Solve 21/71+15/83/2-frac{64{71}-78/83}

$$\frac { \frac { 21 } { 71 } + \frac { 15 } { 83 } } { 2 - \frac { 64 } { 71 } - \frac { 78 } { 83 } }$$

Evaluate

$$3$$

Solution Steps

Least common multiple of 71 and 83 is 5893. Convert \frac{21}{71} and \frac{15}{83} to fractions with denominator 5893.

$$\frac{\frac{1743}{5893}+\frac{1065}{5893}}{2-\frac{64}{71}-\frac{78}{83}}$$

Since \frac{1743}{5893} and \frac{1065}{5893} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1743+1065}{5893}}{2-\frac{64}{71}-\frac{78}{83}}$$

Add 1743 and 1065 to get 2808.

$$\frac{\frac{2808}{5893}}{2-\frac{64}{71}-\frac{78}{83}}$$

Convert 2 to fraction \frac{142}{71}.

$$\frac{\frac{2808}{5893}}{\frac{142}{71}-\frac{64}{71}-\frac{78}{83}}$$

Since \frac{142}{71} and \frac{64}{71} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2808}{5893}}{\frac{142-64}{71}-\frac{78}{83}}$$

Subtract 64 from 142 to get 78.

$$\frac{\frac{2808}{5893}}{\frac{78}{71}-\frac{78}{83}}$$

Least common multiple of 71 and 83 is 5893. Convert \frac{78}{71} and \frac{78}{83} to fractions with denominator 5893.

$$\frac{\frac{2808}{5893}}{\frac{6474}{5893}-\frac{5538}{5893}}$$

Since \frac{6474}{5893} and \frac{5538}{5893} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2808}{5893}}{\frac{6474-5538}{5893}}$$

Subtract 5538 from 6474 to get 936.

$$\frac{\frac{2808}{5893}}{\frac{936}{5893}}$$

Divide \frac{2808}{5893} by \frac{936}{5893} by multiplying \frac{2808}{5893} by the reciprocal of \frac{936}{5893}.

$$\frac{2808}{5893}\times \frac{5893}{936}$$

Multiply \frac{2808}{5893} times \frac{5893}{936} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2808\times 5893}{5893\times 936}$$

Cancel out 5893 in both numerator and denominator.

$$\frac{2808}{936}$$

Divide 2808 by 936 to get 3.

$$3$$

Factor

$$3$$