Solve v=5/3-7/9/frac{1{4}-1/2}

$$v = \frac { \frac { 5 } { 3 } - \frac { 7 } { 9 } } { \frac { 1 } { 4 } - \frac { 1 } { 2 } }$$

Solve for v

$$v = -\frac{32}{9} = -3\frac{5}{9} \approx -3.555555556$$

Steps for Solving Linear Equation

Least common multiple of 3 and 9 is 9. Convert \frac{5}{3} and \frac{7}{9} to fractions with denominator 9.

$$v=\frac{\frac{15}{9}-\frac{7}{9}}{\frac{1}{4}-\frac{1}{2}}$$

Since \frac{15}{9} and \frac{7}{9} have the same denominator, subtract them by subtracting their numerators.

$$v=\frac{\frac{15-7}{9}}{\frac{1}{4}-\frac{1}{2}}$$

Subtract 7 from 15 to get 8.

$$v=\frac{\frac{8}{9}}{\frac{1}{4}-\frac{1}{2}}$$

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

$$v=\frac{\frac{8}{9}}{\frac{1}{4}-\frac{2}{4}}$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$v=\frac{\frac{8}{9}}{\frac{1-2}{4}}$$

Subtract 2 from 1 to get -1.

$$v=\frac{\frac{8}{9}}{-\frac{1}{4}}$$

Divide \frac{8}{9} by -\frac{1}{4} by multiplying \frac{8}{9} by the reciprocal of -\frac{1}{4}.

$$v=\frac{8}{9}\left(-4\right)$$

Express \frac{8}{9}\left(-4\right) as a single fraction.

$$v=\frac{8\left(-4\right)}{9}$$

Multiply 8 and -4 to get -32.

$$v=\frac{-32}{9}$$

Fraction \frac{-32}{9} can be rewritten as -\frac{32}{9} by extracting the negative sign.

$$v=-\frac{32}{9}$$

Assign v

$$v≔-\frac{32}{9}$$