2. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Dr J’s easy ALGEBRA Part 1

3. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Common Algebra terminology Variables Variables are letters that are used instead of numbers in a variety of formulas and equations. The most typical variable letter used is “x” representing the unknown number or value. For example: 2x, 2x 2 +5 (a+b) ÷ (2b+3a) = 0 All of the letters used in the above examples are variables. Coefficients Coefficients are numbers typically used in front of the variables For example: 5x – 5 is a coefficient Equations Equations are mathematical statements that have an Equal sign (=). It typically represent a situation requiring a solution of a some numerical value. For example: 10x - 5 = 0 12y+10 =24 2x 2 +5 = 4x+5

4. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Expression Equations are mathematical statements that does have an Equal sign (=). It typically An expression can contain numbers, variables, and operators such as (plus, minus, divide, or multiply) For example: 10x · 5 12y+10 2x 2 +5 Factors Factors are numbers of terms that when multiply together arrive at the specific number: For instance: 3 and are factors of 12 5 an 2 are factors of 10 3 and 5 are factors of 15 2x and 4x are factors of 8x

5. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Integers Integers are whole numbers that can have a positive (+) or a negative (-) signs For example: 10 5 32 -7 -64 Prime numbers Prime numbers are positive numbers that can only divide by itself or by 1. 2,3,5,7, 11, and 13 are examples or prime numbers Terms Are numbers, variables, or a combination of numbers and variables, typically separated by operator signs. For example: 2x+y 5x 3z+4y 25+3x

6. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Number line 0 1 2 3 4 5-2-3-4 Number line above represents an endless series of numbers that go in both directions from the zero (0). Numbers to the right of zero represent positive numbers, and to the left of zero, represent the negative numbers. For example number 3 is represented below: 0 1 2 3 4 5-2-3-4 0 1 2 3 4 5-2-3-4 Number 1 0 1 2 3 4 5-2-3-4 Number -2 0 1 2 3 4 5-2-3-4 Number -3.5 0 1 2 3 4 5-2-3-4 Number 2.5

7. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Sometimes it is hard to understand the negative numbers on the number line. To make it a little easier to visualize, you can imagine the following example: If this year the company made a profit of $20,000 it would be represented by +20,000. And if some company lost $10,000 it would be represented by a number -10,000. This would be a clear indication of a loss instead of a gain (profit). When companies see these negative numbers in their report, they become instantly aware that something needs to be done to illuminate the cause of this “negative” activity. Number 0 on the number line represents a starting point. It represents no value at all (no positive or negative. However, in mathematics, zero does represent a result of expressions and many equations. For example: 10-10 =0 5x+2 =0

8. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Adding positive numbers and variables: When adding positive numbers and variables, no special considerations are needed, simply add the terms as usual For example: 10+5 =15 5x+3x = 8x 32 +32 = 64 5+5+10=20 4y+6y+10y=20y Adding negative numbers and variables: When adding two negative numbers and variables, special considerations are needed. simply add the terms as they were both positive, and then put a negative sign in front of the result. For example: (-2)+(-5) = -7 (-10)+(-4) = -14 (-4x)+(-5x) = -9x (-6)+(-4)+(-5) = -15 The result of addition is called the SUM

9. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Subtracting positive numbers and variables: When subtracting positive numbers and variables, no special considerations are needed, simply subtract the terms as usual. For example: 10-5 = 5 5x-3x = 2x 32 -32 = 0 15-5-2= 8 20y-10y-2y=8y Subtracting negative numbers and variables: When subtracting negative numbers and variables, special considerations are needed. Simply change the subtraction problem into addition problem. For example: 10-(-5) = 10+(+5) = 15 20-(-10) = 20+(+10) = 30 -12-(-7) = -12+(+7) = -5 NOTE: In the last example, because -12 is a greater value number, we subtracted 7 from 12 and the number became -5 because 12 had a negative value. The result of Subtraction is called the DIFFERENCE

10. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Multiplying numbers and variables: When multiplying numbers and variables in mathematics, one of several ways may be used to represent the multiplication procedure. For example: 10x5 = 25 (x is used to show multiplication sign) 5x·3x = 15x (a dot is used to show multiplication sign) 2y or 10x (when no operator is shown between the numbers and letters, it also mean that a multiplication sign exist between them). Therefore the expression 2y means 2·y or 10x means 10·y 10 * 5 = 50 (sometimes an asterisk (*) is used to show multiplication sign) Dividing numbers and variables: When dividing numbers and variables also one of several ways may be used to represent the division procedure. For example: 10÷5 = 2 (divide symbol used to show division) 15x / 3x = 5 (a slash is used to show division sign) Sometimes a single line is used to demonstrate division: 10+5x 3x+2 3 8 or The result of multiplication is called the PRODUCT The result of division is called the QUOTIENT

11. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Multiplying numbers with the same sign: When multiplying or dividing numbers or variables, where both terms have the same sign (plus or minus), the result would always be positive: 10·5 = 50 (-5x) · (-3x) = 15x -7 x -3 = 21 25÷5 = 5 (-10)÷(-2) = 5 (-a) ÷ (-b) = a ÷ b Multiplying numbers with the different signs: When multiplying or dividing numbers or variables, where terms have different signs (plus or minus), the result would always be negative: -5·5 = -25 5x · (-3x) = -15x -7 x 3 = -21 -10÷5 = -2 -10y÷2y = -5 a · -b = -ab

12. Previous Page Next Page EXIT Created by Professor James A. Sinclair, Ph.D. MMXI Absolute values Absolute value, regardless of the sign simply show how far a given value is from the 0 on the number line. Absolute values are shown between two thin lines and are always positive. For example: -8 = 8 -32 = 32 In absolute values, the sign inside the lines is simply disregarded However, if the minus sign appears before the lines, the result is quite different. For example: 8= 8 -8 = -8 - 8 - 10-4= -6 -