Evaluate the Expression (c·a)/(a·c) = 0: True or False?

Q: Why doesn't the fraction equal zero after canceling?

When you cancel variables, you're dividing them out, not making them disappear! $ \frac{c \cdot a}{a \cdot c} $ becomes $ \frac{1}{1} = 1 $, just like $ \frac{5}{5} = 1 $.

Q: Can I cancel variables that aren't exactly the same?

No! You can only cancel identical factors. For example, you can cancel $ \frac{x}{x} $ but not $ \frac{x}{x^2} $ or $ \frac{a}{b} $.

Q: How do I know when a fraction simplifies to 1?

Any fraction where the numerator and denominator are identical (and non-zero) equals 1. Examples: $ \frac{7}{7} = 1 $, $ \frac{xy}{xy} = 1 $, $ \frac{abc}{abc} = 1 $.

Fraction Simplification with Variable Cancellation

Indicate whether true or false

$\frac{c\cdot a}{a\cdot c}=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine if the equation is correct

00:05 Let's reduce what we can

00:10 When we can reduce the entire fraction, we are left with 1

00:13 Therefore the equation is not correct

00:16 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

Indicate whether true or false

$\frac{c\cdot a}{a\cdot c}=0$

Step-by-step solution

Let's simplify the expression on the left side of the proposed equation:

$\frac{\not{c}\cdot \not{a}}{\not{a}\cdot \not{c}}\stackrel{?}{= }0 \\ 1 \stackrel{?}{= }0$ Clearly, we get a false statement because: 1 is different from: 0

$\boxed{ 1 \stackrel{!}{\neq }0}$ Therefore, the proposed equation is not correct,

Which means the correct answer is answer B.

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Rule: Cancel identical factors in numerator and denominator completely
Technique: $\frac{c \cdot a}{a \cdot c} = \frac{1 \cdot 1}{1 \cdot 1} = 1$ after cancellation
Check: Any fraction with same numerator and denominator equals 1 ✓

Common Mistakes

Avoid these frequent errors

Thinking cancellation makes the entire fraction equal zero
Don't assume that crossing out variables means the fraction becomes 0! When you cancel identical factors, you're left with 1, not 0. Always remember that any non-zero number divided by itself equals 1.

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 doesn't the fraction equal zero after canceling?

When you cancel variables, you're dividing them out, not making them disappear! $\frac{c \cdot a}{a \cdot c}$ becomes $\frac{1}{1} = 1$ , just like $\frac{5}{5} = 1$ .

What if one of the variables is zero?

Great question! If either a or c equals zero, then the fraction would be $\frac{0}{0}$ , which is undefined, not zero. We assume variables are non-zero unless stated otherwise.

Can I cancel variables that aren't exactly the same?

No! You can only cancel identical factors. For example, you can cancel $\frac{x}{x}$ but not $\frac{x}{x^2}$ or $\frac{a}{b}$ .

How do I know when a fraction simplifies to 1?

Any fraction where the numerator and denominator are identical (and non-zero) equals 1. Examples: $\frac{7}{7} = 1$ , $\frac{xy}{xy} = 1$ , $\frac{abc}{abc} = 1$ .

Is there a quick way to spot these problems?

Yes! Look for fractions where the numerator and denominator have the same factors, just possibly in different order. Multiplication is commutative, so $c \cdot a = a \cdot c$ .

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