Expressions & Equations Vocabulary

Expressions & Equations associative property : The sum of three numbers is the same no matter how they are grouped using parentheses. (12+4)+7=23 or 12+(4+7)=23 The product of three numbers is the same no matter how they are grouped using parentheses. 3x(4x5)=60 or (3x4)x5=60

Expressions & Equations

coefficient

Expressions & Equations commutative property: Factors or addends can trade places without changing the product or sum. 2 x 6 = 6 x = Doesn’t apply to subtraction or division

Expressions & Equations distributive property: a (b + c)= ab + ac a (b - c)= ab – ac A separate presentation explores this idea.

Expressions & Equations

Sometimes a superscript is not available. 7^3 also means 7 x 7 x 7 The ^ symbol is called a carat.

Expressions & Equations Expression: A mathematical phrase without an equal sign It can use numbers, variables, and operations in any combination. It represents a mathematical relationship.

Expressions & Equations

Factor: An integer that divides evenly into another. (translation: it is a number you multiply by another number to get a product.)

Expressions & Equations

6 x 3 = 18 factorsproduct

Expressions & Equations Variable: A quantity that changes or can have different values. A symbol, usually a letter, that can stand for a variable quantity.

Expressions & Equations 2n + 3 = 11 variable

Expressions & Equations dependent variable: In a function, a variable whose value is determined by the value of the related independent variable

Expressions & Equations independent variable: A variable in a mathematical equation whose value determines that of a dependent variable

bikes2345 wheels46810 The number of bikes is the independent variable; the number of wheels depends on the number of bikes, and is therefore the dependent variable.

Expressions & Equations Identity Property: Your identity doesn’t change. It’s who you are. The are two identity properties in math: one for multiplication and one for addition.

Expressions & Equations You can discover the identity properties. What do you multiply a number by that doesn’t change the number? What do you add to a number that doesn’t change the number?

Expressions & Equations identity element: An identity element, for some particular operation, returns the input unchanged. For example, for multiplication, the identity element is 1, because a x 1 = a For addition, the identity element is 0, because a + 0 = a

Expressions & Equations The identity for multiplication is one, because multiplying by one doesn’t change the number. The identity for addition is zero, because adding zero to a number doesn’t change the number.

Expressions & Equations

Infinite: Having no boundaries or limits ∞

E xpressions & Equations Multiplier: Multiplier is no longer a common term. It is the second number in a two-part multiplication problem. Example: 450 multiplicand x 30 multiplier product We usually use the word "factor" now. "Multiplier" is an older way of naming things.

Expressions & Equations Order of Operations: Rules describing what sequence to use in evaluating expressions. (1)Evaluate within grouping symbols. (2)Do powers or roots. (3)Multiply or divide left to right. (4) Add or subtract left to right

Expressions & Equations ordered pairs: two numbers which identify the location of a point on a Cartesian grid. The first number tells the x-value, and the second number the y-value. The common format is (9, 7) or (-5, 3).

Expressions & Equations Power: also known as an exponent. The superscripted number tells to which power the base number is raised, or in other words, how many times the base number will be used as a factor.

Expressions & Equations Sum: The total when numbers are added = is the sum.

Expressions & Equations Term: A number, variable, product, or quotient in an expression. A term is not a sum or difference 5x + 12 term

Expressions & Equations Term: An expression is made of one or more terms. Fractions (division problems) and variables with a coefficient are each counted as one term. The coefficient is NOT split from the variable.

Expressions & Equations Term: Find the terms in the following examples. 3b + ½ -2y 5x m -6c – 3h g

Expressions & Equations 3b + ½ -2y3 terms 5x m3 terms -6c – 3h g4 terms

Expressions & Equations How to “read aloud” the > and < signs: One is read “greater than” while the other is read “less than.” The important part is getting them with the right sign!

Expressions & Equations The alligator wants to eat the most he can get, so the open end of his jaws are nearest the largest part. Means “greater than”

Expressions & Equations notation for multiplication (e.g., 3x, 3(4)): Several different ways can indicate that two numbers must be multiplied. 3 x 4 = 12 was the first notation we learned.

Expressions & Equations

Numbers in parentheses can also indicate multiplication. 5(3)=15 because 5(3) means 5 multiplied by 3.

Expressions & Equations It is used less frequently, but an asterisk can also indicate multiplication. 9*6=54 because 9*6 means 9 multiplied by 6.

Expressions & Equations Graphs: give a visual representation of numerical information. The can be a number line, a Cartesian grid, a pie chart, a bar graph, a histogram, a line graph, or several other kinds.

Expressions & Equations Tables: organize numerical information by categorizing the numbers and their labels. GraduatesDanville High Lee AcademyChester High

Expressions & Equations x/x: Anytime a number is divided by itself, it is equal to 1. Remember, if a pie is cut into 6 pieces and you have all 6 pieces, you have 1 pie.

Expressions & Equations

x(a+ b): the Distributive Property states that the factor on the outside of the parentheses is to be multiplied by both terms inside the parentheses. Example: 2(a+5)=2a+10

Expressions & Equations =: the symbol meaning “equals” or “is equal to.” All equations use this symbol. The expressions on either side of this symbol should be equivalent or the equation is not true.