Question: 2/7 ÷ 8/14 = 4/12 = 8

Solution

To solve the problem \(\frac{9}{7} \div \frac{8}{14} - \frac{4}{12} - 8\), follow these steps:

First, solve the division:

Rewrite the division as multiplication by the reciprocal:

\[ \frac{9}{7} \times \frac{14}{8} \]

Simplify \(\frac{14}{8}\):

\[ \frac{14}{8} = \frac{7}{4} \]

Multiply \(\frac{9}{7} \times \frac{7}{4}\):

Cancel the 7 in the numerator and the denominator:

\[ \frac{9}{1} \times \frac{1}{4} = \frac{9}{4} \]

Next, simplify \(\frac{4}{12}\):

\[ \frac{4}{12} = \frac{1}{3} \]

Subtract \(\frac{1}{3}\) from \(\frac{9}{4}\):

To subtract the fractions, find a common denominator:

\[ \frac{9}{4} = \frac{27}{12}, \quad \frac{1}{3} = \frac{4}{12} \]

Subtract the fractions:

\[ \frac{27}{12} - \frac{4}{12} = \frac{23}{12} \]

Now subtract 8:

Convert 8 to a fraction with denominator 12:

\[ 8 = \frac{96}{12} \]

Subtract \(\frac{96}{12}\) from \(\frac{23}{12}\):

\[ \frac{23}{12} - \frac{96}{12} = \frac{-73}{12} \]

The final answer is:

\[ \frac{-73}{12} \]