Solve q:r=3:5

$$q : r = 3 : 5$$

Solve for q

$$q=\frac{3r}{5}$$

$$r\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5r, the least common multiple of r,5.

$$5q=3r$$

Divide both sides by 5.

$$\frac{5q}{5}=\frac{3r}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$q=\frac{3r}{5}$$

Solve for r

$$r=\frac{5q}{3}$$

$$q\neq 0$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5r, the least common multiple of r,5.

$$5q=3r$$

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

$$3r=5q$$

Divide both sides by 3.

$$\frac{3r}{3}=\frac{5q}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$r=\frac{5q}{3}$$

Variable r cannot be equal to 0.

$$r=\frac{5q}{3}\text{, }r\neq 0$$