Simplify the Expression: 34a/(8a·4b) Step-by-Step Solution

Fraction Simplification with Variable Cancellation

Simplify the following expression:

34a/(8a4b)=? 34a/(8a\cdot4b)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this problem together.
00:11 First, write division as a fraction. Ready?
00:17 Great! Now, reduce any parts that you can.
00:20 Break down thirty four into the factors seventeen and two.
00:29 Next, break down four into the factors two and two.
00:36 Let's reduce again. Can you see what simplifies?
00:45 And there you have it! That's 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 expression:

34a/(8a4b)=? 34a/(8a\cdot4b)=\text{?}

2

Step-by-step solution

Let's first write the exercise as a fraction:

34a8a×4b= \frac{34a}{8a\times4b}=

We'll reduce between the a in both the numerator and the denominator of the fraction:

348×4b= \frac{34}{8\times4b}=

Let's proceed to write the 34 in the numerator of the fraction as a smaller multiplication exercise:

17×28×4b= \frac{17\times2}{8\times4b}=

Let's write the 4 in the denominator of the fraction as a smaller multiplication exercise:

17×28×2×2b= \frac{17\times2}{8\times2\times2b}=

We'll reduce between the 2 in the numerator and denominator of the fraction:

178×2b=1716b \frac{17}{8\times2b}=\frac{17}{16b}

3

Final Answer

1716a \frac{17}{16}a

Key Points to Remember

Essential concepts to master this topic
  • Cancellation Rule: Cancel identical variables from numerator and denominator first
  • Technique: Factor numbers before reducing: 34 = 17 × 2
  • Check: Verify by multiplying result by denominator: 1716b×16b=17 \frac{17}{16b} \times 16b = 17

Common Mistakes

Avoid these frequent errors
  • Forgetting to cancel variables before simplifying numbers
    Don't leave the variable 'a' in both numerator and denominator = missed simplification! This makes the fraction look more complicated than it needs to be. Always cancel identical variables first, then work with the remaining numbers.

Practice Quiz

Test your knowledge with interactive questions

\( 60:(10\times2)= \)

FAQ

Everything you need to know about this question

Why did the 'a' disappear from my final answer?

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Great question! The variable 'a' was in both the numerator (34a) and denominator (8a). When the same variable appears in both places, they cancel out completely, just like 55=1 \frac{5}{5} = 1 .

How do I know which numbers to factor?

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Look for common factors between the numerator and denominator. Here, both 34 and the denominator had factors of 2, so factoring 34 = 17 × 2 helped us cancel the 2's.

What if there were different variables in numerator and denominator?

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If variables are different (like 'a' in numerator and 'b' in denominator), you cannot cancel them. They stay in your final answer as separate variables.

Can I cancel numbers the same way I cancel variables?

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Yes! Numbers follow the same rule. If the same number appears as a factor in both numerator and denominator, you can cancel them. That's why 28×2 \frac{2}{8 \times 2} becomes 18 \frac{1}{8} .

How do I check if my simplified fraction is correct?

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Multiply your answer by the original denominator. You should get the original numerator! Here: 1716b×(8a×4b)=1716b×32ab=17a \frac{17}{16b} \times (8a \times 4b) = \frac{17}{16b} \times 32ab = 17a

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