Solve 4/21+6/91+8/273+10/651+frac{12}{1333}

$$\frac{ 4 }{ 21 } + \frac{ 6 }{ 91 } + \frac{ 8 }{ 273 } + \frac{ 10 }{ 651 } + \frac{ 12 }{ 1333 }$$

Evaluate

$$\frac{40}{129}\approx 0.310077519$$

Solution Steps

Least common multiple of 21 and 91 is 273. Convert \frac{4}{21} and \frac{6}{91} to fractions with denominator 273.

$$\frac{52}{273}+\frac{18}{273}+\frac{8}{273}+\frac{10}{651}+\frac{12}{1333}$$

Since \frac{52}{273} and \frac{18}{273} have the same denominator, add them by adding their numerators.

$$\frac{52+18}{273}+\frac{8}{273}+\frac{10}{651}+\frac{12}{1333}$$

Add 52 and 18 to get 70.

$$\frac{70}{273}+\frac{8}{273}+\frac{10}{651}+\frac{12}{1333}$$

Since \frac{70}{273} and \frac{8}{273} have the same denominator, add them by adding their numerators.

$$\frac{70+8}{273}+\frac{10}{651}+\frac{12}{1333}$$

Add 70 and 8 to get 78.

$$\frac{78}{273}+\frac{10}{651}+\frac{12}{1333}$$

Reduce the fraction \frac{78}{273} to lowest terms by extracting and canceling out 39.

$$\frac{2}{7}+\frac{10}{651}+\frac{12}{1333}$$

Least common multiple of 7 and 651 is 651. Convert \frac{2}{7} and \frac{10}{651} to fractions with denominator 651.

$$\frac{186}{651}+\frac{10}{651}+\frac{12}{1333}$$

Since \frac{186}{651} and \frac{10}{651} have the same denominator, add them by adding their numerators.

$$\frac{186+10}{651}+\frac{12}{1333}$$

Add 186 and 10 to get 196.

$$\frac{196}{651}+\frac{12}{1333}$$

Reduce the fraction \frac{196}{651} to lowest terms by extracting and canceling out 7.

$$\frac{28}{93}+\frac{12}{1333}$$

Least common multiple of 93 and 1333 is 3999. Convert \frac{28}{93} and \frac{12}{1333} to fractions with denominator 3999.

$$\frac{1204}{3999}+\frac{36}{3999}$$

Since \frac{1204}{3999} and \frac{36}{3999} have the same denominator, add them by adding their numerators.

$$\frac{1204+36}{3999}$$

Add 1204 and 36 to get 1240.

$$\frac{1240}{3999}$$

Reduce the fraction \frac{1240}{3999} to lowest terms by extracting and canceling out 31.

$$\frac{40}{129}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{3 \cdot 43} = 0.31007751937984496$$