Certainly, let's solve the given problem step-by-step.
1. We start with the mixed fraction [tex]\( 6 \frac{1}{2} \)[/tex]. In order to work with it more easily, we convert it to an improper fraction or a decimal. [tex]\( 6 \frac{1}{2} \)[/tex] can be written as:
[tex]\[
6 + \frac{1}{2} = 6.5
\][/tex]
2. Next, we have the fraction [tex]\(\frac{7}{11} \)[/tex]. We will keep it as a fraction for now, but we'll convert it to a decimal to facilitate subtraction. [tex]\(\frac{7}{11} \)[/tex] is approximately:
[tex]\[
0.6363636363636364
\][/tex]
3. Now we subtract [tex]\(\frac{7}{11} \)[/tex] from [tex]\( 6.5 \)[/tex]. The decimal representation of this operation is:
[tex]\[
6.5 - 0.6363636363636364 = 5.863636363636363
\][/tex]
So, the solution is:
[tex]\[
6.5 - 0.6363636363636364 = 5.863636363636363
\][/tex]
Therefore, the mixed fraction [tex]\(6 \frac{1}{2} \)[/tex] subtracted by the fraction [tex]\(\frac{7}{11} \)[/tex] results in approximately [tex]\( 5.863636363636363 \)[/tex].
