Solve the Algebraic Fraction: 12a/(7x·4b) Simplification

Fraction Simplification with Common Factor Cancellation

12a/(7x4b)=? 12a/(7x\cdot4b)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's write division as a fraction
00:07 Let's break down 12 into factors 4 and 3
00:17 Let's reduce what we can
00:23 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

12a/(7x4b)=? 12a/(7x\cdot4b)=\text{?}

2

Step-by-step solution

Let's begin by writing the exercise as a fraction:

12a7x×4b= \frac{12a}{7x\times4b}=

Next we'll factor the numerator of the fraction into a smaller multiplication exercise:

4×3a7x×4b= \frac{4\times3a}{7x\times4b}=

Let's now reduce the 4 in both the numerator and denominator of the fraction:

3a7xb \frac{3a}{7xb}

3

Final Answer

3a7xb \frac{3a}{7xb}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Factor numerator and denominator to identify common factors
  • Technique: Cancel 4 from both 4×3a4×7xb \frac{4 \times 3a}{4 \times 7xb}
  • Check: Verify no more common factors exist in 3a7xb \frac{3a}{7xb}

Common Mistakes

Avoid these frequent errors
  • Canceling terms that aren't factors
    Don't cancel 12 and 7 directly = ax×4b \frac{a}{x \times 4b} which is wrong! You can only cancel common factors that multiply the entire numerator and denominator. Always factor first, then cancel identical factors.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why do I need to factor 12 before simplifying?

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Factoring reveals hidden common factors between numerator and denominator! Writing 12 as 4 × 3 shows the 4 that cancels with 4 in the denominator.

Can I cancel the 'a' with 'b' or the '3' with '7'?

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No! You can only cancel identical factors. Different variables like a and b are completely separate, and different numbers like 3 and 7 don't cancel.

How do I know when I'm done simplifying?

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You're done when no common factors remain between numerator and denominator. Check each number and variable - if nothing appears in both top and bottom, you're finished!

What if the denominator has multiple terms being multiplied?

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Treat the entire multiplication as one denominator: 7x×4b=28xb 7x \times 4b = 28xb . Then factor and cancel as usual. The key is identifying what multiplies together.

Should I multiply out 7×4 in the denominator?

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It's often better to keep factors separate like 7x⋅4b so you can easily spot common factors with the numerator. Only multiply out after canceling.

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