Solve a:b=3:4

$$a : b = 3 : 4$$

Solve for a

$$a=\frac{3b}{4}$$

$$b\neq 0$$

Steps for Solving Linear Equation

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

$$4a=3b$$

Divide both sides by 4.

$$\frac{4a}{4}=\frac{3b}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$a=\frac{3b}{4}$$

Solve for b

$$b=\frac{4a}{3}$$

$$a\neq 0$$

Steps for Solving Linear Equation

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

$$4a=3b$$

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

$$3b=4a$$

Divide both sides by 3.

$$\frac{3b}{3}=\frac{4a}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$b=\frac{4a}{3}$$

Variable b cannot be equal to 0.

$$b=\frac{4a}{3}\text{, }b\neq 0$$