Solve 2845/63-3721/84/(frac{7{3}-10/9)divfrac{13}{4}}div31

$$\frac{ \frac{ 2845 }{ 63 } - \frac{ 3721 }{ 84 } }{ ( \frac{ 7 }{ 3 } - \frac{ 10 }{ 9 } ) \div \frac{ 13 }{ 4 } } \div 31$$

Evaluate

$$\frac{13}{176}\approx 0.073863636$$

Solution Steps

Express \frac{\frac{\frac{2845}{63}-\frac{3721}{84}}{\frac{\frac{7}{3}-\frac{10}{9}}{\frac{13}{4}}}}{31} as a single fraction.

$$\frac{\frac{2845}{63}-\frac{3721}{84}}{\frac{\frac{7}{3}-\frac{10}{9}}{\frac{13}{4}}\times 31}$$

Least common multiple of 63 and 84 is 252. Convert \frac{2845}{63} and \frac{3721}{84} to fractions with denominator 252.

$$\frac{\frac{11380}{252}-\frac{11163}{252}}{\frac{\frac{7}{3}-\frac{10}{9}}{\frac{13}{4}}\times 31}$$

Since \frac{11380}{252} and \frac{11163}{252} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11380-11163}{252}}{\frac{\frac{7}{3}-\frac{10}{9}}{\frac{13}{4}}\times 31}$$

Subtract 11163 from 11380 to get 217.

$$\frac{\frac{217}{252}}{\frac{\frac{7}{3}-\frac{10}{9}}{\frac{13}{4}}\times 31}$$

Reduce the fraction \frac{217}{252} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{31}{36}}{\frac{\frac{7}{3}-\frac{10}{9}}{\frac{13}{4}}\times 31}$$

Least common multiple of 3 and 9 is 9. Convert \frac{7}{3} and \frac{10}{9} to fractions with denominator 9.

$$\frac{\frac{31}{36}}{\frac{\frac{21}{9}-\frac{10}{9}}{\frac{13}{4}}\times 31}$$

Since \frac{21}{9} and \frac{10}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{31}{36}}{\frac{\frac{21-10}{9}}{\frac{13}{4}}\times 31}$$

Subtract 10 from 21 to get 11.

$$\frac{\frac{31}{36}}{\frac{\frac{11}{9}}{\frac{13}{4}}\times 31}$$

Divide \frac{11}{9} by \frac{13}{4} by multiplying \frac{11}{9} by the reciprocal of \frac{13}{4}.

$$\frac{\frac{31}{36}}{\frac{11}{9}\times \frac{4}{13}\times 31}$$

Multiply \frac{11}{9} times \frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{31}{36}}{\frac{11\times 4}{9\times 13}\times 31}$$

Do the multiplications in the fraction \frac{11\times 4}{9\times 13}.

$$\frac{\frac{31}{36}}{\frac{44}{117}\times 31}$$

Express \frac{44}{117}\times 31 as a single fraction.

$$\frac{\frac{31}{36}}{\frac{44\times 31}{117}}$$

Multiply 44 and 31 to get 1364.

$$\frac{\frac{31}{36}}{\frac{1364}{117}}$$

Divide \frac{31}{36} by \frac{1364}{117} by multiplying \frac{31}{36} by the reciprocal of \frac{1364}{117}.

$$\frac{31}{36}\times \frac{117}{1364}$$

Multiply \frac{31}{36} times \frac{117}{1364} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 117}{36\times 1364}$$

Do the multiplications in the fraction \frac{31\times 117}{36\times 1364}.

$$\frac{3627}{49104}$$

Reduce the fraction \frac{3627}{49104} to lowest terms by extracting and canceling out 279.

$$\frac{13}{176}$$

Factor

$$\frac{13}{2 ^ {4} \cdot 11} = 0.07386363636363637$$