Solve a/b=c/d

$$\frac { a } { b } = \frac { c } { d }$$

Solve for a

$$a=\frac{bc}{d}$$

$$b\neq 0\text{ and }d\neq 0$$

Steps for Solving Linear Equation

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

$$da=bc$$

Divide both sides by d.

$$\frac{da}{d}=\frac{bc}{d}$$

Dividing by d undoes the multiplication by d.

$$a=\frac{bc}{d}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{ad}{c}\text{, }&d\neq 0\text{ and }a\neq 0\text{ and }c\neq 0\\b\neq 0\text{, }&c=0\text{ and }a=0\text{ and }d\neq 0\end{matrix}\right.$$

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 bd, the least common multiple of b,d.

$$da=bc$$

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

$$bc=da$$

The equation is in standard form.

$$cb=ad$$

Divide both sides by c.

$$\frac{cb}{c}=\frac{ad}{c}$$

Dividing by c undoes the multiplication by c.

$$b=\frac{ad}{c}$$

Variable b cannot be equal to 0.

$$b=\frac{ad}{c}\text{, }b\neq 0$$