Solve (3/8+7/9)+(3/5+2/6)

$$( \frac { 3 } { 8 } + \frac { 7 } { 9 } ) + ( \frac { 3 } { 5 } + \frac { 2 } { 6 } )$$

Evaluate

$$\frac{751}{360}\approx 2.086111111$$

Solution Steps

Least common multiple of 8 and 9 is 72. Convert \frac{3}{8} and \frac{7}{9} to fractions with denominator 72.

$$\frac{27}{72}+\frac{56}{72}+\frac{3}{5}+\frac{2}{6}$$

Since \frac{27}{72} and \frac{56}{72} have the same denominator, add them by adding their numerators.

$$\frac{27+56}{72}+\frac{3}{5}+\frac{2}{6}$$

Add 27 and 56 to get 83.

$$\frac{83}{72}+\frac{3}{5}+\frac{2}{6}$$

Least common multiple of 72 and 5 is 360. Convert \frac{83}{72} and \frac{3}{5} to fractions with denominator 360.

$$\frac{415}{360}+\frac{216}{360}+\frac{2}{6}$$

Since \frac{415}{360} and \frac{216}{360} have the same denominator, add them by adding their numerators.

$$\frac{415+216}{360}+\frac{2}{6}$$

Add 415 and 216 to get 631.

$$\frac{631}{360}+\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{631}{360}+\frac{1}{3}$$

Least common multiple of 360 and 3 is 360. Convert \frac{631}{360} and \frac{1}{3} to fractions with denominator 360.

$$\frac{631}{360}+\frac{120}{360}$$

Since \frac{631}{360} and \frac{120}{360} have the same denominator, add them by adding their numerators.

$$\frac{631+120}{360}$$

Add 631 and 120 to get 751.

$$\frac{751}{360}$$

Factor

$$\frac{751}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 2\frac{31}{360} = 2.0861111111111112$$