Solve {r}{134/11}{273/11}{+822/11}{959/12}{46frac{1}{2}}

$$\left. \begin{array} { r } { 13 \frac { 4 } { 11 } } \\ { 27 \frac { 3 } { 11 } } \\ { + 82 \frac { 2 } { 11 } } \\ { 95 \frac { 9 } { 12 } } \\ { 46 \frac { 1 } { 2 } } \end{array} \right.$$

Evaluate

$$\frac{11663}{44}\approx 265.068181818$$

Solution Steps

Multiply 13 and 11 to get 143.

$$\frac{143+4}{11}+\frac{27\times 11+3}{11}+\frac{82\times 11+2}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Add 143 and 4 to get 147.

$$\frac{147}{11}+\frac{27\times 11+3}{11}+\frac{82\times 11+2}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Multiply 27 and 11 to get 297.

$$\frac{147}{11}+\frac{297+3}{11}+\frac{82\times 11+2}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Add 297 and 3 to get 300.

$$\frac{147}{11}+\frac{300}{11}+\frac{82\times 11+2}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Since \frac{147}{11} and \frac{300}{11} have the same denominator, add them by adding their numerators.

$$\frac{147+300}{11}+\frac{82\times 11+2}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Add 147 and 300 to get 447.

$$\frac{447}{11}+\frac{82\times 11+2}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Multiply 82 and 11 to get 902.

$$\frac{447}{11}+\frac{902+2}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Add 902 and 2 to get 904.

$$\frac{447}{11}+\frac{904}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Since \frac{447}{11} and \frac{904}{11} have the same denominator, add them by adding their numerators.

$$\frac{447+904}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Add 447 and 904 to get 1351.

$$\frac{1351}{11}+\frac{95\times 12+9}{12}+\frac{46\times 2+1}{2}$$

Multiply 95 and 12 to get 1140.

$$\frac{1351}{11}+\frac{1140+9}{12}+\frac{46\times 2+1}{2}$$

Add 1140 and 9 to get 1149.

$$\frac{1351}{11}+\frac{1149}{12}+\frac{46\times 2+1}{2}$$

Reduce the fraction \frac{1149}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1351}{11}+\frac{383}{4}+\frac{46\times 2+1}{2}$$

Least common multiple of 11 and 4 is 44. Convert \frac{1351}{11} and \frac{383}{4} to fractions with denominator 44.

$$\frac{5404}{44}+\frac{4213}{44}+\frac{46\times 2+1}{2}$$

Since \frac{5404}{44} and \frac{4213}{44} have the same denominator, add them by adding their numerators.

$$\frac{5404+4213}{44}+\frac{46\times 2+1}{2}$$

Add 5404 and 4213 to get 9617.

$$\frac{9617}{44}+\frac{46\times 2+1}{2}$$

Multiply 46 and 2 to get 92.

$$\frac{9617}{44}+\frac{92+1}{2}$$

Add 92 and 1 to get 93.

$$\frac{9617}{44}+\frac{93}{2}$$

Least common multiple of 44 and 2 is 44. Convert \frac{9617}{44} and \frac{93}{2} to fractions with denominator 44.

$$\frac{9617}{44}+\frac{2046}{44}$$

Since \frac{9617}{44} and \frac{2046}{44} have the same denominator, add them by adding their numerators.

$$\frac{9617+2046}{44}$$

Add 9617 and 2046 to get 11663.

$$\frac{11663}{44}$$

Factor

$$\frac{107 \cdot 109}{2 ^ {2} \cdot 11} = 265\frac{3}{44} = 265.0681818181818$$