To determine the opposite of the fraction \(\frac{6}{7}\), we follow these steps:
1. Understand the Concept of Opposites:
The opposite of a number is what you get when you change its sign. If the number is positive, like \(\frac{6}{7}\), its opposite will be negative. Conversely, if the number were negative, its opposite would be positive.
2. Apply the Concept:
Since \(\frac{6}{7}\) is a positive fraction, its opposite would be the negative of \(\frac{6}{7}\). Thus, we simply change the sign from positive to negative.
3. Write the Opposite:
The negative of \(\frac{6}{7}\) is \(-\frac{6}{7}\).
4. Convert to Decimal (if necessary):
If you need the decimal form, you would represent \(-\frac{6}{7}\) as its decimal equivalent. As given:
[tex]\[
\frac{6}{7} \approx 0.8571428571428571
\][/tex]
Therefore, the opposite number would be:
[tex]\[
-0.8571428571428571
\][/tex]
So, the opposite of [tex]\(\frac{6}{7}\)[/tex] is [tex]\(-\frac{6}{7}\)[/tex] or approximately [tex]\(-0.8571428571428571\)[/tex] in decimal form.
