Solve 35/8-(3/8-(3/4+5/8))

$$3 \frac{ 5 }{ 8 } -( \frac{ 3 }{ 8 } -( \frac{ 3 }{ 4 } + \frac{ 5 }{ 8 } ))$$

Evaluate

$$\frac{37}{8}=4.625$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\frac{24+5}{8}-\left(\frac{3}{8}-\left(\frac{3}{4}+\frac{5}{8}\right)\right)$$

Add 24 and 5 to get 29.

$$\frac{29}{8}-\left(\frac{3}{8}-\left(\frac{3}{4}+\frac{5}{8}\right)\right)$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{29}{8}-\left(\frac{3}{8}-\left(\frac{6}{8}+\frac{5}{8}\right)\right)$$

Since \frac{6}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{29}{8}-\left(\frac{3}{8}-\frac{6+5}{8}\right)$$

Add 6 and 5 to get 11.

$$\frac{29}{8}-\left(\frac{3}{8}-\frac{11}{8}\right)$$

Since \frac{3}{8} and \frac{11}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29}{8}-\frac{3-11}{8}$$

Subtract 11 from 3 to get -8.

$$\frac{29}{8}-\frac{-8}{8}$$

Divide -8 by 8 to get -1.

$$\frac{29}{8}-\left(-1\right)$$

The opposite of -1 is 1.

$$\frac{29}{8}+1$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{29}{8}+\frac{8}{8}$$

Since \frac{29}{8} and \frac{8}{8} have the same denominator, add them by adding their numerators.

$$\frac{29+8}{8}$$

Add 29 and 8 to get 37.

$$\frac{37}{8}$$

Factor

$$\frac{37}{2 ^ {3}} = 4\frac{5}{8} = 4.625$$