Solve -47/8-(-51/2)+(-41/4)-(+31/8)=

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

Evaluate

$$-\frac{27}{4}=-6.75$$

Solution Steps

Multiply 4 and 8 to get 32.

$$-\frac{32+7}{8}-\left(-\frac{5\times 2+1}{2}\right)-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

Add 32 and 7 to get 39.

$$-\frac{39}{8}-\left(-\frac{5\times 2+1}{2}\right)-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

Multiply 5 and 2 to get 10.

$$-\frac{39}{8}-\left(-\frac{10+1}{2}\right)-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

Add 10 and 1 to get 11.

$$-\frac{39}{8}-\left(-\frac{11}{2}\right)-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

The opposite of -\frac{11}{2} is \frac{11}{2}.

$$-\frac{39}{8}+\frac{11}{2}-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

Least common multiple of 8 and 2 is 8. Convert -\frac{39}{8} and \frac{11}{2} to fractions with denominator 8.

$$-\frac{39}{8}+\frac{44}{8}-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

Since -\frac{39}{8} and \frac{44}{8} have the same denominator, add them by adding their numerators.

$$\frac{-39+44}{8}-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

Add -39 and 44 to get 5.

$$\frac{5}{8}-\frac{4\times 4+1}{4}-\frac{3\times 8+1}{8}$$

Multiply 4 and 4 to get 16.

$$\frac{5}{8}-\frac{16+1}{4}-\frac{3\times 8+1}{8}$$

Add 16 and 1 to get 17.

$$\frac{5}{8}-\frac{17}{4}-\frac{3\times 8+1}{8}$$

Least common multiple of 8 and 4 is 8. Convert \frac{5}{8} and \frac{17}{4} to fractions with denominator 8.

$$\frac{5}{8}-\frac{34}{8}-\frac{3\times 8+1}{8}$$

Since \frac{5}{8} and \frac{34}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-34}{8}-\frac{3\times 8+1}{8}$$

Subtract 34 from 5 to get -29.

$$-\frac{29}{8}-\frac{3\times 8+1}{8}$$

Multiply 3 and 8 to get 24.

$$-\frac{29}{8}-\frac{24+1}{8}$$

Add 24 and 1 to get 25.

$$-\frac{29}{8}-\frac{25}{8}$$

Since -\frac{29}{8} and \frac{25}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-29-25}{8}$$

Subtract 25 from -29 to get -54.

$$\frac{-54}{8}$$

Reduce the fraction \frac{-54}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{27}{4}$$

Factor

$$-\frac{27}{4} = -6\frac{3}{4} = -6.75$$