Solve 21/6+(33/5div11/8)

$$2 \frac { 1 } { 6 } + ( 3 \frac { 3 } { 5 } \div 1 \frac { 1 } { 8 } )$$

Evaluate

$$\frac{161}{30}\approx 5.366666667$$

Solution Steps

Multiply 2 and 6 to get 12.

$$\frac{12+1}{6}+\frac{\frac{3\times 5+3}{5}}{\frac{1\times 8+1}{8}}$$

Add 12 and 1 to get 13.

$$\frac{13}{6}+\frac{\frac{3\times 5+3}{5}}{\frac{1\times 8+1}{8}}$$

Divide \frac{3\times 5+3}{5} by \frac{1\times 8+1}{8} by multiplying \frac{3\times 5+3}{5} by the reciprocal of \frac{1\times 8+1}{8}.

$$\frac{13}{6}+\frac{\left(3\times 5+3\right)\times 8}{5\left(1\times 8+1\right)}$$

Multiply 3 and 5 to get 15.

$$\frac{13}{6}+\frac{\left(15+3\right)\times 8}{5\left(1\times 8+1\right)}$$

Add 15 and 3 to get 18.

$$\frac{13}{6}+\frac{18\times 8}{5\left(1\times 8+1\right)}$$

Multiply 18 and 8 to get 144.

$$\frac{13}{6}+\frac{144}{5\left(1\times 8+1\right)}$$

Multiply 1 and 8 to get 8.

$$\frac{13}{6}+\frac{144}{5\left(8+1\right)}$$

Add 8 and 1 to get 9.

$$\frac{13}{6}+\frac{144}{5\times 9}$$

Multiply 5 and 9 to get 45.

$$\frac{13}{6}+\frac{144}{45}$$

Reduce the fraction \frac{144}{45} to lowest terms by extracting and canceling out 9.

$$\frac{13}{6}+\frac{16}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{13}{6} and \frac{16}{5} to fractions with denominator 30.

$$\frac{65}{30}+\frac{96}{30}$$

Since \frac{65}{30} and \frac{96}{30} have the same denominator, add them by adding their numerators.

$$\frac{65+96}{30}$$

Add 65 and 96 to get 161.

$$\frac{161}{30}$$

Factor

$$\frac{7 \cdot 23}{2 \cdot 3 \cdot 5} = 5\frac{11}{30} = 5.366666666666666$$