Solve 133/4-2/(-2frac{1{2})-(-3/4)}

$$13 \frac { 3 } { 4 } - \frac { 2 } { ( - 2 \frac { 1 } { 2 } ) - ( - \frac { 3 } { 4 } ) }$$

Evaluate

$$\frac{417}{28}\approx 14.892857143$$

Solution Steps

Multiply 13 and 4 to get 52.

$$\frac{52+3}{4}-\frac{2}{-\frac{2\times 2+1}{2}-\left(-\frac{3}{4}\right)}$$

Add 52 and 3 to get 55.

$$\frac{55}{4}-\frac{2}{-\frac{2\times 2+1}{2}-\left(-\frac{3}{4}\right)}$$

Multiply 2 and 2 to get 4.

$$\frac{55}{4}-\frac{2}{-\frac{4+1}{2}-\left(-\frac{3}{4}\right)}$$

Add 4 and 1 to get 5.

$$\frac{55}{4}-\frac{2}{-\frac{5}{2}-\left(-\frac{3}{4}\right)}$$

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

$$\frac{55}{4}-\frac{2}{-\frac{5}{2}+\frac{3}{4}}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{5}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{55}{4}-\frac{2}{-\frac{10}{4}+\frac{3}{4}}$$

Since -\frac{10}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{55}{4}-\frac{2}{\frac{-10+3}{4}}$$

Add -10 and 3 to get -7.

$$\frac{55}{4}-\frac{2}{-\frac{7}{4}}$$

Divide 2 by -\frac{7}{4} by multiplying 2 by the reciprocal of -\frac{7}{4}.

$$\frac{55}{4}-2\left(-\frac{4}{7}\right)$$

Express 2\left(-\frac{4}{7}\right) as a single fraction.

$$\frac{55}{4}-\frac{2\left(-4\right)}{7}$$

Multiply 2 and -4 to get -8.

$$\frac{55}{4}-\frac{-8}{7}$$

Fraction \frac{-8}{7} can be rewritten as -\frac{8}{7} by extracting the negative sign.

$$\frac{55}{4}-\left(-\frac{8}{7}\right)$$

The opposite of -\frac{8}{7} is \frac{8}{7}.

$$\frac{55}{4}+\frac{8}{7}$$

Least common multiple of 4 and 7 is 28. Convert \frac{55}{4} and \frac{8}{7} to fractions with denominator 28.

$$\frac{385}{28}+\frac{32}{28}$$

Since \frac{385}{28} and \frac{32}{28} have the same denominator, add them by adding their numerators.

$$\frac{385+32}{28}$$

Add 385 and 32 to get 417.

$$\frac{417}{28}$$

Factor

$$\frac{3 \cdot 139}{2 ^ {2} \cdot 7} = 14\frac{25}{28} = 14.892857142857142$$