Solve (57/36-41/18+11/72)*36/78-frac{1{2}}

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

Evaluate

$$1$$

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.

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

Convert 78 to fraction \frac{156}{2}.

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

Since \frac{156}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 156 to get 155.

$$\frac{\frac{155}{2}}{\frac{155}{2}}$$

Divide \frac{155}{2} by \frac{155}{2} to get 1.

$$1$$

Factor

$$1$$