Solve H=-3/frac{4{9}}+-1/2/-6

$$H = \frac { - 3 } { \frac { 4 } { 9 } } + \frac { - \frac { 1 } { 2 } } { - 6 }$$

Solve for H

$$H = -\frac{20}{3} = -6\frac{2}{3} \approx -6.666666667$$

Steps for Solving Linear Equation

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

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

Express -3\times \frac{9}{4} as a single fraction.

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

Multiply -3 and 9 to get -27.

$$H=\frac{-27}{4}+\frac{-\frac{1}{2}}{-6}$$

Fraction \frac{-27}{4} can be rewritten as -\frac{27}{4} by extracting the negative sign.

$$H=-\frac{27}{4}+\frac{-\frac{1}{2}}{-6}$$

Express \frac{-\frac{1}{2}}{-6} as a single fraction.

$$H=-\frac{27}{4}+\frac{-1}{2\left(-6\right)}$$

Multiply 2 and -6 to get -12.

$$H=-\frac{27}{4}+\frac{-1}{-12}$$

Fraction \frac{-1}{-12} can be simplified to \frac{1}{12} by removing the negative sign from both the numerator and the denominator.

$$H=-\frac{27}{4}+\frac{1}{12}$$

Least common multiple of 4 and 12 is 12. Convert -\frac{27}{4} and \frac{1}{12} to fractions with denominator 12.

$$H=-\frac{81}{12}+\frac{1}{12}$$

Since -\frac{81}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$H=\frac{-81+1}{12}$$

Add -81 and 1 to get -80.

$$H=\frac{-80}{12}$$

Reduce the fraction \frac{-80}{12} to lowest terms by extracting and canceling out 4.

$$H=-\frac{20}{3}$$

Assign H

$$H≔-\frac{20}{3}$$