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PreAlgebra
Definitions
36
Mathematics
7th Grade
12/15/2007

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Term
 mathematical expression
Definition
 is any combination of numbers and operations
Term
 to evaluate
Definition
 evaluate an expression, you find its numerical value
Term
 variables
Definition
 Variables are placeholders, usually letters, that represent numbers
Term
 An algebraic expression
Definition
 An algebraic expression is a combination of variables, numbers and at least one operation
Term
 Commutative property of addition and multiplication
Definition
 Commutative property of addition and multiplication - The order in which numbers are added or multiplied does not change the sum or product
Term
 Associative property of addition and multiplication
Definition
 Associative property of addition and multiplication - The way in which numbers are grouped does not change the sum or the product
Term
 The product
Definition
 Identity property of addition and multiplication o The sum of a number and zero is that number 6 + 0 = 6 o The product of a number and one is the number 6 * 1 = 6
Term
 Multiplicative property of zero
Definition
 Multiplicative property of zero o The product of a number and zero is zero 6 * 0 = 0
Term
 AN equation
Definition
 An equation is an algebraic expression having an EQUAL sign. When solving an equation you are solving for a variable
Term
 coordinate system ordered pairs
Definition
 Using the coordinate system we can locate ordered pairs made up of one point from the x-axis and one point from the y-axis.  The ordered pair (0,0) is called the origin
Term
 Integers
Definition
 Integers are the whole numbers and their opposites
Term
 The absolute value of a number
Definition
 The absolute value of a number is the distance the number is away from zero o Absolute values are always positive
Term
 Adding Integers
Definition
 To ADD integers with the SAME sign, ADD the absolute value and give the result the SAME sign as the integers  To ADD integers with DIFFERENT signs, SUBTRACT their absolute values and give the result the sign of the greater value.
Term
 Subtracting integers
Definition
 To SUBTRACT an integer, ADD its ADDITIVE INVERSE
Term
 Multipying integers
Definition
 The product of two integers with the SAME sign is positive  The product of two integers with DIFFERENT signs is negative
Term
 Dividing integers
Definition
 The quotient of two integers with the SAME sign is positive  The quotient of two integers with DIFFERENT signs is negative
Term
 The Distributive Property
Definition
 sum of two numbers multiplied by a number is the sum of the products of the numbers originally added and that number o a(b + c) = ab + ac
Term
 Simplifying Algebraic Expressions
Definition
 Use the distributive property to simplify algebraic expressions
Term
 Solving Equations by Adding or Subtracting
Definition
 Isolate the unknown variable by adding or subtracting the inverse to BOTH sides o Example: x + 10 = 14, x + 10 – 10 = 14 – 10, x = 4
Term
 Solving Equations by Multiplying and Dividing
Definition
 Isolate the unknown variable by multiplying or dividing the inverse to BOTH sides o Example: 8d = 64, 8d/8 = 64/8, d = 8
Term
 Solving Two step equations
Definition
 Combine like terms.  To solve equations you can use inverse operations (“undo” each other, or using the opposite) to isolate the variable in which you are solving for  To “undo” addition you would subtract  To “undo” subtraction you would add  To “undo” multiplication you would divide  To “undo” division you would multiply
Term
 Writing Two Step Equations
Definition
 Turn verbal sentences into two step equations  When you multiply or divide each side of an inequality by a negative integer, you must reverse the order symbol
Term
 A formula
Definition
 A formula shows the relationship among certain quantities  A formula is a mathematical equation
Term
 Area
Definition
 Area is the space occupied in square units, inside of the perimeter  The Area of a rectangle is the length times width o Area = l x w, recorded in square units i.e. cm2
Term
 Powers
Definition
 Area is the space occupied in square units, inside of the perimeter  The Area of a rectangle is the length times width o Area = l x w, recorded in square units i.e. cm2
Term
 ExponentBase
Definition
 An exponent tells how many times a number, called the base, is used as a factor.
Term
 Factor
Definition
 A factor is a whole number multiplied by another number to produce a product. All numbers multiplied together are the factors.
Term
 A composite number
Definition
 A composite number is a whole number greater than one and has more than two factors.
Term
 Greatest Common Factor (GCF)
Definition
 Greatest Common Factor (GCF)  Find all prime factors of two or more numbers  Identify common factors among all numbers  Multiply common factors together
Term
 Simplifying Algebraic Fractions
Definition
 Simplifying Algebraic Fractions  Find all prime factors using factor trees of both the numerator and denominator  Cancel out common prime factors from both (remember any number over the same number equals one)  Multiply the remaining factors of the numerator and denominator
Term
 Multiplying and Dividing Monomials
Definition
 Multiplying and Dividing Monomials  When multiplying powers ADD the exponents  When dividing powers SUBTRACT the exponents
Term
 Negative exponents
Definition
 Negative Exponents  A number to a negative exponent is written as a fraction as 1 over the power  a -3 = 1/a3
Term
 Scientific notation
Definition
 Express a number in standard form and scientific notation.  Compare and order numbers in scientific notation
Term
 Least Common Multiple (LCM)
Definition
 Least Common Multiple  Find the least common multiple of two or more numbers.  Find the least common denominator of two or more fractions.  Find all prime factors using factor trees of two or more numbers  Identify all common prime factors of any of the numbers  Multiply all remaining factors together along with the common factors only once
Term
 least common denominator
Definition
 Least Common Denominator (LCD)  Find the least common multiple (LCM) of the denominators
Term
 SUGGESTIONS FOR PREPARING FOR EXAM
Definition
 1. Eat a good breakfast to get you started and to keep you alert throughout the exam. 2. Be sure you have everything you need for the exam (e.g. pen, pencil, eraser, watch, etc.) 3. Make sure you know what room the exam is held in and arrive there with plenty of time to spare. Choose a good seat away from the aisles, doorways, and the teacher's desk (where everyone hands in the exam). 4. Take a deep breath, think positive and relax. 5. Once you have the exam, skim the entire exam first to get an idea of what materials are asked, and how the exam is organized. 6. Read the directions. Make sure you understand them fully before you start the exam. 7. Clarify any ambiguous questions with the instructor before you start the exam. 8. Budget your time according to the point value of each section. Bring a watch with you to keep track of the time. Do not get carried away answering one question. 9. Establish priorities. Do the easy items first because it is a confidence builder. Save the difficult items for last. 10. Re-read what you have done. Make changes
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