The given expression is:
[tex]$ \frac{-85}{0} $[/tex]
In mathematics, division by zero is undefined. This is because there is no real number that you can multiply by 0 to get -85. Let's break this down step-by-step:
1. Understanding Division by Zero: Division by zero is a concept that creates an undefined situation in arithmetic and algebra. Essentially, any number divided by zero does not yield a finite, defined result.
2. Principle of Division: Division is the inverse of multiplication. This means that if we have a division problem [tex]\( a \div b = c \)[/tex], it implies that [tex]\( b \times c = a \)[/tex]. For example, if [tex]\( 6 \div 3 = 2 \)[/tex], then [tex]\( 3 \times 2 = 6 \)[/tex].
3. Applying Division by Zero:
- Let’s say we have [tex]\( c = \frac{-85}{0} \)[/tex].
- This would imply that [tex]\( 0 \times c = -85 \)[/tex].
- However, multiplying any number by 0 always results in 0, not -85. Therefore, there is no real number [tex]\( c \)[/tex] that satisfies this equation.
4. Conclusion: Since no real number can satisfy the division of -85 by 0, the expression [tex]\( \frac{-85}{0} \)[/tex] is undefined.
Therefore, the result of the expression [tex]\( \frac{-85}{0} \)[/tex] is:
[tex]$ \text{undefined} $[/tex]
