Solve (57/56-41/8+1/12)*36/78-frac{1{2}}

$$\frac { ( 5 \frac { 7 } { 56 } - 4 \frac { 1 } { 8 } + \frac { 1 } { 12 } ) \times 36 } { 78 - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{78}{155}\approx 0.503225806$$

Solution Steps

Multiply 5 and 56 to get 280.

$$\frac{\left(\frac{280+7}{56}-\frac{4\times 8+1}{8}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Add 280 and 7 to get 287.

$$\frac{\left(\frac{287}{56}-\frac{4\times 8+1}{8}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Reduce the fraction \frac{287}{56} to lowest terms by extracting and canceling out 7.

$$\frac{\left(\frac{41}{8}-\frac{4\times 8+1}{8}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Multiply 4 and 8 to get 32.

$$\frac{\left(\frac{41}{8}-\frac{32+1}{8}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Add 32 and 1 to get 33.

$$\frac{\left(\frac{41}{8}-\frac{33}{8}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Since \frac{41}{8} and \frac{33}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{41-33}{8}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Subtract 33 from 41 to get 8.

$$\frac{\left(\frac{8}{8}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Divide 8 by 8 to get 1.

$$\frac{\left(1+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{\left(\frac{12}{12}+\frac{1}{12}\right)\times 36}{78-\frac{1}{2}}$$

Since \frac{12}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12+1}{12}\times 36}{78-\frac{1}{2}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{13}{12}\times 36}{78-\frac{1}{2}}$$

Express \frac{13}{12}\times 36 as a single fraction.

$$\frac{\frac{13\times 36}{12}}{78-\frac{1}{2}}$$

Multiply 13 and 36 to get 468.

$$\frac{\frac{468}{12}}{78-\frac{1}{2}}$$

Divide 468 by 12 to get 39.

$$\frac{39}{78-\frac{1}{2}}$$

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

$$\frac{39}{\frac{156}{2}-\frac{1}{2}}$$

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

$$\frac{39}{\frac{156-1}{2}}$$

Subtract 1 from 156 to get 155.

$$\frac{39}{\frac{155}{2}}$$

Divide 39 by \frac{155}{2} by multiplying 39 by the reciprocal of \frac{155}{2}.

$$39\times \frac{2}{155}$$

Express 39\times \frac{2}{155} as a single fraction.

$$\frac{39\times 2}{155}$$

Multiply 39 and 2 to get 78.

$$\frac{78}{155}$$

Factor

$$\frac{2 \cdot 3 \cdot 13}{5 \cdot 31} = 0.5032258064516129$$