Verify if (c²ba)/(bac) = 1/c: Fraction Simplification Challenge

Q: Why can't I cancel c² with c completely?

Because $ c^2 = c \cdot c $! When you have $ \frac{c^2}{c} $, you can only cancel one factor of c, leaving you with $ c $, not 1.

Q: What's the difference between c and 1/c?

These are completely different! If c = 2, then c = 2 but $ \frac{1}{c} = \frac{1}{2} $. They're reciprocals of each other, not equal values.

Q: How do I know which factors to cancel first?

Look for identical factors in both numerator and denominator. In this problem: b appears once in each, a appears once in each, and c appears once in the denominator but twice in the numerator.

Q: Can I multiply instead of canceling?

Canceling is a form of division! When you cancel $ \frac{b}{b} $, you're dividing both by b. Don't multiply - that would make the fraction more complex, not simpler.

Q: What if all the variables have different values?

The simplification works the same way regardless of what values a, b, and c represent (as long as they're not zero). The algebra stays consistent!

Fraction Simplification with Variable Cancellation

Indicate whether true or false

$\frac{c^2\cdot b\cdot a}{b\cdot a\cdot c}=\frac{1}{c}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's see if this equation is correct.

00:17 First, break down the exponent into smaller multiplications.

00:26 Now, simplify everything that we can.

00:38 Compare the expressions. Notice they are opposites, so they are not the same.

00:47 And that's how we find the solution to this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Indicate whether true or false

$\frac{c^2\cdot b\cdot a}{b\cdot a\cdot c}=\frac{1}{c}$

Step-by-step solution

To solve this problem, we'll focus on simplifying the fraction:

Given: $\frac{c^2 \cdot b \cdot a}{b \cdot a \cdot c}$ .

Step 1: Identify and cancel common factors from the numerator and the denominator. Note that both the numerator and the denominator have $b$ , $a$ , and $c$ as common factors.

Step 2: Cancel $b$ and $a$ from both the numerator and the denominator to simplify:

\frac{c^2 \cdot b \cdot a}{b \cdot a \cdot c} = \frac{c^2}{c}

Step 3: Simplify the remaining expression by canceling $c$ from the numerator and denominator:

\frac{c^2}{c} = c

The simplified expression is $c$ , not $\frac{1}{c}$ .

Therefore, the given statement that $\frac{c^2 \cdot b \cdot a}{b \cdot a \cdot c} = \frac{1}{c}$ is Not true.

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Cancellation Rule: Cancel identical factors from numerator and denominator
Technique: Remove common factors systematically: $\frac{c^2 \cdot b \cdot a}{b \cdot a \cdot c} = \frac{c^2}{c} = c$
Check: Verify final result doesn't equal the given comparison value ✓

Common Mistakes

Avoid these frequent errors

Canceling factors that don't match exactly
Don't cancel $c^2$ with just $c$ completely = wrong simplification! This ignores that $c^2 = c \cdot c$ , so only one $c$ cancels. Always identify matching factors precisely before canceling.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification shown below is correct:

$\frac{7}{7\cdot8}=8$

FAQ

Everything you need to know about this question

Why can't I cancel c² with c completely?

Because $c^2 = c \cdot c$ ! When you have $\frac{c^2}{c}$ , you can only cancel one factor of c, leaving you with $c$ , not 1.

What's the difference between c and 1/c?

These are completely different! If c = 2, then c = 2 but $\frac{1}{c} = \frac{1}{2}$ . They're reciprocals of each other, not equal values.

How do I know which factors to cancel first?

Look for identical factors in both numerator and denominator. In this problem: b appears once in each, a appears once in each, and c appears once in the denominator but twice in the numerator.

Can I multiply instead of canceling?

Canceling is a form of division! When you cancel $\frac{b}{b}$ , you're dividing both by b. Don't multiply - that would make the fraction more complex, not simpler.

What if all the variables have different values?

The simplification works the same way regardless of what values a, b, and c represent (as long as they're not zero). The algebra stays consistent!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Factorization questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime