Solve the Expression: 0:-m/b+c with Given Variable Values

Q: What's the difference between 0÷a and a÷0?

0÷a = 0 (zero divided by any non-zero number is zero), but a÷0 is undefined (division by zero is impossible). In our problem, we have $ \frac{0}{-\frac{3}{409}} $, which equals 0.

Q: Why does the order of operations matter here?

We must follow PEMDAS/BODMAS! First handle the division $ 0 ÷ (-\frac{m}{b}) $, which gives us 0, then add c. If we added c first, we'd get the wrong answer.

Q: How do I substitute negative fractions correctly?

When substituting $ m = -\frac{1}{205} $, be careful with signs! The expression becomes $ -\frac{-\frac{1}{205}}{-7} $. Remember: negative divided by negative equals positive.

Q: Do I need to simplify the fraction before dividing?

No! Since we're dividing zero by any non-zero number, the result is always 0. Whether the denominator is $ -\frac{3}{409} $ or simplified doesn't matter - zero divided by anything (except zero) equals zero.

Q: How can I check my final answers?

For case 1: $ 0 ÷ (-\frac{3}{409}) + 8 = 0 + 8 = 8 ✓ $For case 2: $ 0 ÷ (\frac{1}{1435}) + 3004 = 0 + 3004 = 3004 ✓ $

Zero Division Properties with Variable Substitution

In front of you an algebraic expression:

$0:-\frac{m}{b}+c$

Replace and calculate

$m=3,b=409,c=8$
$m=-\frac{1}{205},b=-7,c=3004$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Place and calculate

00:03 Let's write division as a fraction

00:10 0 divided by any number is always equal to 0

00:19 Let's substitute in our exercise and continue solving

00:26 This is the simplified expression

00:31 Let's start by substituting the first option

00:38 Now let's substitute the second option

00:42 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

In front of you an algebraic expression:

$0:-\frac{m}{b}+c$

Replace and calculate

$m=3,b=409,c=8$
$m=-\frac{1}{205},b=-7,c=3004$

Step-by-step solution

Let's start with the first option.

Let's substitute the given data into the expression:

$0:-\frac{3}{409}+8=$

We'll solve the exercise from left to right, noting that we are first dividing by zero.

Let's remember the rule:

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

In other words, any number divided by zero will equal zero, therefore:

$\frac{0}{-\frac{3}{409}}=0$

Now we got the exercise:

$0+8=8$

Let's continue with the second option.

Let's substitute the given data into the expression:

$0:-\frac{-\frac{1}{205}}{-7}+3004=$

As we can see, just like in the first option, we are first dividing by zero.

Any number divided by zero will equal zero, therefore we got the exercise:

$0+3004=3004$

Therefore the final answer is:

$1=8,2=3004$

Final Answer

$1=8,2=3004$

Key Points to Remember

Essential concepts to master this topic

Zero Division Rule: Any number divided by zero equals zero
Technique: Substitute values first, then apply $\frac{0}{-\frac{3}{409}} = 0$
Check: Verify final result: $0 + 8 = 8$ and $0 + 3004 = 3004$ ✓

Common Mistakes

Avoid these frequent errors

Confusing zero division with division by zero
Don't think that dividing zero by a number is undefined = wrong answer! Division BY zero is undefined, but zero divided by any non-zero number always equals zero. Always remember: $\frac{0}{a} = 0$ when a ≠ 0.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

What's the difference between 0÷a and a÷0?

0÷a = 0 (zero divided by any non-zero number is zero), but a÷0 is undefined (division by zero is impossible). In our problem, we have $\frac{0}{-\frac{3}{409}}$ , which equals 0.

Why does the order of operations matter here?

We must follow PEMDAS/BODMAS! First handle the division $0 ÷ (-\frac{m}{b})$ , which gives us 0, then add c. If we added c first, we'd get the wrong answer.

How do I substitute negative fractions correctly?

When substituting $m = -\frac{1}{205}$ , be careful with signs! The expression becomes $-\frac{-\frac{1}{205}}{-7}$ . Remember: negative divided by negative equals positive.

Do I need to simplify the fraction before dividing?

No! Since we're dividing zero by any non-zero number, the result is always 0. Whether the denominator is $-\frac{3}{409}$ or simplified doesn't matter - zero divided by anything (except zero) equals zero.

How can I check my final answers?

For case 1: $0 ÷ (-\frac{3}{409}) + 8 = 0 + 8 = 8 ✓$
For case 2: $0 ÷ (\frac{1}{1435}) + 3004 = 0 + 3004 = 3004 ✓$

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