Solve (11/10+7div(31/12-15/8))*11/59

$$( 1 \frac { 1 } { 10 } + 7 \div ( 3 \frac { 1 } { 12 } - 1 \frac { 5 } { 8 } ) ) \times 1 \frac { 1 } { 59 }$$

Evaluate

$$6$$

Solution Steps

Multiply 1 and 10 to get 10.

$$\left(\frac{10+1}{10}+\frac{7}{\frac{3\times 12+1}{12}-\frac{1\times 8+5}{8}}\right)\times \frac{1\times 59+1}{59}$$

Add 10 and 1 to get 11.

$$\left(\frac{11}{10}+\frac{7}{\frac{3\times 12+1}{12}-\frac{1\times 8+5}{8}}\right)\times \frac{1\times 59+1}{59}$$

Multiply 3 and 12 to get 36.

$$\left(\frac{11}{10}+\frac{7}{\frac{36+1}{12}-\frac{1\times 8+5}{8}}\right)\times \frac{1\times 59+1}{59}$$

Add 36 and 1 to get 37.

$$\left(\frac{11}{10}+\frac{7}{\frac{37}{12}-\frac{1\times 8+5}{8}}\right)\times \frac{1\times 59+1}{59}$$

Multiply 1 and 8 to get 8.

$$\left(\frac{11}{10}+\frac{7}{\frac{37}{12}-\frac{8+5}{8}}\right)\times \frac{1\times 59+1}{59}$$

Add 8 and 5 to get 13.

$$\left(\frac{11}{10}+\frac{7}{\frac{37}{12}-\frac{13}{8}}\right)\times \frac{1\times 59+1}{59}$$

Least common multiple of 12 and 8 is 24. Convert \frac{37}{12} and \frac{13}{8} to fractions with denominator 24.

$$\left(\frac{11}{10}+\frac{7}{\frac{74}{24}-\frac{39}{24}}\right)\times \frac{1\times 59+1}{59}$$

Since \frac{74}{24} and \frac{39}{24} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{11}{10}+\frac{7}{\frac{74-39}{24}}\right)\times \frac{1\times 59+1}{59}$$

Subtract 39 from 74 to get 35.

$$\left(\frac{11}{10}+\frac{7}{\frac{35}{24}}\right)\times \frac{1\times 59+1}{59}$$

Divide 7 by \frac{35}{24} by multiplying 7 by the reciprocal of \frac{35}{24}.

$$\left(\frac{11}{10}+7\times \frac{24}{35}\right)\times \frac{1\times 59+1}{59}$$

Express 7\times \frac{24}{35} as a single fraction.

$$\left(\frac{11}{10}+\frac{7\times 24}{35}\right)\times \frac{1\times 59+1}{59}$$

Multiply 7 and 24 to get 168.

$$\left(\frac{11}{10}+\frac{168}{35}\right)\times \frac{1\times 59+1}{59}$$

Reduce the fraction \frac{168}{35} to lowest terms by extracting and canceling out 7.

$$\left(\frac{11}{10}+\frac{24}{5}\right)\times \frac{1\times 59+1}{59}$$

Least common multiple of 10 and 5 is 10. Convert \frac{11}{10} and \frac{24}{5} to fractions with denominator 10.

$$\left(\frac{11}{10}+\frac{48}{10}\right)\times \frac{1\times 59+1}{59}$$

Since \frac{11}{10} and \frac{48}{10} have the same denominator, add them by adding their numerators.

$$\frac{11+48}{10}\times \frac{1\times 59+1}{59}$$

Add 11 and 48 to get 59.

$$\frac{59}{10}\times \frac{1\times 59+1}{59}$$

Multiply 1 and 59 to get 59.

$$\frac{59}{10}\times \frac{59+1}{59}$$

Add 59 and 1 to get 60.

$$\frac{59}{10}\times \frac{60}{59}$$

Multiply \frac{59}{10} times \frac{60}{59} by multiplying numerator times numerator and denominator times denominator.

$$\frac{59\times 60}{10\times 59}$$

Cancel out 59 in both numerator and denominator.

$$\frac{60}{10}$$

Divide 60 by 10 to get 6.

$$6$$

Factor

$$2\times 3$$