Solve 9/frac{7{2}}-5/7-2/1-frac{4{7}}

$$\frac { 9 } { \frac { 7 } { 2 } } - \frac { \frac { 5 } { 7 } - 2 } { 1 - \frac { 4 } { 7 } }$$

Evaluate

$$\frac{39}{7}\approx 5.571428571$$

Solution Steps

Divide 9 by \frac{7}{2} by multiplying 9 by the reciprocal of \frac{7}{2}.

$$9\times \frac{2}{7}-\frac{\frac{5}{7}-2}{1-\frac{4}{7}}$$

Express 9\times \frac{2}{7} as a single fraction.

$$\frac{9\times 2}{7}-\frac{\frac{5}{7}-2}{1-\frac{4}{7}}$$

Multiply 9 and 2 to get 18.

$$\frac{18}{7}-\frac{\frac{5}{7}-2}{1-\frac{4}{7}}$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{18}{7}-\frac{\frac{5}{7}-\frac{14}{7}}{1-\frac{4}{7}}$$

Since \frac{5}{7} and \frac{14}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18}{7}-\frac{\frac{5-14}{7}}{1-\frac{4}{7}}$$

Subtract 14 from 5 to get -9.

$$\frac{18}{7}-\frac{-\frac{9}{7}}{1-\frac{4}{7}}$$

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

$$\frac{18}{7}-\frac{-\frac{9}{7}}{\frac{7}{7}-\frac{4}{7}}$$

Since \frac{7}{7} and \frac{4}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18}{7}-\frac{-\frac{9}{7}}{\frac{7-4}{7}}$$

Subtract 4 from 7 to get 3.

$$\frac{18}{7}-\frac{-\frac{9}{7}}{\frac{3}{7}}$$

Divide -\frac{9}{7} by \frac{3}{7} by multiplying -\frac{9}{7} by the reciprocal of \frac{3}{7}.

$$\frac{18}{7}-\left(-\frac{9}{7}\times \frac{7}{3}\right)$$

Multiply -\frac{9}{7} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18}{7}-\frac{-9\times 7}{7\times 3}$$

Cancel out 7 in both numerator and denominator.

$$\frac{18}{7}-\frac{-9}{3}$$

Divide -9 by 3 to get -3.

$$\frac{18}{7}-\left(-3\right)$$

The opposite of -3 is 3.

$$\frac{18}{7}+3$$

Convert 3 to fraction \frac{21}{7}.

$$\frac{18}{7}+\frac{21}{7}$$

Since \frac{18}{7} and \frac{21}{7} have the same denominator, add them by adding their numerators.

$$\frac{18+21}{7}$$

Add 18 and 21 to get 39.

$$\frac{39}{7}$$

Factor

$$\frac{3 \cdot 13}{7} = 5\frac{4}{7} = 5.571428571428571$$