Solve 3/2{(1/4-3/2)div(3/2+frac{1}{6})}=

$$\frac { 3 } { 2 } \{ ( \frac { 1 } { 4 } - \frac { 3 } { 2 } ) \div ( \frac { 3 } { 2 } + \frac { 1 } { 6 } ) \} =$$

Evaluate

$$-\frac{9}{8}=-1.125$$

Solution Steps

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

$$\frac{3}{2}\times \frac{\frac{1}{4}-\frac{6}{4}}{\frac{3}{2}+\frac{1}{6}}$$

Since \frac{1}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}\times \frac{\frac{1-6}{4}}{\frac{3}{2}+\frac{1}{6}}$$

Subtract 6 from 1 to get -5.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{3}{2}+\frac{1}{6}}$$

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

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{9}{6}+\frac{1}{6}}$$

Since \frac{9}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{9+1}{6}}$$

Add 9 and 1 to get 10.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{10}{6}}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{5}{3}}$$

Divide -\frac{5}{4} by \frac{5}{3} by multiplying -\frac{5}{4} by the reciprocal of \frac{5}{3}.

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

Multiply -\frac{5}{4} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}\times \frac{-5\times 3}{4\times 5}$$

Do the multiplications in the fraction \frac{-5\times 3}{4\times 5}.

$$\frac{3}{2}\times \frac{-15}{20}$$

Reduce the fraction \frac{-15}{20} to lowest terms by extracting and canceling out 5.

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

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

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

Do the multiplications in the fraction \frac{3\left(-3\right)}{2\times 4}.

$$\frac{-9}{8}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$-\frac{9}{8}$$

Factor

$$-\frac{9}{8} = -1\frac{1}{8} = -1.125$$