step 1: \\(8\\frac{5}{6} \\div 2\\frac{2}{3}\\) step 2: \\(\\frac{53}{6} \\div \\frac{8}{3}\\) step 3…

Explanation:

Step1: Identify the operation

The problem is to divide the mixed numbers (8\frac{5}{6}) and (2\frac{2}{3}), so we start with (8\frac{5}{6}\div2\frac{2}{3}).

Step2: Convert mixed to improper

Convert (8\frac{5}{6}) to (\frac{8\times6 + 5}{6}=\frac{53}{6}) and (2\frac{2}{3}) to (\frac{2\times3+2}{3}=\frac{8}{3}), so we have (\frac{53}{6}\div\frac{8}{3}).

Step3: Invert and multiply

Dividing by a fraction is multiplying by its reciprocal, so (\frac{53}{6}\div\frac{8}{3}=\frac{53}{6}\times\frac{3}{8}) (note: the original Step 3 had a typo, it should be (\frac{53}{6}\times\frac{3}{8}) not (\frac{6}{53}\times\frac{3}{8})).

Step4: Multiply numerators and denominators

Multiply numerators: (53\times3 = 159), denominators: (6\times8=48), so (\frac{159}{48}).

Step5: Simplify the fraction

Convert (\frac{159}{48}) to a mixed number: (159\div48 = 3) with a remainder of (15), so (3\frac{15}{48}), and simplify (\frac{15}{48}) to (\frac{5}{16}), so (3\frac{5}{16}) (or keep as (3\frac{15}{48}) if not simplifying further).

Answer:

If we simplify (3\frac{15}{48}), the result is (3\frac{5}{16}) (or (\frac{53}{16}) as an improper fraction, or (3\frac{15}{48}) as is). The correct simplified form of (3\frac{15}{48}) is (3\frac{5}{16}) (since (\frac{15\div3}{48\div3}=\frac{5}{16})).