Solve Complex Fraction Division: (12m/3n)÷(36n/5m)

Complex Fraction Division with Variable Terms

Solve the following problem:

12m3n:36n5m=? \frac{12m}{3n}:\frac{36n}{5m}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Division is also multiplication by the reciprocal
00:14 Make sure to multiply numerator by numerator and denominator by denominator
00:26 Let's factor 36 into 12 and 3
00:35 Let's reduce what we can
00:41 Let's calculate 3 times 3
00:47 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

Solve the following problem:

12m3n:36n5m=? \frac{12m}{3n}:\frac{36n}{5m}=\text{?}

2

Step-by-step solution

Let's flip the second fraction to get a multiplication exercise:

12m3n×5m36n= \frac{12m}{3n}\times\frac{5m}{36n}=

We'll combine the fractions into one exercise:

12m×5m3n×36n= \frac{12m\times5m}{3n\times36n}=

Let's factor 36 into a smaller multiplication exercise:

12m×5m3n×12×3n= \frac{12m\times5m}{3n\times12\times3n}=

We'll reduce the 12 in both the numerator and denominator of the fraction:

m×5m3n×3n=5m29n2 \frac{m\times5m}{3n\times3n}=\frac{5m^2}{9n^2}

3

Final Answer

5m29n2 \frac{5m^2}{9n^2}

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Flip the second fraction and multiply instead
  • Technique: Cancel common factors like 12 from numerator and denominator
  • Check: Final answer should have variables in proper form like 5m29n2 \frac{5m^2}{9n^2}

Common Mistakes

Avoid these frequent errors
  • Adding fractions instead of dividing
    Don't try to find common denominators when dividing fractions = wrong operation entirely! Division means multiply by the reciprocal. Always flip the second fraction first, then multiply straight across.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I flip the second fraction when dividing?

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Dividing by a fraction is the same as multiplying by its reciprocal. When you see ab÷cd \frac{a}{b} ÷ \frac{c}{d} , it becomes ab×dc \frac{a}{b} \times \frac{d}{c} !

How do I handle the variables m and n?

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Treat variables just like numbers! When multiplying, add the exponents: m × m = m2 m^2 . When canceling, variables in numerator and denominator can cancel out.

Can I simplify before multiplying?

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Yes, absolutely! Look for common factors you can cancel first. In this problem, the 12 in the numerator cancels with part of 36 in the denominator, making the math easier.

What if my variables end up in the denominator?

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That's perfectly normal! Many fraction problems result in variables in the denominator. Just make sure your final answer is fully simplified and matches the form given in the answer choices.

How do I know if I factored 36 correctly?

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Check your factoring: 36 = 12 × 3. You can verify by multiplying back: 12 × 3 = 36 ✓. This helps you see which factors can cancel with other parts of the fraction.

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