Solve left(57/36-41/18+11/72right)36div78-1/2

$$\left( 5 \frac{ 7 }{ 36 } -4 \frac{ 1 }{ 18 } +1 \frac{ 1 }{ 72 } \right) 36 \div 78- \frac{ 1 }{ 2 }$$

Evaluate

$$\frac{77}{156}\approx 0.493589744$$

Solution Steps

Multiply 5 and 36 to get 180.

$$\frac{\left(\frac{180+7}{36}-\frac{4\times 18+1}{18}+\frac{1\times 72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Add 180 and 7 to get 187.

$$\frac{\left(\frac{187}{36}-\frac{4\times 18+1}{18}+\frac{1\times 72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Multiply 4 and 18 to get 72.

$$\frac{\left(\frac{187}{36}-\frac{72+1}{18}+\frac{1\times 72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Add 72 and 1 to get 73.

$$\frac{\left(\frac{187}{36}-\frac{73}{18}+\frac{1\times 72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Least common multiple of 36 and 18 is 36. Convert \frac{187}{36} and \frac{73}{18} to fractions with denominator 36.

$$\frac{\left(\frac{187}{36}-\frac{146}{36}+\frac{1\times 72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Since \frac{187}{36} and \frac{146}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{187-146}{36}+\frac{1\times 72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Subtract 146 from 187 to get 41.

$$\frac{\left(\frac{41}{36}+\frac{1\times 72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Multiply 1 and 72 to get 72.

$$\frac{\left(\frac{41}{36}+\frac{72+1}{72}\right)\times 36}{78}-\frac{1}{2}$$

Add 72 and 1 to get 73.

$$\frac{\left(\frac{41}{36}+\frac{73}{72}\right)\times 36}{78}-\frac{1}{2}$$

Least common multiple of 36 and 72 is 72. Convert \frac{41}{36} and \frac{73}{72} to fractions with denominator 72.

$$\frac{\left(\frac{82}{72}+\frac{73}{72}\right)\times 36}{78}-\frac{1}{2}$$

Since \frac{82}{72} and \frac{73}{72} have the same denominator, add them by adding their numerators.

$$\frac{\frac{82+73}{72}\times 36}{78}-\frac{1}{2}$$

Add 82 and 73 to get 155.

$$\frac{\frac{155}{72}\times 36}{78}-\frac{1}{2}$$

Express \frac{155}{72}\times 36 as a single fraction.

$$\frac{\frac{155\times 36}{72}}{78}-\frac{1}{2}$$

Multiply 155 and 36 to get 5580.

$$\frac{\frac{5580}{72}}{78}-\frac{1}{2}$$

Reduce the fraction \frac{5580}{72} to lowest terms by extracting and canceling out 36.

$$\frac{\frac{155}{2}}{78}-\frac{1}{2}$$

Express \frac{\frac{155}{2}}{78} as a single fraction.

$$\frac{155}{2\times 78}-\frac{1}{2}$$

Multiply 2 and 78 to get 156.

$$\frac{155}{156}-\frac{1}{2}$$

Least common multiple of 156 and 2 is 156. Convert \frac{155}{156} and \frac{1}{2} to fractions with denominator 156.

$$\frac{155}{156}-\frac{78}{156}$$

Since \frac{155}{156} and \frac{78}{156} have the same denominator, subtract them by subtracting their numerators.

$$\frac{155-78}{156}$$

Subtract 78 from 155 to get 77.

$$\frac{77}{156}$$

Factor

$$\frac{7 \cdot 11}{2 ^ {2} \cdot 3 \cdot 13} = 0.4935897435897436$$