Solve 53/8-[33/5-{13/8-(3/4-frac{1}{2}-frac{1}{4})}]

$$5 \frac { 3 } { 8 } - [ 3 \frac { 3 } { 5 } - \{ 1 \frac { 3 } { 8 } - ( \frac { 3 } { 4 } - \frac { 1 } { 2 } - \frac { 1 } { 4 } ) \} ]$$

Evaluate

$$\frac{63}{20}=3.15$$

Solution Steps

Multiply 5 and 8 to get 40.

$$\frac{40+3}{8}-\left(\frac{3\times 5+3}{5}-\left(\frac{1\times 8+3}{8}-\left(\frac{3}{4}-\frac{1}{2}-\frac{1}{4}\right)\right)\right)$$

Add 40 and 3 to get 43.

$$\frac{43}{8}-\left(\frac{3\times 5+3}{5}-\left(\frac{1\times 8+3}{8}-\left(\frac{3}{4}-\frac{1}{2}-\frac{1}{4}\right)\right)\right)$$

Multiply 3 and 5 to get 15.

$$\frac{43}{8}-\left(\frac{15+3}{5}-\left(\frac{1\times 8+3}{8}-\left(\frac{3}{4}-\frac{1}{2}-\frac{1}{4}\right)\right)\right)$$

Add 15 and 3 to get 18.

$$\frac{43}{8}-\left(\frac{18}{5}-\left(\frac{1\times 8+3}{8}-\left(\frac{3}{4}-\frac{1}{2}-\frac{1}{4}\right)\right)\right)$$

Multiply 1 and 8 to get 8.

$$\frac{43}{8}-\left(\frac{18}{5}-\left(\frac{8+3}{8}-\left(\frac{3}{4}-\frac{1}{2}-\frac{1}{4}\right)\right)\right)$$

Add 8 and 3 to get 11.

$$\frac{43}{8}-\left(\frac{18}{5}-\left(\frac{11}{8}-\left(\frac{3}{4}-\frac{1}{2}-\frac{1}{4}\right)\right)\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{43}{8}-\left(\frac{18}{5}-\left(\frac{11}{8}-\left(\frac{3}{4}-\frac{2}{4}-\frac{1}{4}\right)\right)\right)$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43}{8}-\left(\frac{18}{5}-\left(\frac{11}{8}-\left(\frac{3-2}{4}-\frac{1}{4}\right)\right)\right)$$

Subtract 2 from 3 to get 1.

$$\frac{43}{8}-\left(\frac{18}{5}-\left(\frac{11}{8}-\left(\frac{1}{4}-\frac{1}{4}\right)\right)\right)$$

Subtract \frac{1}{4} from \frac{1}{4} to get 0.

$$\frac{43}{8}-\left(\frac{18}{5}-\left(\frac{11}{8}-0\right)\right)$$

Subtract 0 from \frac{11}{8} to get \frac{11}{8}.

$$\frac{43}{8}-\left(\frac{18}{5}-\frac{11}{8}\right)$$

Least common multiple of 5 and 8 is 40. Convert \frac{18}{5} and \frac{11}{8} to fractions with denominator 40.

$$\frac{43}{8}-\left(\frac{144}{40}-\frac{55}{40}\right)$$

Since \frac{144}{40} and \frac{55}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43}{8}-\frac{144-55}{40}$$

Subtract 55 from 144 to get 89.

$$\frac{43}{8}-\frac{89}{40}$$

Least common multiple of 8 and 40 is 40. Convert \frac{43}{8} and \frac{89}{40} to fractions with denominator 40.

$$\frac{215}{40}-\frac{89}{40}$$

Since \frac{215}{40} and \frac{89}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{215-89}{40}$$

Subtract 89 from 215 to get 126.

$$\frac{126}{40}$$

Reduce the fraction \frac{126}{40} to lowest terms by extracting and canceling out 2.

$$\frac{63}{20}$$

Factor

$$\frac{3 ^ {2} \cdot 7}{2 ^ {2} \cdot 5} = 3\frac{3}{20} = 3.15$$