Solve 11*5/8+0.625*13+9/17*14+20div18/9

$$11 \times \frac{ 5 }{ 8 } +0.625 \times 13+ \frac{ 9 }{ 17 } \times 14+20 \div 1 \frac { 8 } { 9 }$$

Evaluate

$$33$$

Solution Steps

Express 11\times \frac{5}{8} as a single fraction.

$$\frac{11\times 5}{8}+0.625\times 13+\frac{9}{17}\times 14+\frac{20}{\frac{1\times 9+8}{9}}$$

Multiply 11 and 5 to get 55.

$$\frac{55}{8}+0.625\times 13+\frac{9}{17}\times 14+\frac{20}{\frac{1\times 9+8}{9}}$$

Multiply 0.625 and 13 to get 8.125.

$$\frac{55}{8}+8.125+\frac{9}{17}\times 14+\frac{20}{\frac{1\times 9+8}{9}}$$

Convert decimal number 8.125 to fraction \frac{8125}{1000}. Reduce the fraction \frac{8125}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{55}{8}+\frac{65}{8}+\frac{9}{17}\times 14+\frac{20}{\frac{1\times 9+8}{9}}$$

Since \frac{55}{8} and \frac{65}{8} have the same denominator, add them by adding their numerators.

$$\frac{55+65}{8}+\frac{9}{17}\times 14+\frac{20}{\frac{1\times 9+8}{9}}$$

Add 55 and 65 to get 120.

$$\frac{120}{8}+\frac{9}{17}\times 14+\frac{20}{\frac{1\times 9+8}{9}}$$

Divide 120 by 8 to get 15.

$$15+\frac{9}{17}\times 14+\frac{20}{\frac{1\times 9+8}{9}}$$

Express \frac{9}{17}\times 14 as a single fraction.

$$15+\frac{9\times 14}{17}+\frac{20}{\frac{1\times 9+8}{9}}$$

Multiply 9 and 14 to get 126.

$$15+\frac{126}{17}+\frac{20}{\frac{1\times 9+8}{9}}$$

Convert 15 to fraction \frac{255}{17}.

$$\frac{255}{17}+\frac{126}{17}+\frac{20}{\frac{1\times 9+8}{9}}$$

Since \frac{255}{17} and \frac{126}{17} have the same denominator, add them by adding their numerators.

$$\frac{255+126}{17}+\frac{20}{\frac{1\times 9+8}{9}}$$

Add 255 and 126 to get 381.

$$\frac{381}{17}+\frac{20}{\frac{1\times 9+8}{9}}$$

Divide 20 by \frac{1\times 9+8}{9} by multiplying 20 by the reciprocal of \frac{1\times 9+8}{9}.

$$\frac{381}{17}+\frac{20\times 9}{1\times 9+8}$$

Multiply 20 and 9 to get 180.

$$\frac{381}{17}+\frac{180}{1\times 9+8}$$

Multiply 1 and 9 to get 9.

$$\frac{381}{17}+\frac{180}{9+8}$$

Add 9 and 8 to get 17.

$$\frac{381}{17}+\frac{180}{17}$$

Since \frac{381}{17} and \frac{180}{17} have the same denominator, add them by adding their numerators.

$$\frac{381+180}{17}$$

Add 381 and 180 to get 561.

$$\frac{561}{17}$$

Divide 561 by 17 to get 33.

$$33$$

Factor

$$3\times 11$$