Solve (4-5/8)-(5-3/4)+(3-1/2-3/8)

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

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Convert 4 to fraction \frac{32}{8}.

$$\frac{32}{8}-\frac{5}{8}-\left(5-\frac{3}{4}\right)+3-\frac{1}{2}-\frac{3}{8}$$

Since \frac{32}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-5}{8}-\left(5-\frac{3}{4}\right)+3-\frac{1}{2}-\frac{3}{8}$$

Subtract 5 from 32 to get 27.

$$\frac{27}{8}-\left(5-\frac{3}{4}\right)+3-\frac{1}{2}-\frac{3}{8}$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{27}{8}-\left(\frac{20}{4}-\frac{3}{4}\right)+3-\frac{1}{2}-\frac{3}{8}$$

Since \frac{20}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27}{8}-\frac{20-3}{4}+3-\frac{1}{2}-\frac{3}{8}$$

Subtract 3 from 20 to get 17.

$$\frac{27}{8}-\frac{17}{4}+3-\frac{1}{2}-\frac{3}{8}$$

Least common multiple of 8 and 4 is 8. Convert \frac{27}{8} and \frac{17}{4} to fractions with denominator 8.

$$\frac{27}{8}-\frac{34}{8}+3-\frac{1}{2}-\frac{3}{8}$$

Since \frac{27}{8} and \frac{34}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-34}{8}+3-\frac{1}{2}-\frac{3}{8}$$

Subtract 34 from 27 to get -7.

$$-\frac{7}{8}+3-\frac{1}{2}-\frac{3}{8}$$

Convert 3 to fraction \frac{24}{8}.

$$-\frac{7}{8}+\frac{24}{8}-\frac{1}{2}-\frac{3}{8}$$

Since -\frac{7}{8} and \frac{24}{8} have the same denominator, add them by adding their numerators.

$$\frac{-7+24}{8}-\frac{1}{2}-\frac{3}{8}$$

Add -7 and 24 to get 17.

$$\frac{17}{8}-\frac{1}{2}-\frac{3}{8}$$

Least common multiple of 8 and 2 is 8. Convert \frac{17}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{17}{8}-\frac{4}{8}-\frac{3}{8}$$

Since \frac{17}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-4}{8}-\frac{3}{8}$$

Subtract 4 from 17 to get 13.

$$\frac{13}{8}-\frac{3}{8}$$

Since \frac{13}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-3}{8}$$

Subtract 3 from 13 to get 10.

$$\frac{10}{8}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$