Simplify the Expression: xyz/(3x·4y·5z) Step-by-Step Solution

Q: Why can I cancel the x, y, and z variables?

You can cancel variables because any non-zero number divided by itself equals 1. Since $ \frac{x}{x} = 1 $, $ \frac{y}{y} = 1 $, and $ \frac{z}{z} = 1 $, they all disappear from the fraction!

Q: What if one of the variables was zero?

If any variable (x, y, or z) equals zero, then the entire numerator becomes zero, making the whole fraction equal to 0. The denominator would be non-zero, so the answer would be 0, not $ \frac{1}{60} $.

Q: Do I multiply 3×4×5 all at once or step by step?

Either way works! You can calculate step by step: 3×4 = 12, then 12×5 = 60. Or all at once if you're comfortable with it. The important thing is getting the correct product: 60.

Q: How do I know I simplified completely?

Your expression is fully simplified when you have no common factors left to cancel. Here, after canceling xyz, you're left with $ \frac{1}{60} $ - a simple fraction with no variables!

Q: Can this method work with more complex expressions?

Absolutely! The same cancellation principle applies to any algebraic fraction. Just identify matching factors in the numerator and denominator, cancel them out, then simplify what remains.

Algebraic Simplification with Variable Cancellation

Simplify the following expression:

$x\cdot y\cdot z/(3x\cdot4y\cdot5z)=\text{?}$

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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

00:09 Let's reduce what we can

00:20 Let's calculate 4 times 5

00:23 Let's calculate 3 times 20

00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following expression:

$x\cdot y\cdot z/(3x\cdot4y\cdot5z)=\text{?}$

Step-by-step solution

First let's write the exercise as a fraction:

$\frac{x\times y\times z}{3x\times4y\times5z}=$

Then we'll cancel out the x, the Y, and the z from both the numerator and denominator of the fraction:

$\frac{1}{3\times4\times5}=$

Then, we'll multiply the expression in the denominator from left to right:

$\frac{1}{3\times4\times5}=\frac{1}{12\times5}=\frac{1}{60}$

Final Answer

$\frac{1}{60}$

Key Points to Remember

Essential concepts to master this topic

Cancellation Rule: Variables in numerator and denominator cancel completely
Technique: Cancel xyz/xyz leaves 1/(3×4×5) = 1/60
Check: Substitute any values: x=2, y=3, z=4 gives 24/360 = 1/15... wait, that's wrong! Let me recalculate: 1/60 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply all coefficients in denominator
Don't calculate 3×4×5 as just 12 or 15 = wrong answer 1/12 or 1/15! This happens when you multiply only some numbers, not all three. Always multiply ALL coefficients: 3×4×5 = 60.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can I cancel the x, y, and z variables?

You can cancel variables because any non-zero number divided by itself equals 1. Since $\frac{x}{x} = 1$ , $\frac{y}{y} = 1$ , and $\frac{z}{z} = 1$ , they all disappear from the fraction!

What if one of the variables was zero?

If any variable (x, y, or z) equals zero, then the entire numerator becomes zero, making the whole fraction equal to 0. The denominator would be non-zero, so the answer would be 0, not $\frac{1}{60}$ .

Do I multiply 3×4×5 all at once or step by step?

Either way works! You can calculate step by step: 3×4 = 12, then 12×5 = 60. Or all at once if you're comfortable with it. The important thing is getting the correct product: 60.

How do I know I simplified completely?

Your expression is fully simplified when you have no common factors left to cancel. Here, after canceling xyz, you're left with $\frac{1}{60}$ - a simple fraction with no variables!

Can this method work with more complex expressions?

Absolutely! The same cancellation principle applies to any algebraic fraction. Just identify matching factors in the numerator and denominator, cancel them out, then simplify what remains.

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Simplify the Expression: xyz/(3x·4y·5z) Step-by-Step Solution

Algebraic Simplification with Variable Cancellation

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can I cancel the x, y, and z variables?

What if one of the variables was zero?

Do I multiply 3×4×5 all at once or step by step?

How do I know I simplified completely?

Can this method work with more complex expressions?

🌟 Unlock Your Math Potential

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