Simplify the Fraction 36/18 Using a Factor of 6

Fraction Simplification with Common Factors

Simplify the following fraction by a factor of 6.

3618= \frac{36}{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 6
00:03 Divide the fraction by the given factor
00:06 Make sure to divide both numerator and denominator
00:09 Calculate the quotients
00:13 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 following fraction by a factor of 6.

3618= \frac{36}{18}=

2

Step-by-step solution

We will reduce in the following way, divide the numerator by 6 and the denominator by 6:

36:618:6=63 \frac{36:6}{18:6}=\frac{6}{3}

3

Final Answer

63 \frac{6}{3}

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Divide both numerator and denominator by same factor
  • Technique: 36÷6 = 6 and 18÷6 = 3 gives 63 \frac{6}{3}
  • Check: Verify 6 and 3 have no common factors besides 1 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing only the numerator or denominator by the factor
    Don't divide just 36÷6 = 6 and leave 18 unchanged = 618 \frac{6}{18} ! This creates an incorrect fraction that's not equivalent to the original. Always divide both the numerator AND denominator by the same factor.

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

Why do I divide by 6 specifically?

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The problem asks you to simplify by a factor of 6. This means 6 must divide evenly into both 36 and 18. Since 36÷6 = 6 and 18÷6 = 3, we get 63 \frac{6}{3} .

Can I simplify 63 \frac{6}{3} further?

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Yes! 63=2 \frac{6}{3} = 2 , but the question specifically asks to simplify by a factor of 6, so 63 \frac{6}{3} is the correct answer for this problem.

What if the factor doesn't divide evenly?

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The factor must divide evenly into both the numerator and denominator. If 6 didn't divide evenly into both 36 and 18, you couldn't use it as a common factor for simplification.

How do I know 63 \frac{6}{3} is equivalent to 3618 \frac{36}{18} ?

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Both fractions equal 2 when you divide: 3618=2 \frac{36}{18} = 2 and 63=2 \frac{6}{3} = 2 . Equivalent fractions always have the same decimal value!

Why isn't 12 \frac{1}{2} the right answer?

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While 3618 \frac{36}{18} does equal 12 \frac{1}{2} when fully simplified, the question asks you to simplify by a factor of 6 specifically, not to the lowest terms.

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