Correct Answer: Option C

Explanation

Convert each mixed number to an improper fraction:

7 \(\frac{1}{12}\) = 7 + \(\frac{1}{12}\) = \(\frac{84}{12} + \frac{1}{12}\) = \(\frac{85}{12}\)
4 \(\frac{3}{4}\) = 4 + \(\frac{3}{4}\) = \(\frac{16}{4}\) + \(\frac{3}{4}\) = \(\frac{19}{4}\)
2 \(\frac{1}{2}\) = 2 + \(\frac{1}{2}\) = \(\frac{4}{2}\) + \(\frac{1}{2}\) = \(\frac{5}{2}\)

Now calculate: \(\frac{85}{12} − \frac{19}{4} + \frac{5}{2}\)

Common denominator = 12

\(\frac{85}{12}\) − (\(\frac{19}{4}\) \(\times\) \(\frac{3}{3}\)) + (\(\frac{5}{2}\) \(\times\) \(\frac{6}{6}\))

= \(\frac{85}{12}\) − \(\frac{57}{12}\) + \(\frac{30}{12}\)
= (\(\frac{85 − 57 + 30)}{12}\)
= \(\frac{(58)}{12}\)
= \(\frac{29}{6}\) = 4 \(\frac{5}{6}\).

There is an explanation video available below.

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