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

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

Evaluate

$$-\frac{57}{4}=-14.25$$

Solution Steps

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

$$2-\frac{\frac{10}{4}+\frac{3}{4}}{1-\frac{4}{5}}$$

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

$$2-\frac{\frac{10+3}{4}}{1-\frac{4}{5}}$$

Add 10 and 3 to get 13.

$$2-\frac{\frac{13}{4}}{1-\frac{4}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$2-\frac{\frac{13}{4}}{\frac{5}{5}-\frac{4}{5}}$$

Since \frac{5}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{\frac{13}{4}}{\frac{5-4}{5}}$$

Subtract 4 from 5 to get 1.

$$2-\frac{\frac{13}{4}}{\frac{1}{5}}$$

Divide \frac{13}{4} by \frac{1}{5} by multiplying \frac{13}{4} by the reciprocal of \frac{1}{5}.

$$2-\frac{13}{4}\times 5$$

Express \frac{13}{4}\times 5 as a single fraction.

$$2-\frac{13\times 5}{4}$$

Multiply 13 and 5 to get 65.

$$2-\frac{65}{4}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{8}{4}-\frac{65}{4}$$

Since \frac{8}{4} and \frac{65}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-65}{4}$$

Subtract 65 from 8 to get -57.

$$-\frac{57}{4}$$

Factor

$$-\frac{57}{4} = -14\frac{1}{4} = -14.25$$