Solving an equation using Multiplication and Division
A variable is a symbol that represents a number. Usually we use the letters like n, t, or x for variables. For instance, we might say that s stands for the side-length of a square. The perimeter of the square can be given by 4 × s. The area of the square can be given by s × s. When working with the variables, it can be very helpful to use a letter which will remind you of what the variable stands for.
An expression is a mathematical sum or difference of mathematical terms which can use numbers, variables, or both.
An equation is a statement that 2 numbers or expressions are equal. Equations are useful for relating the variables and numbers. Many word problems can be written down easily as equations with the little practice. Many simple rules are there for simplifying equations.
When an equation has a variable, the solution to the equation is the number which makes the equation true when we are replacing the variable with its value.
When a variable can be divided by some number, we can use multiplication on both the sides to solve for variable.
When a variable can be multiplied by some number, we can use division on both the sides to solve for the variable.
To solve a multiplication equation, use inverse operation of division. Divide both the sides by 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 the sides of an equation by the same nonzero number produces an equivalent equation. We can adapt this property to state that if we divide both sides the equation by the same nonzero number, we can obtain an equivalent equation.
This fact follows from knowing that multiplying by reciprocal of the number is the same thing as dividing by that number.
c • 1/e is equivalent to c ÷ e
Multiplication in the algebra will have the "x" next to a number. The process will be the combination of multiplication and division to solve for "x". To get "x" alone, we do the opposite operation. To solve the division equation, use the inverse operation of the multiplication. Multiply both the sides by same number. Any operation performed on one side should also be done to the other side.