Solve A=1-(-1/2)*(-5/3)-4/3:(1/2-1)+frac{1}{6}

$$A = 1 - ( - \frac { 1 } { 2 } ) \cdot ( - \frac { 5 } { 3 } ) - \frac { 4 } { 3 } : ( \frac { 1 } { 2 } - 1 ) + \frac { 1 } { 6 }$$

Solve for A

$$A=3$$

Steps for Solving Linear Equation

Multiply -\frac{1}{2} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$A=1-\frac{-\left(-5\right)}{2\times 3}-\frac{\frac{4}{3}}{\frac{1}{2}-1}+\frac{1}{6}$$

Do the multiplications in the fraction \frac{-\left(-5\right)}{2\times 3}.

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

Convert 1 to fraction \frac{6}{6}.

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

Since \frac{6}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 6 to get 1.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 1 to get -1.

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

Divide \frac{4}{3} by -\frac{1}{2} by multiplying \frac{4}{3} by the reciprocal of -\frac{1}{2}.

$$A=\frac{1}{6}-\frac{4}{3}\left(-2\right)+\frac{1}{6}$$

Express \frac{4}{3}\left(-2\right) as a single fraction.

$$A=\frac{1}{6}-\frac{4\left(-2\right)}{3}+\frac{1}{6}$$

Multiply 4 and -2 to get -8.

$$A=\frac{1}{6}-\frac{-8}{3}+\frac{1}{6}$$

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

$$A=\frac{1}{6}-\left(-\frac{8}{3}\right)+\frac{1}{6}$$

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

$$A=\frac{1}{6}+\frac{8}{3}+\frac{1}{6}$$

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{8}{3} to fractions with denominator 6.

$$A=\frac{1}{6}+\frac{16}{6}+\frac{1}{6}$$

Since \frac{1}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.

$$A=\frac{1+16}{6}+\frac{1}{6}$$

Add 1 and 16 to get 17.

$$A=\frac{17}{6}+\frac{1}{6}$$

Since \frac{17}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$A=\frac{17+1}{6}$$

Add 17 and 1 to get 18.

$$A=\frac{18}{6}$$

Divide 18 by 6 to get 3.

$$A=3$$

Assign A

$$A≔3$$