Solve 12div(1/3+3/4)quad5/9div1/26+frac{4}{9}*26quadfrac{9}{17}*(51+frac{17}{27})-frac{17}{27}

$$12 \div ( \frac { 1 } { 3 } + \frac { 3 } { 4 } ) \quad \frac { 5 } { 9 } \div \frac { 1 } { 26 } + \frac { 4 } { 9 } \times 26 \quad \frac { 9 } { 17 } \times ( 51 + \frac { 17 } { 27 } ) - \frac { 17 } { 27 }$$

Evaluate

$$\frac{186655}{243}\approx 768.127572016$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{12}{\frac{4}{12}+\frac{9}{12}}\times \frac{5}{9}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12}{\frac{4+9}{12}}\times \frac{5}{9}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Add 4 and 9 to get 13.

$$\frac{\frac{12}{\frac{13}{12}}\times \frac{5}{9}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Divide 12 by \frac{13}{12} by multiplying 12 by the reciprocal of \frac{13}{12}.

$$\frac{12\times \frac{12}{13}\times \frac{5}{9}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Express 12\times \frac{12}{13} as a single fraction.

$$\frac{\frac{12\times 12}{13}\times \frac{5}{9}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Multiply 12 and 12 to get 144.

$$\frac{\frac{144}{13}\times \frac{5}{9}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Multiply \frac{144}{13} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{144\times 5}{13\times 9}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Do the multiplications in the fraction \frac{144\times 5}{13\times 9}.

$$\frac{\frac{720}{117}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Reduce the fraction \frac{720}{117} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{80}{13}}{\frac{1}{26}}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Divide \frac{80}{13} by \frac{1}{26} by multiplying \frac{80}{13} by the reciprocal of \frac{1}{26}.

$$\frac{80}{13}\times 26+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Express \frac{80}{13}\times 26 as a single fraction.

$$\frac{80\times 26}{13}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Multiply 80 and 26 to get 2080.

$$\frac{2080}{13}+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Divide 2080 by 13 to get 160.

$$160+\frac{4}{9}\times \frac{26\times 17+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Multiply 26 and 17 to get 442.

$$160+\frac{4}{9}\times \frac{442+9}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Add 442 and 9 to get 451.

$$160+\frac{4}{9}\times \frac{451}{17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Multiply \frac{4}{9} times \frac{451}{17} by multiplying numerator times numerator and denominator times denominator.

$$160+\frac{4\times 451}{9\times 17}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Do the multiplications in the fraction \frac{4\times 451}{9\times 17}.

$$160+\frac{1804}{153}\left(51+\frac{17}{27}\right)-\frac{17}{27}$$

Convert 51 to fraction \frac{1377}{27}.

$$160+\frac{1804}{153}\left(\frac{1377}{27}+\frac{17}{27}\right)-\frac{17}{27}$$

Since \frac{1377}{27} and \frac{17}{27} have the same denominator, add them by adding their numerators.

$$160+\frac{1804}{153}\times \frac{1377+17}{27}-\frac{17}{27}$$

Add 1377 and 17 to get 1394.

$$160+\frac{1804}{153}\times \frac{1394}{27}-\frac{17}{27}$$

Multiply \frac{1804}{153} times \frac{1394}{27} by multiplying numerator times numerator and denominator times denominator.

$$160+\frac{1804\times 1394}{153\times 27}-\frac{17}{27}$$

Do the multiplications in the fraction \frac{1804\times 1394}{153\times 27}.

$$160+\frac{2514776}{4131}-\frac{17}{27}$$

Reduce the fraction \frac{2514776}{4131} to lowest terms by extracting and canceling out 17.

$$160+\frac{147928}{243}-\frac{17}{27}$$

Convert 160 to fraction \frac{38880}{243}.

$$\frac{38880}{243}+\frac{147928}{243}-\frac{17}{27}$$

Since \frac{38880}{243} and \frac{147928}{243} have the same denominator, add them by adding their numerators.

$$\frac{38880+147928}{243}-\frac{17}{27}$$

Add 38880 and 147928 to get 186808.

$$\frac{186808}{243}-\frac{17}{27}$$

Least common multiple of 243 and 27 is 243. Convert \frac{186808}{243} and \frac{17}{27} to fractions with denominator 243.

$$\frac{186808}{243}-\frac{153}{243}$$

Since \frac{186808}{243} and \frac{153}{243} have the same denominator, subtract them by subtracting their numerators.

$$\frac{186808-153}{243}$$

Subtract 153 from 186808 to get 186655.

$$\frac{186655}{243}$$

Factor

$$\frac{5 \cdot 7 \cdot 5333}{3 ^ {5}} = 768\frac{31}{243} = 768.1275720164609$$