Simplify the Fraction 16/32 Using Factor 8: Step-by-Step

Fraction Simplification with Common Factors

Simplify the following fraction by the factor 8:

1632= \frac{16}{32}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's reduce the fraction by dividing it by 8.
00:09 We need to divide both the top number and the bottom number by the same factor.
00:15 Make sure you divide both the numerator and the denominator.
00:19 Now, calculate the results for each division.
00:23 And that gives us the answer to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Simplify the following fraction by the factor 8:

1632= \frac{16}{32}=

2

Step-by-step solution

Let's reduce in the following way, divide the numerator by 8 and the denominator by 8:

16:832:8=24 \frac{16:8}{32:8}=\frac{2}{4}

3

Final Answer

24 \frac{2}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Divide both numerator and denominator by the same factor
  • Technique: Find 16÷8=2 and 32÷8=4 to get 24 \frac{2}{4}
  • Check: Verify 2×8=16 and 4×8=32, so 24 \frac{2}{4} equals original ✓

Common Mistakes

Avoid these frequent errors
  • Dividing numerator and denominator by different factors
    Don't divide 16 by 8 but 32 by 4 = 28 \frac{2}{8} which isn't equivalent to the original! This changes the fraction's value completely. Always divide both parts by the exact 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 can't I simplify 1632 \frac{16}{32} to 12 \frac{1}{2} directly?

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You could simplify to 12 \frac{1}{2} by dividing by 16, but the problem specifically asks you to use factor 8. Following directions shows you understand the step-by-step process!

What if I get 24 \frac{2}{4} but the answer choices show simplified fractions?

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24 \frac{2}{4} is correct when using factor 8! Some problems want you to stop at this step, while others ask you to simplify further to 12 \frac{1}{2} . Always read what the question asks for.

How do I know factor 8 will work for both 16 and 32?

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Check if 8 divides evenly into both numbers: 16÷8=2 (no remainder) and 32÷8=4 (no remainder). If either division has a remainder, that factor won't work!

Is 24 \frac{2}{4} in simplest form?

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No, 24 \frac{2}{4} can be simplified further to 12 \frac{1}{2} by dividing both parts by 2. But since this problem only asked to use factor 8, 24 \frac{2}{4} is the correct answer!

What happens if I use the wrong factor?

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  • Using factor 4: 16÷432÷4=48 \frac{16÷4}{32÷4} = \frac{4}{8}
  • Using factor 16: 16÷1632÷16=12 \frac{16÷16}{32÷16} = \frac{1}{2}
  • Only factor 8 gives the expected answer for this specific problem!

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