Solve [(1-1/2)^2+5/12-1/5]*(7/4-frac{1}{8}+frac{5}{12})+frac{3}{7}-frac{1}{5}

$$[ ( 1 - \frac { 1 } { 2 } ) ^ { 2 } + \frac { 5 } { 12 } - \frac { 1 } { 5 } ] \cdot ( \frac { 7 } { 4 } - \frac { 1 } { 8 } + \frac { 5 } { 12 } ) + \frac { 3 } { 7 } - \frac { 1 } { 5 }$$

Evaluate

$$\frac{2977}{2520}\approx 1.181349206$$

Solution Steps

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\left(\left(\frac{1}{2}\right)^{2}+\frac{5}{12}-\frac{1}{5}\right)\left(\frac{7}{4}-\frac{1}{8}+\frac{5}{12}\right)+\frac{3}{7}-\frac{1}{5}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\left(\frac{1}{4}+\frac{5}{12}-\frac{1}{5}\right)\left(\frac{7}{4}-\frac{1}{8}+\frac{5}{12}\right)+\frac{3}{7}-\frac{1}{5}$$

Add \frac{1}{4} and \frac{5}{12} to get \frac{2}{3}.

$$\left(\frac{2}{3}-\frac{1}{5}\right)\left(\frac{7}{4}-\frac{1}{8}+\frac{5}{12}\right)+\frac{3}{7}-\frac{1}{5}$$

Subtract \frac{1}{5} from \frac{2}{3} to get \frac{7}{15}.

$$\frac{7}{15}\left(\frac{7}{4}-\frac{1}{8}+\frac{5}{12}\right)+\frac{3}{7}-\frac{1}{5}$$

Subtract \frac{1}{8} from \frac{7}{4} to get \frac{13}{8}.

$$\frac{7}{15}\left(\frac{13}{8}+\frac{5}{12}\right)+\frac{3}{7}-\frac{1}{5}$$

Add \frac{13}{8} and \frac{5}{12} to get \frac{49}{24}.

$$\frac{7}{15}\times \frac{49}{24}+\frac{3}{7}-\frac{1}{5}$$

Multiply \frac{7}{15} and \frac{49}{24} to get \frac{343}{360}.

$$\frac{343}{360}+\frac{3}{7}-\frac{1}{5}$$

Add \frac{343}{360} and \frac{3}{7} to get \frac{3481}{2520}.

$$\frac{3481}{2520}-\frac{1}{5}$$

Subtract \frac{1}{5} from \frac{3481}{2520} to get \frac{2977}{2520}.

$$\frac{2977}{2520}$$

Factor

$$\frac{13 \cdot 229}{2 ^ {3} \cdot 3 ^ {2} \cdot 5 \cdot 7} = 1\frac{457}{2520} = 1.1813492063492064$$