Solve 7-(-11/8)+21/2-(-3/4)

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

Evaluate

$$\frac{91}{8}=11.375$$

Solution Steps

Multiply 1 and 8 to get 8.

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

Add 8 and 1 to get 9.

$$7-\left(-\frac{9}{8}\right)+\frac{2\times 2+1}{2}-\left(-\frac{3}{4}\right)$$

The opposite of -\frac{9}{8} is \frac{9}{8}.

$$7+\frac{9}{8}+\frac{2\times 2+1}{2}-\left(-\frac{3}{4}\right)$$

Convert 7 to fraction \frac{56}{8}.

$$\frac{56}{8}+\frac{9}{8}+\frac{2\times 2+1}{2}-\left(-\frac{3}{4}\right)$$

Since \frac{56}{8} and \frac{9}{8} have the same denominator, add them by adding their numerators.

$$\frac{56+9}{8}+\frac{2\times 2+1}{2}-\left(-\frac{3}{4}\right)$$

Add 56 and 9 to get 65.

$$\frac{65}{8}+\frac{2\times 2+1}{2}-\left(-\frac{3}{4}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{65}{8}+\frac{4+1}{2}-\left(-\frac{3}{4}\right)$$

Add 4 and 1 to get 5.

$$\frac{65}{8}+\frac{5}{2}-\left(-\frac{3}{4}\right)$$

Least common multiple of 8 and 2 is 8. Convert \frac{65}{8} and \frac{5}{2} to fractions with denominator 8.

$$\frac{65}{8}+\frac{20}{8}-\left(-\frac{3}{4}\right)$$

Since \frac{65}{8} and \frac{20}{8} have the same denominator, add them by adding their numerators.

$$\frac{65+20}{8}-\left(-\frac{3}{4}\right)$$

Add 65 and 20 to get 85.

$$\frac{85}{8}-\left(-\frac{3}{4}\right)$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$\frac{85}{8}+\frac{3}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{85}{8} and \frac{3}{4} to fractions with denominator 8.

$$\frac{85}{8}+\frac{6}{8}$$

Since \frac{85}{8} and \frac{6}{8} have the same denominator, add them by adding their numerators.

$$\frac{85+6}{8}$$

Add 85 and 6 to get 91.

$$\frac{91}{8}$$

Factor

$$\frac{7 \cdot 13}{2 ^ {3}} = 11\frac{3}{8} = 11.375$$