To find the value of [tex]\(\frac{0}{5} \div \frac{0}{8}\)[/tex], we need to follow these steps:
1. Understand the division operation for fractions:
When dividing by a fraction, we multiply by its reciprocal. So,
[tex]\[
a \div b = a \times \frac{1}{b}
\][/tex]
2. Apply this to our specific case:
[tex]\[
\frac{0}{5} \div \frac{0}{8} = \frac{0}{5} \times \frac{8}{0}
\][/tex]
3. Recognize the issue:
When we attempt to divide zero by a non-zero number, the result is zero. But when multiplying or dividing by zero in a denominator, it becomes undefined because division by zero is not defined. Specifically, here we need to perform multiplication involving a zero in the denominator, which doesn't make sense in standard arithmetic.
Therefore,
[tex]\[
\frac{0}{5} \div \frac{0}{8}
\][/tex]
is undefined. This is because any expression involving division by zero lacks a meaningful result within the standard rules of arithmetic and rational numbers.
