Solve [2/3(7/4div-2/3)]div(1/2+frac{2}{3})

$$[ \frac { 2 } { 3 } ( \frac { 7 } { 4 } \div \frac { - 2 } { 3 } ) ] \div ( \frac { 1 } { 2 } + \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{3}{2}=-1.5$$

Solution Steps

Divide \frac{7}{4} by \frac{-2}{3} by multiplying \frac{7}{4} by the reciprocal of \frac{-2}{3}.

$$\frac{\frac{2}{3}\times \frac{7\times 3}{4\left(-2\right)}}{\frac{1}{2}+\frac{2}{3}}$$

Multiply 7 and 3 to get 21.

$$\frac{\frac{2}{3}\times \frac{21}{4\left(-2\right)}}{\frac{1}{2}+\frac{2}{3}}$$

Multiply 4 and -2 to get -8.

$$\frac{\frac{2}{3}\times \frac{21}{-8}}{\frac{1}{2}+\frac{2}{3}}$$

Fraction \frac{21}{-8} can be rewritten as -\frac{21}{8} by extracting the negative sign.

$$\frac{\frac{2}{3}\left(-\frac{21}{8}\right)}{\frac{1}{2}+\frac{2}{3}}$$

Multiply \frac{2}{3} times -\frac{21}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\left(-21\right)}{3\times 8}}{\frac{1}{2}+\frac{2}{3}}$$

Do the multiplications in the fraction \frac{2\left(-21\right)}{3\times 8}.

$$\frac{\frac{-42}{24}}{\frac{1}{2}+\frac{2}{3}}$$

Reduce the fraction \frac{-42}{24} to lowest terms by extracting and canceling out 6.

$$\frac{-\frac{7}{4}}{\frac{1}{2}+\frac{2}{3}}$$

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

$$\frac{-\frac{7}{4}}{\frac{3}{6}+\frac{4}{6}}$$

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

$$\frac{-\frac{7}{4}}{\frac{3+4}{6}}$$

Add 3 and 4 to get 7.

$$\frac{-\frac{7}{4}}{\frac{7}{6}}$$

Divide -\frac{7}{4} by \frac{7}{6} by multiplying -\frac{7}{4} by the reciprocal of \frac{7}{6}.

$$-\frac{7}{4}\times \frac{6}{7}$$

Multiply -\frac{7}{4} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7\times 6}{4\times 7}$$

Do the multiplications in the fraction \frac{-7\times 6}{4\times 7}.

$$\frac{-42}{28}$$

Reduce the fraction \frac{-42}{28} to lowest terms by extracting and canceling out 14.

$$-\frac{3}{2}$$

Factor

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$