Solve (-3+1/4)(1/2+1)(-2/3+frac{1/2)+1}{-1+(-frac{2}{3}+1)div[(-frac{3}{4})(-1)]}

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

Evaluate

$$-\frac{243}{80}=-3.0375$$

Solution Steps

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

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

Since -\frac{12}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add -12 and 1 to get -11.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add 1 and 2 to get 3.

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

Multiply -\frac{11}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-11\times 3}{4\times 2}.

$$\frac{\frac{-33}{8}\left(-\frac{2}{3}+\frac{1}{2}\right)+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Fraction \frac{-33}{8} can be rewritten as -\frac{33}{8} by extracting the negative sign.

$$\frac{-\frac{33}{8}\left(-\frac{2}{3}+\frac{1}{2}\right)+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{-\frac{33}{8}\left(-\frac{4}{6}+\frac{3}{6}\right)+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Since -\frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{33}{8}\times \frac{-4+3}{6}+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Add -4 and 3 to get -1.

$$\frac{-\frac{33}{8}\left(-\frac{1}{6}\right)+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Multiply -\frac{33}{8} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-33\left(-1\right)}{8\times 6}+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Do the multiplications in the fraction \frac{-33\left(-1\right)}{8\times 6}.

$$\frac{\frac{33}{48}+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Reduce the fraction \frac{33}{48} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{11}{16}+1}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{\frac{11}{16}+\frac{16}{16}}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Since \frac{11}{16} and \frac{16}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11+16}{16}}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Add 11 and 16 to get 27.

$$\frac{\frac{27}{16}}{-1+\frac{-\frac{2}{3}+1}{-\frac{3}{4}\left(-1\right)}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{27}{16}}{-1+\frac{-\frac{2}{3}+\frac{3}{3}}{-\frac{3}{4}\left(-1\right)}}$$

Since -\frac{2}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27}{16}}{-1+\frac{\frac{-2+3}{3}}{-\frac{3}{4}\left(-1\right)}}$$

Add -2 and 3 to get 1.

$$\frac{\frac{27}{16}}{-1+\frac{\frac{1}{3}}{-\frac{3}{4}\left(-1\right)}}$$

Multiply -\frac{3}{4} and -1 to get \frac{3}{4}.

$$\frac{\frac{27}{16}}{-1+\frac{\frac{1}{3}}{\frac{3}{4}}}$$

Divide \frac{1}{3} by \frac{3}{4} by multiplying \frac{1}{3} by the reciprocal of \frac{3}{4}.

$$\frac{\frac{27}{16}}{-1+\frac{1}{3}\times \frac{4}{3}}$$

Multiply \frac{1}{3} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{27}{16}}{-1+\frac{1\times 4}{3\times 3}}$$

Do the multiplications in the fraction \frac{1\times 4}{3\times 3}.

$$\frac{\frac{27}{16}}{-1+\frac{4}{9}}$$

Convert -1 to fraction -\frac{9}{9}.

$$\frac{\frac{27}{16}}{-\frac{9}{9}+\frac{4}{9}}$$

Since -\frac{9}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27}{16}}{\frac{-9+4}{9}}$$

Add -9 and 4 to get -5.

$$\frac{\frac{27}{16}}{-\frac{5}{9}}$$

Divide \frac{27}{16} by -\frac{5}{9} by multiplying \frac{27}{16} by the reciprocal of -\frac{5}{9}.

$$\frac{27}{16}\left(-\frac{9}{5}\right)$$

Multiply \frac{27}{16} times -\frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\left(-9\right)}{16\times 5}$$

Do the multiplications in the fraction \frac{27\left(-9\right)}{16\times 5}.

$$\frac{-243}{80}$$

Fraction \frac{-243}{80} can be rewritten as -\frac{243}{80} by extracting the negative sign.

$$-\frac{243}{80}$$

Factor

$$-\frac{243}{80} = -3\frac{3}{80} = -3.0375$$