Solve 33/8-18/9+21/5

$$3 \frac { 3 } { 8 } - 1 \frac { 8 } { 9 } + 2 \frac { 1 } { 5 }$$

Evaluate

$$\frac{1327}{360}\approx 3.686111111$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\frac{24+3}{8}-\frac{1\times 9+8}{9}+\frac{2\times 5+1}{5}$$

Add 24 and 3 to get 27.

$$\frac{27}{8}-\frac{1\times 9+8}{9}+\frac{2\times 5+1}{5}$$

Multiply 1 and 9 to get 9.

$$\frac{27}{8}-\frac{9+8}{9}+\frac{2\times 5+1}{5}$$

Add 9 and 8 to get 17.

$$\frac{27}{8}-\frac{17}{9}+\frac{2\times 5+1}{5}$$

Least common multiple of 8 and 9 is 72. Convert \frac{27}{8} and \frac{17}{9} to fractions with denominator 72.

$$\frac{243}{72}-\frac{136}{72}+\frac{2\times 5+1}{5}$$

Since \frac{243}{72} and \frac{136}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{243-136}{72}+\frac{2\times 5+1}{5}$$

Subtract 136 from 243 to get 107.

$$\frac{107}{72}+\frac{2\times 5+1}{5}$$

Multiply 2 and 5 to get 10.

$$\frac{107}{72}+\frac{10+1}{5}$$

Add 10 and 1 to get 11.

$$\frac{107}{72}+\frac{11}{5}$$

Least common multiple of 72 and 5 is 360. Convert \frac{107}{72} and \frac{11}{5} to fractions with denominator 360.

$$\frac{535}{360}+\frac{792}{360}$$

Since \frac{535}{360} and \frac{792}{360} have the same denominator, add them by adding their numerators.

$$\frac{535+792}{360}$$

Add 535 and 792 to get 1327.

$$\frac{1327}{360}$$

Factor

$$\frac{1327}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 3\frac{247}{360} = 3.686111111111111$$