Opposite Operations Solving Simple Algebraic Expressions with Opposite

Opposite Operations Solving Simple Algebraic Expressions with Opposite Operations

�Operations are the various ways we can manipulate numbers in an expression. ◦ Common operations: �Addition �Subtraction �Multiplication �Division �Exponentiation �Grouping a+b a–b axb a÷b an (a + b) – c ◦ There are others, but you get the point Mathematical Operations

�Often in algebraic expressions we are confronted by a number we do not know, a variable (so called because its value can change) �When an expression contains a single variable, we can solve for that variable fairly easily using Opposite Operations. The Variable Concept

� Each operation in algebra has an opposite that will undo it, an opposite operation ◦ Opposite operations: �Addition and subtraction are opposites ◦ If you add 5 to a number, you can undo that by subtracting 5 from the new number �Multiplication and division are opposites ◦ If you multiply a number by 3, you can undo that by dividing the new number by 3. �Exponents and Roots are opposites ◦ If you square a number, you can undo that by taking the square root of the new number �Parenthesis do not have an opposite operation (they simply organize, or “chunk”, the expression) Opposite Operations

� “Do any combination of opposite operations that was done to the unknown, or that the unknown is doing, in order to isolate the unknown. ” X+5=9 Right now, 5 is being added to X, so let’s do the opposite operation: subtract 5 from it ** Keep in mind that both sides of the equation are equal to each other. Therefore, if you change one side you MUST change the other side in the EXACT SAME WAY!!!!** X+5– 5=9– 5 Now we just simplify: X=4 Using Opposite Operations

�Let’s try another: What is happening to ‘n’? It has been squared. What is the opposite of that operation? The square root. Try Another

� When the Unknown is Doing Something

� Alternative when the Unknown is on the Bottom of a Fraction

� How, and Why, Does That Work?