Evaluate the Algebraic Fraction: (a-bc)/(b·-c) = 0

Q: When does a fraction equal zero?

A fraction equals zero only when the numerator is zero AND the denominator is nonzero. If both numerator and denominator are zero, the fraction is undefined, not zero!

Q: What happens if both parts become zero?

When both numerator and denominator equal zero, you get $ \frac{0}{0} $, which is undefined. This is different from zero - it means the expression has no meaningful value.

Q: How do I check if this fraction can be zero?

Set the numerator $ a - bc = 0 $, so $ a = bc $. Then check: does the denominator $ -(bc) $ become zero too? If yes, the fraction is undefined, not zero.

Q: Why does the negative sign matter in the denominator?

The denominator $ b \cdot (-c) = -(bc) $ is the negative of the product $ bc $. When $ a = bc $, the denominator becomes $ -a $, which is nonzero unless $ a = 0 $.

Q: Could this fraction ever equal zero?

Yes! The fraction equals zero when $ a = bc $ AND $ bc \neq 0 $. But the question asks if it's always zero, which is false since it depends on specific values of a, b, and c.

Algebraic Fractions with Zero Conditions

Indicate whether true or false

$\frac{a-b\operatorname{\cdot}c}{b\operatorname{\cdot}-c}=0$

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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

00:10 Let's use the commutative law and arrange the expression

00:14 Let's compare the expressions

00:19 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

$\frac{a-b\operatorname{\cdot}c}{b\operatorname{\cdot}-c}=0$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Analyze the numerator $a - b \cdot c$ .
Step 2: Analyze the denominator $b \cdot -c$ .
Step 3: Determine conditions for the fraction to be zero.

Now, let's work through each step:
Step 1: The numerator is $a - b \cdot c$ . This becomes zero if $a = b \cdot c$ .
Step 2: The denominator is $b \cdot -c = -(b \cdot c)$ . This simplifies to the negative of the product $b \cdot c$ .
Step 3: For the expression $\frac{a-b \cdot c}{b \cdot -c}$ to equal zero, the numerator must be zero, i.e., $a = b \cdot c$ , but the denominator must not be zero. However, if $a = b \cdot c$ , then the denominator becomes zero because it’s negative of the same product, $-(b \cdot c)$ , creating an undefined scenario rather than zero.

Since making the numerator zero results in the denominator being undefined, the expression cannot be zero. Therefore, the statement is Not true.

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Zero Fraction Rule: Numerator must be zero, denominator must be nonzero
Technique: If $a = bc$ , then numerator becomes zero
Check: Verify denominator doesn't become zero when numerator equals zero ✓

Common Mistakes

Avoid these frequent errors

Assuming fraction equals zero when numerator is zero
Don't just check if numerator equals zero without checking the denominator! When $a = bc$ , the denominator $-(bc)$ also becomes zero, making the fraction undefined, not zero. Always verify that making the numerator zero doesn't simultaneously make the denominator zero.

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

When does a fraction equal zero?

A fraction equals zero only when the numerator is zero AND the denominator is nonzero. If both numerator and denominator are zero, the fraction is undefined, not zero!

What happens if both parts become zero?

When both numerator and denominator equal zero, you get $\frac{0}{0}$ , which is undefined. This is different from zero - it means the expression has no meaningful value.

How do I check if this fraction can be zero?

Set the numerator $a - bc = 0$ , so $a = bc$ . Then check: does the denominator $-(bc)$ become zero too? If yes, the fraction is undefined, not zero.

Why does the negative sign matter in the denominator?

The denominator $b \cdot (-c) = -(bc)$ is the negative of the product $bc$ . When $a = bc$ , the denominator becomes $-a$ , which is nonzero unless $a = 0$ .

Could this fraction ever equal zero?

Yes! The fraction equals zero when $a = bc$ AND $bc \neq 0$ . But the question asks if it's always zero, which is false since it depends on specific values of a, b, and c.

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