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# Algebra I Definition

### Algebra I Definitions and formulas

Variable A letter or symbol used to represent a number
Expression A combination of variables, numbers, grouping symbols, and operational signs.
Whole numbers Counting numbers plus zero. {0,1,2,3...}
What is another name for the counting numbers? Natural numbers
List the set of counting numbers. {1,2,3...}
What are integers? Whole numbers and their opposites
List the set of integers {...-3,-2,-1,0,1,2,3,...}
What are rational numbers? Numbers that can be expressed as a/b where a and b are integers.
What is the value of a variable? It is the number which replaces the variable.
What is the value of an numerical expression? The number named by the numerical expression. 4 + 6 = 10. 10 is the value of the expression 4 + 6
What is a variable expression? An expression that contains a variable.
what is a numerical expression? An expression that names a particular number. 4 + 5 is a numerical expression.
What does "simplifying the expression" mean? Replacing an expression by the simplest name for its value. 4 + 5 can be simplified to 9.
What does "evaluate mean"? To substitute and then simplify
What is the substitution principal? An expression maybe replaced by another expression that has the same value.
What is the formula for the perimeter of a rectangle? P = 2L + 2W
What is the formula for the perimeter of a parallelogram? P = 2a + 2b
What is the formula for the area of a circle? A=πr^2 )(^ means "to the power")
What is the formula for the area of a trapezoid? A = 1/2 h(a + b)
What is the formula for the area of a triangle? A = 1/2 bh
What is the formula for the area of a rectangle? A = lw
What is the formula for the perimeter of a triangle? P = a + b + c
What is the formula for the surface area of a rectangular prism? SA = 2(lw + wh + lh)
Open Sentence Sentences that contain variables
Equation Two expressions set equal to each other.
Domain The set of numbers that a variable may represent
Solution The value(s) of the variable that makes the equation a true statement
Solving Finding the solution of an equation
Grouping symbol A device used to enclose an expression that should be simplified first
How many solutions can an equation have? None,one,or many
Solve The process of finding the value of the variable that will make the open sentence true.
What is the distance formula? d = rt where d = distance; r = rate; and t = time
What is the cost formula? C = np where C = cost; n = number; and p = price
What is a formula? An equation that states a rule about a relationship.
What is the formula for the circumference of a circle? c = π d where d is the diameter c = 2πr where r is the radius
What is the formula for the volume of a cylinder? V = πr^2h where h is the height of the cylinder and r is the radius
What is the formula for the surface area of a cylinder? SA = 2πr^2 + 2πrh or SA = 2πr^2 + πdh where d = diameter.
What is the formula for the volume of a rectangular prism? V = lwh
How do you find the diameter of a circle if you know the radius? d = 2r
What is the formula for the area of a square? A = s^2
What is the formula for the perimeter of a square? P = 4s
What is the formula for the volume of a cone? V = 1/3 π r^2 h ( A cone's volume is 1/3 that of a cylinder)
What is the volume of a pyramid? V = 1/3 Bh where B is the area of the base of the pyramid. h is height of the pyramid.
Origin The zero point on a number line
Negative side Points to the left of the origin
Positive side Points to the right of the origin
Is zero positive or negative? It is neither positive nor negative
Graph A POINT paired with a number
Coordinate A NUMBER that is paired with a point
To Graph is to _____________. place a point on the number line
Inequality symbols > Greater than < Less than
Opposites Numbers that are the same distance from zero but on opposing sides of the origin
What is the opposite of 3? -3
What is the opposite of -5? 5
What is the opposite of zero? Zero
Absolute Value The distance a number is from the origin.
How do you read -X? "The opposite of X"
What is the absolute value of -7? 7
What is the absolute value of 8? 8
What is the symbol for absolute value? ||
closure property For all Real numbers a and b, a + b is a unique number and ab is a unique number
Commutative property of addition For all real numbers a and b, a + b = b + a
Commutative property of multiplication For all real numbers a and b, ab=ba
Associative property of addition For all real numbers a, b, and c, (a + b) + c = a + (b + c)
Associative property of multiplication For all real numbers a, b, and c, (ab)c - a(bc)
Terms Expressions that are added together. 4 + 5 are terms. 3X + 5X are terms.
Factors Expressions that are multiplied together. 4•3 are factors. 2X has two factors: 2 and X
Reflexive property of equality For all real numbers a, a = a
Addition property of equality if a = b, then a + c = b + c
Subtraction property of equality if a = b, then a - c = b - c
Multiplication property of equality if a = b, the ac = bc
Division property of equality if a = b the a/c = b/c
Transform means to ______. change
Equivalent equations equations that have the same solution set
List 5 ways to transform an equation Substitution, subtraction, addition, multiplication, and division
Inverse Operations Operations that UNDO each other
What is the inverse operation of addition? Subtraction
what is the inverse operation of division? Multiplication
What is the cost formula? Cost = number of items x price per item
What is the profit formula? Profit = selling price - buying price
What is the income formula? Income = wage per hour X number of hours worked
What is the total value formula? Total value = value per item X number of items.
Property of opposite of a sum? -(a + b) = -a + (-a) or -a - b
Property of opposite of a difference? -(a - b)= -a + b
What is the definition of subtraction? a - b = a + (-b) (To subtract you add the opposite)
Id property of addition There is a unique number 0 such that for all a, a + 0 = a and 0 + a = a
Property of opposites For every real number a, there is a unique number -a, such that a + (-a) = 0 and (-a) + a = 0
Distributive property with respect to addition a(b + b) = ab + ac
Distributive property with respect to subtraction a(b - c) = ab - ac
Identity property of multiplication There is a unique number 1, such that for every a 1 • a = a and a • 1 = a
Multiplicative property of zero For every real number a, a • 0 = 0 and 0 • a = 0
Multiplicative property of -1 for every real number a, a(-1) = -a and (-1)a = -a
Property of opposites of products (-a)(b) = -ab a(-b) = -ab (-a)(-b) = ab
Property of reciprocals for every nonzero number a, there is a unique number 1/a such that a • 1/a = 1
Property of the reciprocal of the Opposite of a number for every nonzero a, 1/-a = -1/a
Property of the reciprocal of a product 1/ab = 1/a • 1/b
Definition of division a ÷ b = a • 1/b (To divide you multiply by the reciprocal.)
(a + b)/c = ? a/c + b/c
Created by: barr04