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# Algebra I Definition

### Algebra I Definitions and formulas

Question | Answer |
---|---|

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