BPCC Beginning Algebra

Module One

• Numbers - are symbols that we use count or operate with.
• Natural Numbers - or counting numbers are numbers we use to count with and starts with number 1.
• Whole Numbers - Start with zero unlike natural numbers, these are the numbers you operate with.
• Signs Commonly used in Mathematics:
• Equal sign '=' : Determines if an integer is exactly the same as the other integer (a = a).
• Not equal sign '≠' : Determines if an integer is not exactly the same as the other integer (a ≠ b) .
• Greater Than '>': Determines if the integer to the right is more than.
• Less Than '<': Determines if the integer to the right is lesser than.
• Greater Than or Equal to '>=': Determines if the integer to the right is more than or equal to.
• Lesser Than or Equal to '=>': Determines if the integer to the right is lesser than or equal to.  
• Using the number line:
• In a number line, you can see that number, you can see that numbers always begin in zero. There are two kinds of integers in a number line.
• Positive Integers: Greater than zero.
• Negative Integers: Lesser than zero.
• Example: 
• -2 < 0
• -7 < -4
• 2  > 0
• Remember that negative numbers greater when close to zero.
• Absolute value:  Determines how many counts to get to zero.
• Example:
• [4] = 4
• [-5] = 5
• [1/2] = 1/2
• [-1.25] = 1.25
• Compare: In comparing absolute value, you have to bring the numbers out of the absolute value from the absolute value bars then compare.
• Example:
• [-7] < [5] :: False
• 7 > 5 :: True
• [-1.5]  < [1.3] :: False
• -1.5 < 1.3 :: True
• [- 30] < 16 :: False
• 30 > 16 :: True

Module II:


Module III:   

Multiplication and Division of integers

Remember: If two numbers have the same sign, then the answer is positive.

Multiplication:

Example:

• -4 (-3) = + 12
• 4 (3) = + 12
• -4(3) = -12
• 4(-3) = - 12

Note: When you encounter a zero when multiplying then the answer is always zero.

Example: (-5)(3)(17)(0)(8)(123) = 0

Division:

Example:

12 / -4 = (-3)

-12 / -4 = (+3)

Remember that zero dividing a number is undefined.

08.09.15

 Module IV: Order of Operations:

 Remember PEMDAS? If you remember it or not, then here a review of PEMDAS key terms:

• P = Parenthesis: (),[],{} have to be done first.
• E = Exponents: N^n have to be done after parenthesis
• M = Multiplication: have to be done after exponents
• D = Division: have to be done with multiplication
• A = Addition: have to be done after division/multiplication
• S = Subtraction: have to be done after division/multiplication/addition.
• Skip over if and continue to follow if one of the operations are missing.

• Example:  
• 7 + (6 × 5^2 + 3)= 160 

08.23.13

Module V: Like and Unlike Terms

 Terms are variables with exponents, numbers and a certain exponent.

• Numerical coefficients
• The leading number that comes with the variable:
• Example:
• Y; If there is no number before the variable, it means it's the number 1 that is before the variable like: Y -> 1Y
• 2x^3;
• -5
• 2/y
• Like Terms
• They may have different numbers but like terms have the same variables, exponents and other coefficient that make up the terms
• Example:
• 2xy^2 and 5xy^2 are like terms.

• Unlike terms:
• They have different numbers, have different variables, exponents and other coefficient that make up the terms
• Example:
• 3yz and 4z^2 are unlike terms 

10.25.13

Distributive Property

Distributive Property literally distributes numbers to multiply contained numbers. Before solving algebraic expressions, you first had to use distribution of values. Distribution involves in removing parenthesis from the equation by combining terms.

Example:

• 4(x+6y-2z)
• 4x+24y-8z -> Distribute the values to remove the parenthesis.
• -7x-2(4x+3)-8
• 7x-8x-6-8 -> Distribute the values to remove the parenthesis.
• 15x-14 -> combine like terms
• 3(x-6)+2(x+4)
• 3x-18+2x+4 -> Distribute the values to remove the parenthesis.
• 5x-10 -> combine like terms
• 4(x-3)+2
• 4x-12 -> distribute the first term
• 4x-12+2 -> Bring down the second term
• 4x-10 -> combine like terms
• (2x+6)+(5x+8)
• 2x+6+5x+8 -> Bring down the terms
• 7x-2 -> Combine like terms
• 4x+2(x-7) 
• 2x-14 -> Solve the distributing term first
• 2x-14+4x -> Bring down the remaining term.
• 6x-14 -> Combine like terms

11/22/15

Module 6: Solving Linear Equations

·         Addition Property

o   This property allows you to add both sides of a basic linear equation equally.

Example	Explanation
x-5 = 8	Isolate x by adding the inverse additive to the constant.
5+(-5) = 0
X+=8
8+(5) = 13	Use the inverse to add the other side of the equation.
X = 13
13 – 5 = 8

Example	Explanation
-11 = 3+x	Isolate x by adding the inverse additive to the constant.
3+(-3) = 0
-11+= x
-11+(-3)=(-14)	Use the inverse to add the other side of the equation.
X = -14
-11 = 3+(-14)

Example	Explanation
-x=14	Isolate x by adding the inverse additive to the constant.
x/-1 = 14/-1
X = (-14)

Example	Explanation
x-2.5 = 4.8	Isolate x by adding the inverse additive to the constant.
2.5+(-2.5) = 0
X+=4.8
4.8+2.5 = 7.3	Use the inverse to add the other side of the equation.
X = 7.3
7.3-2.5 = 4.8