Solve 109/55+1146/55+9/10-65/18:1frac{2}{3}*2-2frac{13}{15}

$$10 \frac { 9 } { 55 } + 11 \frac { 46 } { 55 } + \frac { 9 } { 10 } - 6 \frac { 5 } { 18 } : 1 \frac { 2 } { 3 } \cdot 2 - 2 \frac { 13 } { 15 }$$

Evaluate

$$\frac{25}{2}=12.5$$

Solution Steps

Multiply 10 and 55 to get 550.

$$\frac{550+9}{55}+\frac{11\times 55+46}{55}+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Add 550 and 9 to get 559.

$$\frac{559}{55}+\frac{11\times 55+46}{55}+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Multiply 11 and 55 to get 605.

$$\frac{559}{55}+\frac{605+46}{55}+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Add 605 and 46 to get 651.

$$\frac{559}{55}+\frac{651}{55}+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Since \frac{559}{55} and \frac{651}{55} have the same denominator, add them by adding their numerators.

$$\frac{559+651}{55}+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Add 559 and 651 to get 1210.

$$\frac{1210}{55}+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Divide 1210 by 55 to get 22.

$$22+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Convert 22 to fraction \frac{220}{10}.

$$\frac{220}{10}+\frac{9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Since \frac{220}{10} and \frac{9}{10} have the same denominator, add them by adding their numerators.

$$\frac{220+9}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Add 220 and 9 to get 229.

$$\frac{229}{10}-\frac{\frac{6\times 18+5}{18}}{\frac{1\times 3+2}{3}}\times 2-\frac{2\times 15+13}{15}$$

Divide \frac{6\times 18+5}{18} by \frac{1\times 3+2}{3} by multiplying \frac{6\times 18+5}{18} by the reciprocal of \frac{1\times 3+2}{3}.

$$\frac{229}{10}-\frac{\left(6\times 18+5\right)\times 3}{18\left(1\times 3+2\right)}\times 2-\frac{2\times 15+13}{15}$$

Cancel out 3 in both numerator and denominator.

$$\frac{229}{10}-\frac{5+6\times 18}{6\left(2+3\right)}\times 2-\frac{2\times 15+13}{15}$$

Multiply 6 and 18 to get 108.

$$\frac{229}{10}-\frac{5+108}{6\left(2+3\right)}\times 2-\frac{2\times 15+13}{15}$$

Add 5 and 108 to get 113.

$$\frac{229}{10}-\frac{113}{6\left(2+3\right)}\times 2-\frac{2\times 15+13}{15}$$

Add 2 and 3 to get 5.

$$\frac{229}{10}-\frac{113}{6\times 5}\times 2-\frac{2\times 15+13}{15}$$

Multiply 6 and 5 to get 30.

$$\frac{229}{10}-\frac{113}{30}\times 2-\frac{2\times 15+13}{15}$$

Express \frac{113}{30}\times 2 as a single fraction.

$$\frac{229}{10}-\frac{113\times 2}{30}-\frac{2\times 15+13}{15}$$

Multiply 113 and 2 to get 226.

$$\frac{229}{10}-\frac{226}{30}-\frac{2\times 15+13}{15}$$

Reduce the fraction \frac{226}{30} to lowest terms by extracting and canceling out 2.

$$\frac{229}{10}-\frac{113}{15}-\frac{2\times 15+13}{15}$$

Least common multiple of 10 and 15 is 30. Convert \frac{229}{10} and \frac{113}{15} to fractions with denominator 30.

$$\frac{687}{30}-\frac{226}{30}-\frac{2\times 15+13}{15}$$

Since \frac{687}{30} and \frac{226}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{687-226}{30}-\frac{2\times 15+13}{15}$$

Subtract 226 from 687 to get 461.

$$\frac{461}{30}-\frac{2\times 15+13}{15}$$

Multiply 2 and 15 to get 30.

$$\frac{461}{30}-\frac{30+13}{15}$$

Add 30 and 13 to get 43.

$$\frac{461}{30}-\frac{43}{15}$$

Least common multiple of 30 and 15 is 30. Convert \frac{461}{30} and \frac{43}{15} to fractions with denominator 30.

$$\frac{461}{30}-\frac{86}{30}$$

Since \frac{461}{30} and \frac{86}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{461-86}{30}$$

Subtract 86 from 461 to get 375.

$$\frac{375}{30}$$

Reduce the fraction \frac{375}{30} to lowest terms by extracting and canceling out 15.

$$\frac{25}{2}$$

Factor

$$\frac{5 ^ {2}}{2} = 12\frac{1}{2} = 12.5$$