Solve (31/12+4,375):198/9/2frac{5{8}-2/3*2frac{5}{14}}

$$\frac { ( 3 \frac { 1 } { 12 } + 4,375 ) : 19 \frac { 8 } { 9 } } { 2 \frac { 5 } { 8 } - \frac { 2 } { 3 } \cdot 2 \frac { 5 } { 14 } }$$

Evaluate

$$\frac{2206554}{10561}\approx 208.934191838$$

Solution Steps

Multiply 3 and 12 to get 36.

$$\frac{\frac{\frac{36+1}{12}+4375}{\frac{19\times 9+8}{9}}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Add 36 and 1 to get 37.

$$\frac{\frac{\frac{37}{12}+4375}{\frac{19\times 9+8}{9}}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Convert 4375 to fraction \frac{52500}{12}.

$$\frac{\frac{\frac{37}{12}+\frac{52500}{12}}{\frac{19\times 9+8}{9}}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Since \frac{37}{12} and \frac{52500}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{37+52500}{12}}{\frac{19\times 9+8}{9}}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Add 37 and 52500 to get 52537.

$$\frac{\frac{\frac{52537}{12}}{\frac{19\times 9+8}{9}}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Multiply 19 and 9 to get 171.

$$\frac{\frac{\frac{52537}{12}}{\frac{171+8}{9}}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Add 171 and 8 to get 179.

$$\frac{\frac{\frac{52537}{12}}{\frac{179}{9}}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Divide \frac{52537}{12} by \frac{179}{9} by multiplying \frac{52537}{12} by the reciprocal of \frac{179}{9}.

$$\frac{\frac{52537}{12}\times \frac{9}{179}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Multiply \frac{52537}{12} times \frac{9}{179} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{52537\times 9}{12\times 179}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Do the multiplications in the fraction \frac{52537\times 9}{12\times 179}.

$$\frac{\frac{472833}{2148}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Reduce the fraction \frac{472833}{2148} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{157611}{716}}{\frac{2\times 8+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Multiply 2 and 8 to get 16.

$$\frac{\frac{157611}{716}}{\frac{16+5}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Add 16 and 5 to get 21.

$$\frac{\frac{157611}{716}}{\frac{21}{8}-\frac{2}{3}\times \frac{2\times 14+5}{14}}$$

Multiply 2 and 14 to get 28.

$$\frac{\frac{157611}{716}}{\frac{21}{8}-\frac{2}{3}\times \frac{28+5}{14}}$$

Add 28 and 5 to get 33.

$$\frac{\frac{157611}{716}}{\frac{21}{8}-\frac{2}{3}\times \frac{33}{14}}$$

Multiply \frac{2}{3} times \frac{33}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{157611}{716}}{\frac{21}{8}-\frac{2\times 33}{3\times 14}}$$

Do the multiplications in the fraction \frac{2\times 33}{3\times 14}.

$$\frac{\frac{157611}{716}}{\frac{21}{8}-\frac{66}{42}}$$

Reduce the fraction \frac{66}{42} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{157611}{716}}{\frac{21}{8}-\frac{11}{7}}$$

Least common multiple of 8 and 7 is 56. Convert \frac{21}{8} and \frac{11}{7} to fractions with denominator 56.

$$\frac{\frac{157611}{716}}{\frac{147}{56}-\frac{88}{56}}$$

Since \frac{147}{56} and \frac{88}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{157611}{716}}{\frac{147-88}{56}}$$

Subtract 88 from 147 to get 59.

$$\frac{\frac{157611}{716}}{\frac{59}{56}}$$

Divide \frac{157611}{716} by \frac{59}{56} by multiplying \frac{157611}{716} by the reciprocal of \frac{59}{56}.

$$\frac{157611}{716}\times \frac{56}{59}$$

Multiply \frac{157611}{716} times \frac{56}{59} by multiplying numerator times numerator and denominator times denominator.

$$\frac{157611\times 56}{716\times 59}$$

Do the multiplications in the fraction \frac{157611\times 56}{716\times 59}.

$$\frac{8826216}{42244}$$

Reduce the fraction \frac{8826216}{42244} to lowest terms by extracting and canceling out 4.

$$\frac{2206554}{10561}$$

Factor

$$\frac{2 \cdot 3 \cdot 7 \cdot 107 \cdot 491}{59 \cdot 179} = 208\frac{9866}{10561} = 208.93419183789413$$