Simplify the Fraction: Reducing 81/18 by a Factor of 9

Fraction Simplification with Greatest Common Factor

Simplify the following fraction by a factor of 9:

8118= \frac{81}{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 9
00:04 Divide the fraction by the given 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
1

Understand the problem

Simplify the following fraction by a factor of 9:

8118= \frac{81}{18}=

2

Step-by-step solution

Let's simplify as follows, divide both the numerator and denominator by 9:

81:918:9=92 \frac{81:9}{18:9}=\frac{9}{2}

3

Final Answer

92 \frac{9}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Divide both numerator and denominator by the same factor
  • Technique: Find common factor first: 81 ÷ 9 = 9, 18 ÷ 9 = 2
  • Check: Verify by multiplication: 9 × 9 = 81, 2 × 9 = 18 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing only the numerator or denominator by the factor
    Don't divide just 81 by 9 to get 9/18 or just 18 by 9 to get 81/2! This changes the value of the fraction completely. Always divide both the top and bottom numbers by the same factor to keep the fraction equivalent.

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 we divide by 9 specifically?

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The problem asks us to simplify by a factor of 9. This means we must use 9 as our common factor. Since both 81 and 18 are divisible by 9, we can divide both by 9 to simplify.

How do I know if 9 divides evenly into both numbers?

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Check the division: 81÷9=9 81 ÷ 9 = 9 (no remainder) and 18÷9=2 18 ÷ 9 = 2 (no remainder). If both divisions give whole numbers, then 9 is a valid common factor!

What if the problem didn't specify dividing by 9?

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You would find the Greatest Common Factor (GCF) of 81 and 18. The GCF is actually 9, so you'd get the same answer! Always look for the largest number that divides both parts.

Can I simplify this fraction further?

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Let's check: 92 \frac{9}{2} cannot be simplified further because 9 and 2 share no common factors other than 1. This fraction is in its simplest form!

Why is my answer different from the other choices?

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Common wrong answers happen when you don't divide both parts: dividing only 81 by 9 gives 9, or dividing 81 by 18 gives 13 \frac{1}{3} . Remember: both numerator and denominator must be divided by the same factor.

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