Simplify 12/18 to a Fraction with Denominator 3: Step-by-Step Reduction

Fraction Reduction with Target Denominators

Simplify the fraction below to the denominator 3:

1218= \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 by dividing the denominator by 3
00:03 Divide the fraction by the appropriate factor
00:06 Make sure to divide both numerator and denominator
00:09 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
1

Understand the problem

Simplify the fraction below to the denominator 3:

1218= \frac{12}{18}=

2

Step-by-step solution

Let's look at the numerator of the fraction. We'll try to find a number that, when divided by 18, gives us a result of 3.

Therefore:

12:618:6=23 \frac{12:6}{18:6}=\frac{2}{3}

3

Final Answer

23 \frac{2}{3}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the greatest common factor to reduce fractions properly
  • Technique: Divide both parts by GCF: 12÷6 = 2, 18÷6 = 3
  • Check: Verify 23 \frac{2}{3} has denominator 3 and equals original 1218 \frac{12}{18} ✓

Common Mistakes

Avoid these frequent errors
  • Dividing numerator and denominator by different numbers
    Don't divide 12 by 2 and 18 by 9 = 62 \frac{6}{2} which is wrong! This breaks the fraction's value completely. Always divide both the numerator and denominator by the same number (the GCF).

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 number to divide by?

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Find the Greatest Common Factor (GCF) of both numbers! For 12 and 18, list factors: 12 has 1,2,3,4,6,12 and 18 has 1,2,3,6,9,18. The largest common factor is 6.

What if the target denominator isn't possible?

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The target denominator must be a factor of the simplified denominator. Since 1218 \frac{12}{18} simplifies to 23 \frac{2}{3} , only denominators 1 and 3 are possible targets.

Can I just guess and check the answers?

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Not recommended! Understanding the reduction process helps you solve any fraction problem. Plus, you'll need this skill for more complex math later.

Why can't the answer be 63 \frac{6}{3} ?

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While 63=2 \frac{6}{3} = 2 , this doesn't equal our original fraction 1218=23 \frac{12}{18} = \frac{2}{3} . Always check that your simplified fraction equals the original value!

Is there a faster way to find the GCF?

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Yes! Use the Euclidean algorithm: divide the larger by smaller, then repeat with remainder. For 18÷12=1 remainder 6, then 12÷6=2 remainder 0, so GCF is 6.

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