Solve (3/8-5/6-2/3):3/4*frac{4}{3}

$$( \frac { 3 } { 8 } - \frac { 5 } { 6 } - \frac { 2 } { 3 } ) : \frac { 3 } { 4 } \cdot \frac { 4 } { 3 }$$

Evaluate

$$-2$$

Solution Steps

Least common multiple of 8 and 6 is 24. Convert \frac{3}{8} and \frac{5}{6} to fractions with denominator 24.

$$\frac{\frac{9}{24}-\frac{20}{24}-\frac{2}{3}}{\frac{3}{4}}\times \frac{4}{3}$$

Since \frac{9}{24} and \frac{20}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-20}{24}-\frac{2}{3}}{\frac{3}{4}}\times \frac{4}{3}$$

Subtract 20 from 9 to get -11.

$$\frac{-\frac{11}{24}-\frac{2}{3}}{\frac{3}{4}}\times \frac{4}{3}$$

Least common multiple of 24 and 3 is 24. Convert -\frac{11}{24} and \frac{2}{3} to fractions with denominator 24.

$$\frac{-\frac{11}{24}-\frac{16}{24}}{\frac{3}{4}}\times \frac{4}{3}$$

Since -\frac{11}{24} and \frac{16}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-11-16}{24}}{\frac{3}{4}}\times \frac{4}{3}$$

Subtract 16 from -11 to get -27.

$$\frac{\frac{-27}{24}}{\frac{3}{4}}\times \frac{4}{3}$$

Reduce the fraction \frac{-27}{24} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{9}{8}}{\frac{3}{4}}\times \frac{4}{3}$$

Divide -\frac{9}{8} by \frac{3}{4} by multiplying -\frac{9}{8} by the reciprocal of \frac{3}{4}.

$$-\frac{9}{8}\times \frac{4}{3}\times \frac{4}{3}$$

Multiply -\frac{9}{8} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\times 4}{8\times 3}\times \frac{4}{3}$$

Do the multiplications in the fraction \frac{-9\times 4}{8\times 3}.

$$\frac{-36}{24}\times \frac{4}{3}$$

Reduce the fraction \frac{-36}{24} to lowest terms by extracting and canceling out 12.

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

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

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

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

$$\frac{-12}{6}$$

Divide -12 by 6 to get -2.

$$-2$$

Factor

$$-2$$