Solve {l}{4/4+6/91+8/43+10/651}{quad+frac{12}{1353}}

$$\left. \begin{array} { l } { \frac { 4 } { 4 } + \frac { 6 } { 91 } + \frac { 8 } { 43 } + \frac { 10 } { 651 } } \\ { \quad + \frac { 12 } { 1353 } } \end{array} \right.$$

Evaluate

$$\frac{209455483}{164122959}\approx 1.27621074$$

Solution Steps

Divide 4 by 4 to get 1.

$$1+\frac{6}{91}+\frac{8}{43}+\frac{10}{651}+\frac{12}{1353}$$

Convert 1 to fraction \frac{91}{91}.

$$\frac{91}{91}+\frac{6}{91}+\frac{8}{43}+\frac{10}{651}+\frac{12}{1353}$$

Since \frac{91}{91} and \frac{6}{91} have the same denominator, add them by adding their numerators.

$$\frac{91+6}{91}+\frac{8}{43}+\frac{10}{651}+\frac{12}{1353}$$

Add 91 and 6 to get 97.

$$\frac{97}{91}+\frac{8}{43}+\frac{10}{651}+\frac{12}{1353}$$

Least common multiple of 91 and 43 is 3913. Convert \frac{97}{91} and \frac{8}{43} to fractions with denominator 3913.

$$\frac{4171}{3913}+\frac{728}{3913}+\frac{10}{651}+\frac{12}{1353}$$

Since \frac{4171}{3913} and \frac{728}{3913} have the same denominator, add them by adding their numerators.

$$\frac{4171+728}{3913}+\frac{10}{651}+\frac{12}{1353}$$

Add 4171 and 728 to get 4899.

$$\frac{4899}{3913}+\frac{10}{651}+\frac{12}{1353}$$

Least common multiple of 3913 and 651 is 363909. Convert \frac{4899}{3913} and \frac{10}{651} to fractions with denominator 363909.

$$\frac{455607}{363909}+\frac{5590}{363909}+\frac{12}{1353}$$

Since \frac{455607}{363909} and \frac{5590}{363909} have the same denominator, add them by adding their numerators.

$$\frac{455607+5590}{363909}+\frac{12}{1353}$$

Add 455607 and 5590 to get 461197.

$$\frac{461197}{363909}+\frac{12}{1353}$$

Reduce the fraction \frac{12}{1353} to lowest terms by extracting and canceling out 3.

$$\frac{461197}{363909}+\frac{4}{451}$$

Least common multiple of 363909 and 451 is 164122959. Convert \frac{461197}{363909} and \frac{4}{451} to fractions with denominator 164122959.

$$\frac{207999847}{164122959}+\frac{1455636}{164122959}$$

Since \frac{207999847}{164122959} and \frac{1455636}{164122959} have the same denominator, add them by adding their numerators.

$$\frac{207999847+1455636}{164122959}$$

Add 207999847 and 1455636 to get 209455483.

$$\frac{209455483}{164122959}$$

Factor

$$\frac{37 \cdot 733 \cdot 7723}{3 \cdot 7 \cdot 11 \cdot 13 \cdot 31 \cdot 41 \cdot 43} = 1\frac{45332524}{164122959} = 1.2762107402657785$$