Solve 3/4quadf*6/g=2/frac{1{3}}

$$\frac { 3 } { 4 } \quad f \cdot \frac { 6 } { g } = \frac { 2 } { \frac { 1 } { 3 } }$$

Solve for f

$$f=\frac{4g}{3}$$

$$g\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4g, the least common multiple of 4,g.

$$\frac{3}{4}f\times 4\times 6=4g\times \frac{2}{\frac{1}{3}}$$

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

$$3f\times 6=4g\times \frac{2}{\frac{1}{3}}$$

Multiply 3 and 6 to get 18.

$$18f=4g\times \frac{2}{\frac{1}{3}}$$

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

$$18f=4g\times 2\times 3$$

Multiply 2 and 3 to get 6.

$$18f=4g\times 6$$

Multiply 4 and 6 to get 24.

$$18f=24g$$

Divide both sides by 18.

$$\frac{18f}{18}=\frac{24g}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$f=\frac{24g}{18}$$

Divide 24g by 18.

$$f=\frac{4g}{3}$$

Solve for g

$$g=\frac{3f}{4}$$

$$f\neq 0$$

Steps for Solving Linear Equation

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4g, the least common multiple of 4,g.

$$\frac{3}{4}f\times 4\times 6=4g\times \frac{2}{\frac{1}{3}}$$

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

$$3f\times 6=4g\times \frac{2}{\frac{1}{3}}$$

Multiply 3 and 6 to get 18.

$$18f=4g\times \frac{2}{\frac{1}{3}}$$

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

$$18f=4g\times 2\times 3$$

Multiply 2 and 3 to get 6.

$$18f=4g\times 6$$

Multiply 4 and 6 to get 24.

$$18f=24g$$

Swap sides so that all variable terms are on the left hand side.

$$24g=18f$$

Divide both sides by 24.

$$\frac{24g}{24}=\frac{18f}{24}$$

Dividing by 24 undoes the multiplication by 24.

$$g=\frac{18f}{24}$$

Divide 18f by 24.

$$g=\frac{3f}{4}$$

Variable g cannot be equal to 0.

$$g=\frac{3f}{4}\text{, }g\neq 0$$