Solve [(3/4-1/2)div4/3+1]div(-3/4+frac{1}{3})frac{3}{2}

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

Evaluate

$$-\frac{171}{40}=-4.275$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{\frac{\frac{3}{4}-\frac{2}{4}}{\frac{4}{3}}+1}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{3-2}{4}}{\frac{4}{3}}+1}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{\frac{1}{4}}{\frac{4}{3}}+1}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

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

$$\frac{\frac{1}{4}\times \frac{3}{4}+1}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

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

$$\frac{\frac{1\times 3}{4\times 4}+1}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

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

$$\frac{\frac{3}{16}+1}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

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

$$\frac{\frac{3}{16}+\frac{16}{16}}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Since \frac{3}{16} and \frac{16}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+16}{16}}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Add 3 and 16 to get 19.

$$\frac{\frac{19}{16}}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{\frac{19}{16}}{-\frac{9}{12}+\frac{4}{12}}\times \frac{3}{2}$$

Since -\frac{9}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{19}{16}}{\frac{-9+4}{12}}\times \frac{3}{2}$$

Add -9 and 4 to get -5.

$$\frac{\frac{19}{16}}{-\frac{5}{12}}\times \frac{3}{2}$$

Divide \frac{19}{16} by -\frac{5}{12} by multiplying \frac{19}{16} by the reciprocal of -\frac{5}{12}.

$$\frac{19}{16}\left(-\frac{12}{5}\right)\times \frac{3}{2}$$

Multiply \frac{19}{16} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\left(-12\right)}{16\times 5}\times \frac{3}{2}$$

Do the multiplications in the fraction \frac{19\left(-12\right)}{16\times 5}.

$$\frac{-228}{80}\times \frac{3}{2}$$

Reduce the fraction \frac{-228}{80} to lowest terms by extracting and canceling out 4.

$$-\frac{57}{20}\times \frac{3}{2}$$

Multiply -\frac{57}{20} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-57\times 3}{20\times 2}$$

Do the multiplications in the fraction \frac{-57\times 3}{20\times 2}.

$$\frac{-171}{40}$$

Fraction \frac{-171}{40} can be rewritten as -\frac{171}{40} by extracting the negative sign.

$$-\frac{171}{40}$$

Factor

$$-\frac{171}{40} = -4\frac{11}{40} = -4.275$$