Solve 7/2*8/21+9/2*frac{4/27}{1-frac{2}{7}}=?

$$\frac { \frac { 7 } { 2 } * \frac { 8 } { 21 } + \frac { 9 } { 2 } * \frac { 4 } { 27 } } { 1 - \frac { 2 } { 7 } } = ?$$

Evaluate

$$\frac{14}{5}=2.8$$

Solution Steps

Multiply \frac{7}{2} times \frac{8}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 8}{2\times 21}+\frac{9}{2}\times \frac{4}{27}}{1-\frac{2}{7}}$$

Do the multiplications in the fraction \frac{7\times 8}{2\times 21}.

$$\frac{\frac{56}{42}+\frac{9}{2}\times \frac{4}{27}}{1-\frac{2}{7}}$$

Reduce the fraction \frac{56}{42} to lowest terms by extracting and canceling out 14.

$$\frac{\frac{4}{3}+\frac{9}{2}\times \frac{4}{27}}{1-\frac{2}{7}}$$

Multiply \frac{9}{2} times \frac{4}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4}{3}+\frac{9\times 4}{2\times 27}}{1-\frac{2}{7}}$$

Do the multiplications in the fraction \frac{9\times 4}{2\times 27}.

$$\frac{\frac{4}{3}+\frac{36}{54}}{1-\frac{2}{7}}$$

Reduce the fraction \frac{36}{54} to lowest terms by extracting and canceling out 18.

$$\frac{\frac{4}{3}+\frac{2}{3}}{1-\frac{2}{7}}$$

Since \frac{4}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+2}{3}}{1-\frac{2}{7}}$$

Add 4 and 2 to get 6.

$$\frac{\frac{6}{3}}{1-\frac{2}{7}}$$

Divide 6 by 3 to get 2.

$$\frac{2}{1-\frac{2}{7}}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{2}{\frac{7}{7}-\frac{2}{7}}$$

Since \frac{7}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{\frac{7-2}{7}}$$

Subtract 2 from 7 to get 5.

$$\frac{2}{\frac{5}{7}}$$

Divide 2 by \frac{5}{7} by multiplying 2 by the reciprocal of \frac{5}{7}.

$$2\times \frac{7}{5}$$

Express 2\times \frac{7}{5} as a single fraction.

$$\frac{2\times 7}{5}$$

Multiply 2 and 7 to get 14.

$$\frac{14}{5}$$

Factor

$$\frac{2 \cdot 7}{5} = 2\frac{4}{5} = 2.8$$