Solve f/a=F/A

$$\frac { f } { a } = \frac { F } { A }$$

Solve for A

$$\left\{\begin{matrix}A=\frac{Fa}{f}\text{, }&F\neq 0\text{ and }a\neq 0\text{ and }f\neq 0\\A\neq 0\text{, }&f=0\text{ and }F=0\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Af=aF$$

The equation is in standard form.

$$fA=Fa$$

Divide both sides by f.

$$\frac{fA}{f}=\frac{Fa}{f}$$

Dividing by f undoes the multiplication by f.

$$A=\frac{Fa}{f}$$

Variable A cannot be equal to 0.

$$A=\frac{Fa}{f}\text{, }A\neq 0$$

Solve for F

$$F=\frac{Af}{a}$$

$$a\neq 0\text{ and }A\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by Aa, the least common multiple of a,A.

$$Af=aF$$

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

$$aF=Af$$

Divide both sides by a.

$$\frac{aF}{a}=\frac{Af}{a}$$

Dividing by a undoes the multiplication by a.

$$F=\frac{Af}{a}$$