Is math more than numbers and operations? Why are variables useful in representing numbers?

Defining Terms An operation in terms of math includes addition, subtraction, multiplication and division. Often variables are useful to represent our numbers. Variables are symbols used to represent unspecified numbers or values. We use this everyday, whether we know it or not. By the end of this presentation, I hope you understand at least a couple of ways we do this.

Addition versus Subtraction Solving Linear Equations with Addition –W–We need both sides to balance; therefore, what we do to one side we do to the other by taking its opposite. –E–Example: Solve c – 22 = 54. (Think what number subtract 22 will equal 54). To solve by hand: c – = c = 76 –D–Does this work? Solving Linear Equations with Subtraction – Again, we need both sides to balance. – Example: Solve x + 7 = 10. (Think what number plus 7 will equal 10). To solve by hand: x + 7 – 7 = 10 – 7 x = 3 – Does this work?

Multiplication versus Division Solving Equations with Multiplication – Lets solve x/2 = 9. We are dividing in this problem. What is the opposite of division? (Multiplication) So to solve by hand: 2(x/2) = 2(9) x= 18 Now check it to see if it is correct. Solving Equations with Division – The opposite of division is multiplication, so we know that we are going to multiply on both sides to remain equality in our problems. – Lets solve 45 = 3x By dividing each side by 3 we get 15 = x or x = 15. Is this correct?

Solving Multi-Step Equations Steps to solve 1. Use the Distributive Property 2. Simplify the expressions on each side 3. Use the Addition and/or Subtraction Properties of Equality to get the variables on one side and the numbers without variables on the other side 4. Simplify the expressions on each side of the equals sign 5. Use the Multiplication or Division Property of Equality to solve

Multi-Step Equations Continued Example: – Solve: p = 8p – 1 2 – p = 2 + 8p – 1 10p = 1 + 8p 10p – 8p = 1 + 8p – 8p 2p = 1 (2p)/2 = ½ p = ½ Is this correct?

Conclusions In what ways is math used in our everyday lives? Lets try to come up with an example on how it is used everyday. This will show how variables can be useful in representing numbers, and it shows that math is more than numbers! (An example could be trying to figure out how to answer the content question: You have $500 in the bank. You need $715 for your trip to the beach. How much more money do you need? Define a variable, set up an equation, determine which operation(s) you will need to solve, and then solve. )