--------------------------------------------Operations with Real Numbers--------------------------------------------
Adding and Subtracting Real NumbersWhat rules must we follow when adding and subtracting real numbers?
When adding real numbers: - if the sign is the same, add the numbers and keep the sign - if the signs are different, find the difference between the two numbers and keep the sign of the LARGER number. |
Multiplying and Dividing Real NumbersWhat rules must we follow when multiplying or dividing real numbers?
When multiplying or dividing real numbers: - if the signs of the two values are the same, the answer is positive - if the signs of the two values are different, the answer is negative |
--------------------------------------------------------GCF and LCM---------------------------------------------------------------
Greatest Common Factor (GCF)What is a factor?
When determining GCF, a factor is any number (or variable) that can be divided into a given value (number and/or variable) evenly. How do you determine what the greatest common factor is? There are a couple of ways you can determine the GCF. One option is to list all of the factors of each number you are working with and then selecting the largest one that appears in both/all of your lists. Another option is to use prime factorization, which requires you to determine the prime factors of each value. After determining which prime factors the values have in common, multiplying the common prime factors together will give the GCF.
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Least Common MultipleWhat is a multiple?
Multiples are numbers that can be divided by a number resulting in an integer. How do we determine the least common multiple? To determine the least common multiple, determine the multiples of each value until you reach the first (lowest) value that both have in common. |
-------------------------------------------------Working with Variables---------------------------------------------------
Defining VariablesWhat is a variable?
A variable is a letter or symbol that represents a number in an algebraic expression or equation. This value of this number can be a single value or can change with respect to another variable. |
Writing Algebraic Expressions and EquationsWhat are the key words that represent each of the algebraic operations?
How do you translate a written phrase into an algebraic expression or equation? |
------------------------------------------------------------Fractions------------------------------------------------------------------
Introduction to FractionsWhat is a fraction?
A fraction consists of three parts: the numerator (top), the denominator (bottom), and the fraction bar (representing division). |
Reducing FractionsWhat does simplest form of a fraction mean?
Simplest form of a fraction is when that the numerator and denominator are both whole integers, and the greatest common factor of the two numbers is one. How do you reduce fractions? To reduce a fraction, determine the greatest common factor (if greater than one), and divide each number by the GCF. |
Adding and Subtracting Fractions |
Multiplying and Dividing Fractions |
How do you add and subtract fractions
The steps for adding and subtracting fractions are similar. 1) Determine if the two fractions have the same denominator. If YES, skip step 2 2) When the denominators are different, find the least common multiple (LCM) of the two denominators and rewrite each fraction with the LCM as the denominator. In order to do this without changing the value of the fraction, you must multiply the numerator by the same number that you multiply the denominator by. (both the numerator and denominator will increase - you are multiplying by 1!!!) 3) Add (or subtract) the values in the numerator, and keep the denominator the same (the two fractions you are adding and the solution will have the same denominator at this point). 4) Reduce the fraction if needed |
How do you multiply and divide fractions?
Multiplying Fractions: 1) Check for common factors between the numerators and denominators of the two fractions, if they exist, cross cancel those factors 2) Multiply the two numerators - this is the numerator for your solution 3) Multiply the two denominators - this is the denominator for your solution 4) Check to make sure the resulting fraction is in simplest form and reduce if needed Dividing Fractions: 1) Keep the first fraction in the problem as written, take the reciprocal of the second fraction, and change the operation to multiplication. 2) Follow the steps for multiplying fractions |
---------------------------------------------------Decimals and Percents---------------------------------------------------
--------------------------------------------Unit Rates and Convnersions--------------------------------------------
Unit RatesWhat is a Unit Rate?
A unit rate represents an amount of one measurement per 1 unit of another measurement. For example sixty miles per 1 hour or $4.50 per 1 pound. |
Unit ConversionsWhat is a Unit Conversion?
A unit conversion involves the translation of a measurement into new units, using conversion factors or unit equivalencies. Essentially, the original value is multiplied by 1, therefore not changing the measurement. |
------------------------------------------------------Order of Operations------------------------------------------------------
Order of Operations
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Evaluating Expressions
To evaluate an expression, you will substitute the given value(s) in for the variables in the expression and then simplify using the rules for order of operations.
Combining Like Terms |
------------------------------------------------Probability and Statistics------------------------------------------------------
Measures of Central Tendency
Theoretical ProbabilityWhat is Theoretical Probability?
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Experimental ProbabilityWhat is experimental Probability?
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--------------------------------------------------------Exponents--------------------------------------------------------
Negative Exponents RuleProduct RulePower RulePower of a Product RuleMultiplying and Dividing Scientific Notation |
Zero Exponent RuleQuotient RulePower of a Quotient RuleScientific Notation vs. Standard NotationAdding and Subtracting Scientific Notation |
-------------------------------------------------------Polynomials-------------------------------------------------------
Identifying PolynomialsWhat terms are used to identify the degree of a polynomial?
What terms are used to identify the number of terms in a polynomial? Subtracting Polynomials
How is subtraction of polynomials different than adding polynomials?
What MUST be done to ensure you subtract your polynomials correctly? Which properties are applied when subtracting polynomials? |
Adding Polynomials
Which terms can be combined?
Which properties are applied when adding polynomials? |
Multiplying Monomials by Binomials (or Trinomials)
Multiplying a Binomial by a Binomial (or Trinomial)
Box Method
Double Distribution Method
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FOIL Method
Vertical Method
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Special Cases of Polynomials
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-------------------------------------------------------Factoring-------------------------------------------------------
FactoringWhat IS factoring?
How is factoring related to the distributive property? What is the first thing you should always look for when you want to factor an expression? |
GCFWhat is a GCF?
How do you determine the GCF of an expression? How do you factor out the GCF of an expression? |
Factoring Expressions in the form x2 + bx + c
How do you factor an equation in this form?
Is it possible to get an expression into this form if it does not initially seem to be in this form?
How can you self-check your work to be sure you have correctly factored the expression?
Are there any special cases that we can look for that follow a specific pattern when factoring?
Is it possible to get an expression into this form if it does not initially seem to be in this form?
How can you self-check your work to be sure you have correctly factored the expression?
Are there any special cases that we can look for that follow a specific pattern when factoring?
Factoring Expressions in the form ax2 + bx + c
What is different about this form?
How can we apply factoring by grouping to expressions in this form?
How can you self-check your work to be sure you have correctly factored the expression?
Are there any special cases that we can look for that follow a specific pattern when factoring?
How can we apply factoring by grouping to expressions in this form?
How can you self-check your work to be sure you have correctly factored the expression?
Are there any special cases that we can look for that follow a specific pattern when factoring?
Factoring by Grouping
How does factoring by grouping work?
What conditions must be present for factoring by grouping to be used?
What is the goal of factoring by grouping?
What conditions must be present for factoring by grouping to be used?
What is the goal of factoring by grouping?