Solving Equations using Division and Multiplication.

A variable is a symbol that represents a number. Usually we use letters such as n, t, or x for variables. For example, we might say that s stands for the side-length of a square. We now treat s as if it were a number we could use. The perimeter of the square is given by 4 * s. The area of the square is given by s * s. When working with variables, it can be helpful to use a letter that will remind you of what the variable stands for.

An expression is a mathematical term or a sum or difference of mathematical terms that may use numbers, variables, or both.

An equation is a statement that two numbers or expressions are equal. Equations are useful for relating variables and numbers. Many word problems can easily be written down as equations with a little practice. Many simple rules exist for simplifying equations.

When an equation has a variable, the solution to the equation is the number that makes the equation true when we replace the variable with its value.

When a variable is divided by some number, we can use multiplication on both sides to solve for the variable.

When a variable is multiplied by some number, we can use division on both sides to solve for the variable.

To solve a multiplication equation, use the inverse operation of division. Divide both sides by the same non - zero number. If a = b, then ac = bc where c ¹ 0

If c = d, then c/e = d/e where e ¹ 0

Multiplying both sides of an equation by the same nonzero number produces an equivalent equation. We may adapt this property to state that if we divide both sides of an equation by the same nonzero number, we obtain an equivalent equation.

This fact follows from knowing that multiplying by the reciprocal of a number is the same thing as dividing by that number.

c * 1/e is equivalent to c / e

Multiplication in algebra will have the x next to a number. The process will be a combination of multiplication and division to solve for x. To get x alone, we do the opposite operation. To solve a division equation, use the inverse operation of multiplication. Multiply both sides by the same number. Any operation done to one side must also be done to the other side.