Solve 31/2+(1/3-[716/42-11280/213-5frac{135}{426})]}*12frac{9}{17}

$$3 \frac { 1 } { 2 } + ( \frac { 1 } { 3 } - [ 7 \frac { 16 } { 42 } - 112 \frac { 80 } { 213 } - 5 \frac { 135 } { 426 } ) ] \} \cdot 12 \frac { 9 } { 17 }$$

Evaluate

$$\frac{56730}{497}\approx 114.144869215$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}+\frac{1}{3}-\left(\frac{7\times 42+16}{42}-\frac{112\times 213+80}{213}-\frac{5\times 426+135}{426}\right)$$

Add 6 and 1 to get 7.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{7\times 42+16}{42}-\frac{112\times 213+80}{213}-\frac{5\times 426+135}{426}\right)$$

Multiply 7 and 42 to get 294.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{294+16}{42}-\frac{112\times 213+80}{213}-\frac{5\times 426+135}{426}\right)$$

Add 294 and 16 to get 310.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{310}{42}-\frac{112\times 213+80}{213}-\frac{5\times 426+135}{426}\right)$$

Reduce the fraction \frac{310}{42} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{155}{21}-\frac{112\times 213+80}{213}-\frac{5\times 426+135}{426}\right)$$

Multiply 112 and 213 to get 23856.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{155}{21}-\frac{23856+80}{213}-\frac{5\times 426+135}{426}\right)$$

Add 23856 and 80 to get 23936.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{155}{21}-\frac{23936}{213}-\frac{5\times 426+135}{426}\right)$$

Least common multiple of 21 and 213 is 1491. Convert \frac{155}{21} and \frac{23936}{213} to fractions with denominator 1491.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{11005}{1491}-\frac{167552}{1491}-\frac{5\times 426+135}{426}\right)$$

Since \frac{11005}{1491} and \frac{167552}{1491} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}+\frac{1}{3}-\left(\frac{11005-167552}{1491}-\frac{5\times 426+135}{426}\right)$$

Subtract 167552 from 11005 to get -156547.

$$\frac{7}{2}+\frac{1}{3}-\left(-\frac{156547}{1491}-\frac{5\times 426+135}{426}\right)$$

Multiply 5 and 426 to get 2130.

$$\frac{7}{2}+\frac{1}{3}-\left(-\frac{156547}{1491}-\frac{2130+135}{426}\right)$$

Add 2130 and 135 to get 2265.

$$\frac{7}{2}+\frac{1}{3}-\left(-\frac{156547}{1491}-\frac{2265}{426}\right)$$

Reduce the fraction \frac{2265}{426} to lowest terms by extracting and canceling out 3.

$$\frac{7}{2}+\frac{1}{3}-\left(-\frac{156547}{1491}-\frac{755}{142}\right)$$

Least common multiple of 1491 and 142 is 2982. Convert -\frac{156547}{1491} and \frac{755}{142} to fractions with denominator 2982.

$$\frac{7}{2}+\frac{1}{3}-\left(-\frac{313094}{2982}-\frac{15855}{2982}\right)$$

Since -\frac{313094}{2982} and \frac{15855}{2982} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}+\frac{1}{3}-\frac{-313094-15855}{2982}$$

Subtract 15855 from -313094 to get -328949.

$$\frac{7}{2}+\frac{1}{3}-\left(-\frac{328949}{2982}\right)$$

The opposite of -\frac{328949}{2982} is \frac{328949}{2982}.

$$\frac{7}{2}+\frac{1}{3}+\frac{328949}{2982}$$

Least common multiple of 3 and 2982 is 2982. Convert \frac{1}{3} and \frac{328949}{2982} to fractions with denominator 2982.

$$\frac{7}{2}+\frac{994}{2982}+\frac{328949}{2982}$$

Since \frac{994}{2982} and \frac{328949}{2982} have the same denominator, add them by adding their numerators.

$$\frac{7}{2}+\frac{994+328949}{2982}$$

Add 994 and 328949 to get 329943.

$$\frac{7}{2}+\frac{329943}{2982}$$

Reduce the fraction \frac{329943}{2982} to lowest terms by extracting and canceling out 3.

$$\frac{7}{2}+\frac{109981}{994}$$

Least common multiple of 2 and 994 is 994. Convert \frac{7}{2} and \frac{109981}{994} to fractions with denominator 994.

$$\frac{3479}{994}+\frac{109981}{994}$$

Since \frac{3479}{994} and \frac{109981}{994} have the same denominator, add them by adding their numerators.

$$\frac{3479+109981}{994}$$

Add 3479 and 109981 to get 113460.

$$\frac{113460}{994}$$

Reduce the fraction \frac{113460}{994} to lowest terms by extracting and canceling out 2.

$$\frac{56730}{497}$$

Factor

$$\frac{2 \cdot 3 \cdot 5 \cdot 31 \cdot 61}{7 \cdot 71} = 114\frac{72}{497} = 114.14486921529175$$