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

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

Evaluate

$$-\frac{105}{8}=-13.125$$

Solution Steps

Multiply -2 and 3 to get -6.

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

Divide -6 by \frac{1}{2} by multiplying -6 by the reciprocal of \frac{1}{2}.

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

Multiply -6 and 2 to get -12.

$$-12+\frac{-2\times \frac{1}{4}}{\frac{1}{3}}-\frac{3\times \frac{1}{4}}{-2}$$

Multiply -2 and \frac{1}{4} to get \frac{-2}{4}.

$$-12+\frac{\frac{-2}{4}}{\frac{1}{3}}-\frac{3\times \frac{1}{4}}{-2}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$-12+\frac{-\frac{1}{2}}{\frac{1}{3}}-\frac{3\times \frac{1}{4}}{-2}$$

Divide -\frac{1}{2} by \frac{1}{3} by multiplying -\frac{1}{2} by the reciprocal of \frac{1}{3}.

$$-12-\frac{1}{2}\times 3-\frac{3\times \frac{1}{4}}{-2}$$

Express -\frac{1}{2}\times 3 as a single fraction.

$$-12+\frac{-3}{2}-\frac{3\times \frac{1}{4}}{-2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-12-\frac{3}{2}-\frac{3\times \frac{1}{4}}{-2}$$

Convert -12 to fraction -\frac{24}{2}.

$$-\frac{24}{2}-\frac{3}{2}-\frac{3\times \frac{1}{4}}{-2}$$

Since -\frac{24}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-24-3}{2}-\frac{3\times \frac{1}{4}}{-2}$$

Subtract 3 from -24 to get -27.

$$-\frac{27}{2}-\frac{3\times \frac{1}{4}}{-2}$$

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

$$-\frac{27}{2}-\frac{\frac{3}{4}}{-2}$$

Express \frac{\frac{3}{4}}{-2} as a single fraction.

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

Multiply 4 and -2 to get -8.

$$-\frac{27}{2}-\frac{3}{-8}$$

Fraction \frac{3}{-8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$-\frac{27}{2}-\left(-\frac{3}{8}\right)$$

The opposite of -\frac{3}{8} is \frac{3}{8}.

$$-\frac{27}{2}+\frac{3}{8}$$

Least common multiple of 2 and 8 is 8. Convert -\frac{27}{2} and \frac{3}{8} to fractions with denominator 8.

$$-\frac{108}{8}+\frac{3}{8}$$

Since -\frac{108}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{-108+3}{8}$$

Add -108 and 3 to get -105.

$$-\frac{105}{8}$$

Factor

$$-\frac{105}{8} = -13\frac{1}{8} = -13.125$$