To solve for the difference between [tex]\(\frac{1261}{4}\)[/tex] and [tex]\(\frac{781}{3}\)[/tex], let's follow these steps:
1. Calculate [tex]\(\frac{1261}{4}\)[/tex]:
Divide 1261 by 4:
[tex]\[
\frac{1261}{4} = 315.25
\][/tex]
2. Calculate [tex]\(\frac{781}{3}\)[/tex]:
Divide 781 by 3:
[tex]\[
\frac{781}{3} = 260.3333333\ldots
\][/tex]
We can round this to a few decimal places for simplicity, i.e., [tex]\(260.3333\)[/tex].
3. Find the difference between the two results:
Subtract [tex]\(\frac{781}{3}\)[/tex] from [tex]\(\frac{1261}{4}\)[/tex]:
[tex]\[
315.25 - 260.3333333\ldots = 54.9166667
\][/tex]
The step-by-step calculations give us a difference of approximately [tex]\(54.9166667\)[/tex].
4. Compare to the given choices:
Evaluate which option matches [tex]\(54.9166667\)[/tex]:
- A. [tex]\(\frac{585}{12}\)[/tex] is calculated as [tex]\(48.75\)[/tex]
- B. [tex]\(\frac{57}{12}\)[/tex] is calculated as [tex]\(4.75\)[/tex]
- C. [tex]\(47^{7/12}\)[/tex] involves mixed fraction formatting that doesn't directly yield our number [tex]\(54.9166667\)[/tex]
- D. [tex]\(48 \frac{1}{3}\)[/tex] is calculated as [tex]\(48.3333\)[/tex] which does not match closely our result.
Upon verification:
- None of the provided options exactly match the calculated difference, but our detailed calculation shows the correct result is approximately [tex]\(54.9166667\)[/tex].
Thus, the answer closest to the actual difference is not among the given options.
