Solve 2-3/4[-8+5(2/3+3/5)]

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

Evaluate

$$\frac{13}{4}=3.25$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$2-\frac{3}{4}\left(-8+5\left(\frac{10}{15}+\frac{9}{15}\right)\right)$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$2-\frac{3}{4}\left(-8+5\times \frac{10+9}{15}\right)$$

Add 10 and 9 to get 19.

$$2-\frac{3}{4}\left(-8+5\times \frac{19}{15}\right)$$

Express 5\times \frac{19}{15} as a single fraction.

$$2-\frac{3}{4}\left(-8+\frac{5\times 19}{15}\right)$$

Multiply 5 and 19 to get 95.

$$2-\frac{3}{4}\left(-8+\frac{95}{15}\right)$$

Reduce the fraction \frac{95}{15} to lowest terms by extracting and canceling out 5.

$$2-\frac{3}{4}\left(-8+\frac{19}{3}\right)$$

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

$$2-\frac{3}{4}\left(-\frac{24}{3}+\frac{19}{3}\right)$$

Since -\frac{24}{3} and \frac{19}{3} have the same denominator, add them by adding their numerators.

$$2-\frac{3}{4}\times \frac{-24+19}{3}$$

Add -24 and 19 to get -5.

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

Multiply \frac{3}{4} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

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

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$2+\frac{5}{4}$$

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

$$\frac{8}{4}+\frac{5}{4}$$

Since \frac{8}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{8+5}{4}$$

Add 8 and 5 to get 13.

$$\frac{13}{4}$$

Factor

$$\frac{13}{2 ^ {2}} = 3\frac{1}{4} = 3.25$$