Let's calculate the quotients

00:12 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 12:

$\frac{6}{24}$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 24, gives us a result of 12:

$\frac{6:2}{24:2}=\frac{3}{12}$

Final Answer

$\frac{3}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both numerator and denominator by same number
Technique: Find what divides 24 to get 12: $24 ÷ 2 = 12$
Check: Verify $\frac{3}{12} = \frac{6}{24}$ by cross-multiplying: 3×24 = 6×12 ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting to change denominators
Don't try to change 24 to 12 by subtracting 12 from both parts = wrong fraction! This doesn't maintain the value of the original fraction. Always divide both numerator and denominator by the same number to keep fractions equivalent.

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 your target denominator! Ask yourself: "What do I divide 24 by to get 12?" Since 24 ÷ 2 = 12, you divide both parts by 2.

What if I can't get exactly the denominator I want?

This happens when the original fraction can't be converted to that specific denominator. For example, $\frac{1}{3}$ cannot become a fraction with denominator 4 because 3 doesn't divide evenly into 4.

Why can't I just change the bottom number to 12?

Changing only the denominator creates a completely different fraction! $\frac{6}{12}$ is not equal to $\frac{6}{24}$ . You must change both parts proportionally.

How can I check if my answer is right?

Use cross-multiplication! For $\frac{3}{12} = \frac{6}{24}$ , multiply diagonally: 3 × 24 = 72 and 6 × 12 = 72. If both products are equal, you're correct!

Is there a faster way to do this?

Yes! Find the greatest common factor (GCF) of the numerator and denominator first. For $\frac{6}{24}$ , the GCF is 6, so divide both by 6 to get $\frac{1}{4}$ , then convert to twelfths.

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