Overview of Math Term 1

Variables

Variable- a letter used to represent 1 or more numbers
Ex. x=12
Value-the number(s) replace by a variable
Variable Expression-a collection of numbers, variables, ad operations
Ex x=12*n+3
Verbal Model-an operation or inequality in word form
Ex- Two cars ran through each tunnel at one time. How many cars were there total if there were 3 tunnels? 5? 10?
Algebraic Model- an operation or inequality using numbers
Modeling-writing a verbal or algebraic model that represents a real life situation
Speed=Distance/Time
Evaluate- to solve an expression

Exponents and Powers

Power- a base multiplied by an exponent
Base- the number or variable that is used as a factor in a power
Exponent- the number of times the base is used as a factor
3
Ex. 2 This is a power, 2 is the base, and 3 is the exponent
Exponential form- turning an expression into a power

Ex 4*4*4*4=4 squared

Order of Operations

When you solve an expression with more than 1 operation, you use the order of operations
Order of Operations-the order in which you solve operations in an operation
1) Solve in grouping symbols (parenthesis and brackets)
2) Exponents (power)
3) Multiplication/ Division (left to right)
4) Addition/ Subtraction (left to right)

Equations and Inequalities

Open Sentence- an equation with 1 or more variables
Ex 2*a=??
Inequality-an open sentence, with no equality sign, and an inequality mark (such as > greater than or < less than)
Ex 1<2, 2>1
Equation- an expression with a correctly placed equality sign
Sales Tax-Price*Tax=Cost

Tables and Graphs

Data- information, facts, or numbers that describe something
Table-a comparison of data in an organized way that relates the x-variable to the y-variable
Graph- (coordinate graph, bar graph, pictograph, etc.) -A comparison of data in a picture like form that compares the x-variable to the y-variable
Plotting-putting a point on a coordinate graph or number line

Functions

Function- a rule that establishes a relationship between two quantities, the output and the input
Output-the y-variable
Input-the x-variable
Rule: for each input there can be only 1 output, but more than one input can have the same output
Input-output table-a table that compares inputs to outputs
Domain-the collection of all the inputs in an input-output table
Range-the collection of all the outputs in an input-output table

Real Numbers

Real numbers-any number that can be correctly graphed on a number line
Origin-0 on a number line
Rule: all numbers to the left of the origin are negative, all the numbers to the right are positive
Absolute value-a numbers distance from 0 on the number line
The absolute value of a variable (Ex A) is represented as |A|
Opposites-two numbers with the same absolute value on the number line
Ex 2 and –2

Adding Real Numbers

When adding real numbers with the same sign:
1) Add absolute values
2) Attach the common sign.
When adding real numbers with a different sign:
1) Subtract the smaller absolute value from the larger absolute value
2) Attach the sign of the number with the larger absolute value

Properties of Addition-

Commutative Property-the order in which things are added does not change the sum
Ex. a+b=b+a
Associative property- the way you group 3 numbers does not change the sum
Ex. (a+b)+c=a+(b+c)
Identity Property- the sum of a number and 0 is the number
Ex. a+0=a
Inverse Property- (property of 0)-the sum of a number and its opposite is 0
Ex. a+(-a)=0

Subtraction of Real Numbers

When subtracting a number, adding the opposite of the number you are subtracting with gives you the same answer-add the opposite
Ex. a-b=a+(-b)

Multiplication of Real Numbers

1) A negative times a negative is a positive
2) A positive times a positive is a positive
3) A negative times a positive or a positive times a negative is a negative

Properties of Multiplication

Commutative Property- the order in which two numbers are multiplied does not change the product
Ex. a*b=b*a
Identity Property- the product of 1 and a number is the number
Ex. a*1=a
Property of 0-the product of a number and 0 is 0
Ex. a*0=0
Property of Opposites-the product of a numeral and –1 is the opposite of that number
Ex. a*(-1)=(-a)

Division of Real Numbers

Reciprocal-the number by which you multiply a number to reach 1
Ex. 2/1 * 1/2 in this case 2 is the reciprocal of 1 and vice versa
To divide a number by a nonzero number, multiply by the reciprocal
a/b=a*1/b
The quotient of two numbers with the same sign is positive. The quotient of two numbers with opposite signs is negative.

Properties of Division

Identity Property- the quotient of a number by 1 is the number
Ex. a/1=a
Property of 0-the quotient of 0 by a number is 0
Ex. a*0=0
(If you divide a number by 0 the answer will remain undecided, because it is impossible to calculate how many times 0 goes into a number)

(Extra stuff)

Pythagoras Theorem- a squared*b squared=c squared
Simple Interest=Principal*rate*time (years)