Solve 1/9+2/23+8/9+21/23

$$\frac{ 1 }{ 9 } + \frac{ 2 }{ 23 } + \frac{ 8 }{ 9 } + \frac{ 21 }{ 23 }$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 9 and 23 is 207. Convert \frac{1}{9} and \frac{2}{23} to fractions with denominator 207.

$$\frac{23}{207}+\frac{18}{207}+\frac{8}{9}+\frac{21}{23}$$

Since \frac{23}{207} and \frac{18}{207} have the same denominator, add them by adding their numerators.

$$\frac{23+18}{207}+\frac{8}{9}+\frac{21}{23}$$

Add 23 and 18 to get 41.

$$\frac{41}{207}+\frac{8}{9}+\frac{21}{23}$$

Least common multiple of 207 and 9 is 207. Convert \frac{41}{207} and \frac{8}{9} to fractions with denominator 207.

$$\frac{41}{207}+\frac{184}{207}+\frac{21}{23}$$

Since \frac{41}{207} and \frac{184}{207} have the same denominator, add them by adding their numerators.

$$\frac{41+184}{207}+\frac{21}{23}$$

Add 41 and 184 to get 225.

$$\frac{225}{207}+\frac{21}{23}$$

Reduce the fraction \frac{225}{207} to lowest terms by extracting and canceling out 9.

$$\frac{25}{23}+\frac{21}{23}$$

Since \frac{25}{23} and \frac{21}{23} have the same denominator, add them by adding their numerators.

$$\frac{25+21}{23}$$

Add 25 and 21 to get 46.

$$\frac{46}{23}$$

Divide 46 by 23 to get 2.

$$2$$

Factor

$$2$$