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

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

Evaluate

$$\frac{71}{8}=8.875$$

Solution Steps

Convert 3 to fraction \frac{12}{4}.

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

Since \frac{12}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

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

Add 12 and 5 to get 17.

$$\frac{17}{4}-\left(-\frac{3}{8}-5+\frac{3}{4}\right)$$

Convert 5 to fraction \frac{40}{8}.

$$\frac{17}{4}-\left(-\frac{3}{8}-\frac{40}{8}+\frac{3}{4}\right)$$

Since -\frac{3}{8} and \frac{40}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{4}-\left(\frac{-3-40}{8}+\frac{3}{4}\right)$$

Subtract 40 from -3 to get -43.

$$\frac{17}{4}-\left(-\frac{43}{8}+\frac{3}{4}\right)$$

Least common multiple of 8 and 4 is 8. Convert -\frac{43}{8} and \frac{3}{4} to fractions with denominator 8.

$$\frac{17}{4}-\left(-\frac{43}{8}+\frac{6}{8}\right)$$

Since -\frac{43}{8} and \frac{6}{8} have the same denominator, add them by adding their numerators.

$$\frac{17}{4}-\frac{-43+6}{8}$$

Add -43 and 6 to get -37.

$$\frac{17}{4}-\left(-\frac{37}{8}\right)$$

The opposite of -\frac{37}{8} is \frac{37}{8}.

$$\frac{17}{4}+\frac{37}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{17}{4} and \frac{37}{8} to fractions with denominator 8.

$$\frac{34}{8}+\frac{37}{8}$$

Since \frac{34}{8} and \frac{37}{8} have the same denominator, add them by adding their numerators.

$$\frac{34+37}{8}$$

Add 34 and 37 to get 71.

$$\frac{71}{8}$$

Factor

$$\frac{71}{2 ^ {3}} = 8\frac{7}{8} = 8.875$$