 # Math is a language, learn the words!

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Math is a language, learn the words!
Basic Vocabulary Math is a language, learn the words!

“Expression” (a math “phrase”)
A name or a symbol for a number x x + 4y - 2 Do you see an equal sign in an expression?

“Statement” (a math sentence)
A meaningful assertion that is either true or false. The most common “statement” is an equation. x + 3 = 5 Another “statement” could be an inequality. x + 3 ≤ 5

“Equivalent Equation”
An equation that means the same thing as the first equation. x = 2 2x = 4 An equation that has the same solution as the first equation.

“Terms” The individual numbers in an
expression or an expression or equation. x x + 4y - 2 1 term 2 terms 3 terms “Monomial” “Binomial” “Trinomial”

A letter or symbol that takes
“Variable” A letter or symbol that takes the place of a number. x + 3 = 5 3x + 4y = 12 ‘x’ and ‘y’ are the variables ‘x’ is the variable What number does ‘x’ represent? What numbers do ‘x’ and ‘y’ represent?

“Coefficient” 3x + 4y - 2 The number in front of a variable
in an expression or an equation. 3x + 4y - 2 3 is the coefficient of ‘x’ 4 is the coefficient of ‘y’

“Constant” A term in an expression or an equation that does not contain a variable 3x + 4y - 2 -2 is a constant (it’s “constantly” -2) 2x + 3 = 5 Both 3 and 5 are constants

two or more numbers together. 2 + 3 = 5 “Addends” The numbers that are added together to get the sum.

“Factors” “Product” 2 x 3 = 6 The numbers that are multiplied
together to get the answer. 2 x 3 = 6 “Product” The answer when factors are multiplied together.

“Quotient” “Dividend” “Divisor” 6÷ 3 = 2 The answer when
one number is divided by another number. 6÷ 3 = 2 “Dividend” “Divisor” The number that is being divided. The number that divides the dividend.

Any number added to its “opposite” (sign) equals zero. 5 + (-5) = 0 Think of the additive inverse of a number as the “opposite” or “negative” of the number. What is the additive inverse of -22?

“Inverse Property of Multiplication”
Any number multiplied by is reciprocal will equal 1. Any number divided by itself will equal 1. What is the multiplicative inverse of -1/7?

Multiplication = 3 x 5 5 + 5 + 5 or 3 rows of 5 items.
“repeated addition.” = 3 x 5 or 3 rows of 5 items.

Multiplication by the inverse or
Division Multiplication by the inverse or reciprocal of a number. This definition is essential when working with fractions!!!

What is the difference between
and ? Nothing! Division by 2 is the same thing as multiplication by ½. (remember the definition of division ?

Order of Operations (PEMDAS)
“Please Excuse My Dear Aunt Sally.” Parentheses Exponents Multiplication Division Addition Subtraction

We use PEMDAS (parentheses) to “associate” the 2 of the 3 numbers together so we know which to add together first. (2 + 3) + 4 2 + (3 + 4) = 5 + 4 = 2 + 7 = 9 = 9 The property says: when adding 3 or more numbers together, it doesn’t matter which two of numbers you add together first (“associate”), you’ll always get the same answer.

Associative Property of Multiplication
2 x 3 x 4 We use PEMDAS (parentheses) to “associate” the 2 of the 3 numbers together. (2 x 3) x 4 2 x (3 x 4) = 6 x 4 = 2 x 12 = 24 = 24 The property says: when multiplying 3 or more numbers together, it doesn’t matter which two of numbers you multiply together first (“associate”), you’ll always get the same answer.

Adding two numbers  doesn’t matter which number comes first. = =

Commutative Property of Multiplication
2 x 3 = 3 x 2 multiplying two numbers  the order of multiplication does not matter.

Distributive Property (of Addition over Multiplication)
This property is important when variables are involved. 2(x + 4) Simplify the following: 2(x + 4) = 2 x + (2 * 4) Distributive property = 2x + 8 multiplication

Vocabulary: Solution of an Equation (that has a variable in it):
the value of the variable that makes the equation true. Can you do this problem in your head?

Definition To solve an Equation (that has a variable in it): to find the value of the variable that makes the equation true. REMEMBER anything you do in math must obey the definitions and properties of math. Solving an equation involves applying properties and operations to equations to find the value of the variable that makes the equation true.

Equality Properties Addition Property of Equality
Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality These properties only apply to equations (not expressions) !!! Do the same thing to the left and right sides of the equal sign. “same thing left, same thing right”

Definitions: Solution to an equation: the value of the variable that makes the equation “true”. Equivalent equation: has the same solution as the original equation: The solution to both equations is x = 2. They are equivalent equations.

Vocabulary Coefficient
The number that multiplies a variable or is “in front of” the variable

Vocabulary Quantity: An measure of a real world physical property (length, width, temperature, pressure, weight, mass, etc.). Formula: An equation that relates two or more quantities, usually represented by variables.

Vocabulary Verbal Model: Writing an equation in words before you
write it in mathematical symbols.

Polynomials POLY nomials
many terms each with the same variable raised to an positive INTEGER power.

Vocabulary Determining the number that the expression simplifies to if you assume a value for ‘x’. Evaluating an expression Evaluate the expression for x = -4

“Like” Terms Which of these terms (if any) are “like” terms?
Simplify means add, subtract, multiply, divide

Power What is a power? Power: An expression formed by repeated
multiplication of the same factor. Exponent Coefficient Base The exponent applies to the number or variable immediately to its left, not to the coefficient !!!

What does it mean? Means: ‘x’ used as an addend 3 times
Means: ‘x’ used as an factor 3 times