Solve 71/12+[12/5+{31/4-(11/2-frac{1}{2})}]

$$7 \frac { 1 } { 12 } + [ 1 \frac { 2 } { 5 } + \{ 3 \frac { 1 } { 4 } - ( 1 \frac { 1 } { 2 } - \frac { 1 } { 2 } ) \} ]$$

Evaluate

$$\frac{161}{15}\approx 10.733333333$$

Solution Steps

Multiply 7 and 12 to get 84.

$$\frac{84+1}{12}+\frac{1\times 5+2}{5}+\frac{3\times 4+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Add 84 and 1 to get 85.

$$\frac{85}{12}+\frac{1\times 5+2}{5}+\frac{3\times 4+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Multiply 1 and 5 to get 5.

$$\frac{85}{12}+\frac{5+2}{5}+\frac{3\times 4+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Add 5 and 2 to get 7.

$$\frac{85}{12}+\frac{7}{5}+\frac{3\times 4+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Least common multiple of 12 and 5 is 60. Convert \frac{85}{12} and \frac{7}{5} to fractions with denominator 60.

$$\frac{425}{60}+\frac{84}{60}+\frac{3\times 4+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Since \frac{425}{60} and \frac{84}{60} have the same denominator, add them by adding their numerators.

$$\frac{425+84}{60}+\frac{3\times 4+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Add 425 and 84 to get 509.

$$\frac{509}{60}+\frac{3\times 4+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Multiply 3 and 4 to get 12.

$$\frac{509}{60}+\frac{12+1}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Add 12 and 1 to get 13.

$$\frac{509}{60}+\frac{13}{4}-\left(\frac{1\times 2+1}{2}-\frac{1}{2}\right)$$

Multiply 1 and 2 to get 2.

$$\frac{509}{60}+\frac{13}{4}-\left(\frac{2+1}{2}-\frac{1}{2}\right)$$

Add 2 and 1 to get 3.

$$\frac{509}{60}+\frac{13}{4}-\left(\frac{3}{2}-\frac{1}{2}\right)$$

Since \frac{3}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{509}{60}+\frac{13}{4}-\frac{3-1}{2}$$

Subtract 1 from 3 to get 2.

$$\frac{509}{60}+\frac{13}{4}-\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$\frac{509}{60}+\frac{13}{4}-1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{509}{60}+\frac{13}{4}-\frac{4}{4}$$

Since \frac{13}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{509}{60}+\frac{13-4}{4}$$

Subtract 4 from 13 to get 9.

$$\frac{509}{60}+\frac{9}{4}$$

Least common multiple of 60 and 4 is 60. Convert \frac{509}{60} and \frac{9}{4} to fractions with denominator 60.

$$\frac{509}{60}+\frac{135}{60}$$

Since \frac{509}{60} and \frac{135}{60} have the same denominator, add them by adding their numerators.

$$\frac{509+135}{60}$$

Add 509 and 135 to get 644.

$$\frac{644}{60}$$

Reduce the fraction \frac{644}{60} to lowest terms by extracting and canceling out 4.

$$\frac{161}{15}$$

Factor

$$\frac{7 \cdot 23}{3 \cdot 5} = 10\frac{11}{15} = 10.733333333333333$$