Math Vocab: Variable- a letter used in a problem Coefficient- a number attached to a variable (multiplication) Integers- the set of all negatives, positives, and zero Absolute value- the positive distance from zero Reflections- picking it up and flipping it over Rotations- movement by up degrees Scale- set of numbers that includes the least and greatest values Interval- how the scale is broken Range- difference between greatest and least Histogram- bar like graph (picture) of a frequency table Bar graph- a graphic form using bars to make comparisons of statistics Bar notation- in repeating decimals the line or bar placed over the digits that repeat Base- in a power, the number used as a factor Circle graphs- a type of statistical graph used to compare parts of a whole Cluster- data that are grouped closely together Common denominator- a common multiple of the denominators of two or more fractions Coordinate system- A plane in which a horizontal number line and a vertical number line intersect at their zero point Cubed- the product in which a number is a factor three times Equation- a mathematical sentence that contains the equal sign (=) Evaluate- to find the value of an expression by replacing variables with numerals Exponent- In a power, the number of times the base is used as a factor Factor- a number that divides into a while number with a remainder of zero Frequency table- a table for organizing a set of data that shows the number of times each item or number appears Greatest common factor (GCF)- the greatest of the common factors of two or more numbers Least common denominator (LCD)- the least common multiple of the denominators of two or more fractions Least common multiple- The least of the common multiples of two or more numbers Line graph- a type of statistical graph using lines to show how values change over a period of time Lower quartile- the median of the lower half of a set of numbers indicated by LQ Mean- the sum of the numbers in a set of data divided by the number of pieces of data Median- the middle number in a set of data when the data are arranged in numerical order. If the data has an even number, the median is the mean of the two middle numbers. Metric system- a base-ten system of measurement using the basic units: meter for length, gram for mass, and liter for capacity Mode- the number(s) or item(s) that appear most often in a set of numbers Multiple- the product of the number and any whole number Negative integer- integer that is less than zero Ordered pair- a pair of numbers used to locate a point in the coordinate system. The ordered pair is written in this form: (x-coordinate, y-coordinate) Origin- the point of intersection of the x-axis and y-axis in a coordinate system Outlier- data that is more than 1.5 times the inter quartile range from the quartiles Positive integer- integer that is greater than zero Power- a number that can be written using an exponent Prime factorization- expressing a composite number as the product of prime numbers Prime number- a whole number greater than 1 that has exactly two factors, 1 and itself Quadrant- one of the four regions into which two perpendicular number lines separate the plane Quartile- one of four equal parts of data from a large set of numbers Ratio- a comparison of two numbers by division Reciprocal- the multiplicative inverse of a number Scientific Notation- a way of expressing a number as the product of a number that is at least 1 but less than 10 and a power of 10 Simplest form- a fraction is in simplest form when the GCF of the numerator and the denominator is 1 Squared- a number multiplied by itself Square root- one of the two equal factors of a number Upper extreme- the greatest number of a set of data Upper quartile- the median of the upper half of a set of numbers X-axis - the horizontal number line which helps to form the coordinate system X-coordinate - the first number of an ordered pair Y-axis- the vertical number line which helps to form the coordinate system Y-coordinate- the second number of an ordered pair Zero pair- the result of pairing one positive counter with one negative counter Problem Solving: 1) Read the Problem A) what you know A) what you need to find 1) Plan of action 1) Reread the problem 1) Solve Algebraic expressions: statement or phrase Equation: equal sign a sentence Three more than seven divided by five. (3+7) ÷ 2=5 Expression Addition Plus, sum, total, more than, increased by, or all together Subtraction Minus, difference, take away, decreased by, less than, or less Multiplication Times, product, of, or twice Division Quotient or fractions Define a Variable Pick a letter Coefficient: number attached to a variable multiplication Evaluating substitution Integers The set of all negatives, positives, and zeros Absolute Value: the positive distance from zero (usually in bars, ask how many units from zero is that number, answer is ALWAYS positive) Rules for Adding Integers: 1) same signs(positive & negative) 1) add numbers…answer get same sign 1) negative + negative = bigger negative 1) negative + positive = the difference between the two numbers with the sign(+ or -) of the larger number Rules for Subtracting Integers: We don't subtract integers, we add the inverses. Inverse Algorithm: L (leave) C (change) O (order) Leave first number, change sign, and make second number opposite. Example: -7 - (-3) = -7 + (+3) Rules for Multiplying Integers: 1) negative x positive = negative 1) negative x negative = positive Rules for Dividing Integers: 1) negative ÷ positive = negative 1) negative ÷ negative = positive Graphing Transformation Reflections: picking it up and flipping it over Function + Equation Function: for every x there is a y Equation: 2x = y Linear equation: 2 variable… equation that yields a line Slope/ y: intercept form of linear equations Y = mx / + or - b Y = x M = slope, that is the change y change x + or - b: is the point the line intersects the y axis Slope = change y (up and down) change x(left and right) Solving System of Equations: Graphically- graph both lines- the solution is the point of intersection Lower Extreme Upper Extreme ß------------------------------------------------------à IQR:inter quartile range(find outlier) Outlier: IQR x 1.5 Ten thousandths Thousandths Hundreths Tenths Ones Tens Hundreds Thousands Ten thousands Zero power rule: any nuber to the zero power is one Tens ones tenths hundreths 10^1 10^0 10^-1 10^-2 Rounding Decimals: Look to the right of place value your rounding to. If it is 4 or lower it stays the same. If it is 5 or higher it increases one. Multiplying Decimals: 1) multiply numbers 1) from the right account for decimal places Dividing Decimals: 1) change divisor to whole number 1) same amount of moves on dividend 1) carry up to quotient 1) divide Every fraction is a division problem Divide denominator into numerator to express fraction as decimals N __ 1 .25 D) N 4) 1 Terminating decimals: end Non-terminating decimals: continues or repeats(bar notation) 1 -__ 3 = .333 K H D S D C M Kilo: 10^3 or 1000 Hecto: 10^2 or 100 Deka: 10^1 or 10 Standard: 10^0 or 1 Deci: 10^ -1 or 1/10 Centi: 10^ -2 or 1/100 Milli: 10^ -3 or 1/1000 Km à m à cm à mm X 1000 x100 x10 Km ß m ß cm ß mm ÷1000 ÷100 ÷10 Prime: factors of one and itself(two factors) Composite: more than two factors One: one factor- multiplicative identity property Prime factorization: we can express every number as a product of its prime numbers Greatest common factor: largest common factor of two or more numbers example: 210, 308: 2 x 7 = 14 Using prime factorization it's the product of all the common factors with least exponent value Least common multiple: the first multiple two or more numbers have in common example: 210, 308 = 4,620 Using prime factorization the product of the different factors with greatest exponent value Checking if Prime 1) Take the square root of number 2) Test all primes up tot he number Example: square root of 97 = 9 Test all primes up to 9 (2,3,5,7) Does 2,3,5,7 go into 9? No This makes 97 prime.