Solve 1-8/3(-3/4)-{2-[3/4-1+2/5(-10+frac{15}{4})-1]}

$$1 - \frac { 8 } { 3 } ( - \frac { 3 } { 4 } ) - \{ 2 - [ \frac { 3 } { 4 } - 1 + \frac { 2 } { 5 } ( - 10 + \frac { 15 } { 4 } ) - 1 ] \}$$

Evaluate

$$-\frac{11}{4}=-2.75$$

Solution Steps

Multiply \frac{8}{3} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{8\left(-3\right)}{3\times 4}-\left(2-\left(\frac{3}{4}-1+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

Do the multiplications in the fraction \frac{8\left(-3\right)}{3\times 4}.

$$1-\frac{-24}{12}-\left(2-\left(\frac{3}{4}-1+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

Divide -24 by 12 to get -2.

$$1-\left(-2\right)-\left(2-\left(\frac{3}{4}-1+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

The opposite of -2 is 2.

$$1+2-\left(2-\left(\frac{3}{4}-1+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

Add 1 and 2 to get 3.

$$3-\left(2-\left(\frac{3}{4}-1+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

Convert 1 to fraction \frac{4}{4}.

$$3-\left(2-\left(\frac{3}{4}-\frac{4}{4}+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

Since \frac{3}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$3-\left(2-\left(\frac{3-4}{4}+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

Subtract 4 from 3 to get -1.

$$3-\left(2-\left(-\frac{1}{4}+\frac{2}{5}\left(-10+\frac{15}{4}\right)-1\right)\right)$$

Convert -10 to fraction -\frac{40}{4}.

$$3-\left(2-\left(-\frac{1}{4}+\frac{2}{5}\left(-\frac{40}{4}+\frac{15}{4}\right)-1\right)\right)$$

Since -\frac{40}{4} and \frac{15}{4} have the same denominator, add them by adding their numerators.

$$3-\left(2-\left(-\frac{1}{4}+\frac{2}{5}\times \frac{-40+15}{4}-1\right)\right)$$

Add -40 and 15 to get -25.

$$3-\left(2-\left(-\frac{1}{4}+\frac{2}{5}\left(-\frac{25}{4}\right)-1\right)\right)$$

Multiply \frac{2}{5} times -\frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$3-\left(2-\left(-\frac{1}{4}+\frac{2\left(-25\right)}{5\times 4}-1\right)\right)$$

Do the multiplications in the fraction \frac{2\left(-25\right)}{5\times 4}.

$$3-\left(2-\left(-\frac{1}{4}+\frac{-50}{20}-1\right)\right)$$

Reduce the fraction \frac{-50}{20} to lowest terms by extracting and canceling out 10.

$$3-\left(2-\left(-\frac{1}{4}-\frac{5}{2}-1\right)\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{1}{4} and \frac{5}{2} to fractions with denominator 4.

$$3-\left(2-\left(-\frac{1}{4}-\frac{10}{4}-1\right)\right)$$

Since -\frac{1}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$3-\left(2-\left(\frac{-1-10}{4}-1\right)\right)$$

Subtract 10 from -1 to get -11.

$$3-\left(2-\left(-\frac{11}{4}-1\right)\right)$$

Convert 1 to fraction \frac{4}{4}.

$$3-\left(2-\left(-\frac{11}{4}-\frac{4}{4}\right)\right)$$

Since -\frac{11}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$3-\left(2-\frac{-11-4}{4}\right)$$

Subtract 4 from -11 to get -15.

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

The opposite of -\frac{15}{4} is \frac{15}{4}.

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

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

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

Since \frac{8}{4} and \frac{15}{4} have the same denominator, add them by adding their numerators.

$$3-\frac{8+15}{4}$$

Add 8 and 15 to get 23.

$$3-\frac{23}{4}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{12}{4}-\frac{23}{4}$$

Since \frac{12}{4} and \frac{23}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-23}{4}$$

Subtract 23 from 12 to get -11.

$$-\frac{11}{4}$$

Factor

$$-\frac{11}{4} = -2\frac{3}{4} = -2.75$$