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

2. “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?

3. “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

4. “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.

5. “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”

6. 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?

7. “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’

8. “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

9. “Sum” “Addends” 2 + 3 = 5 The answer when you add
two or more numbers together.
2 + 3 = 5
“Addends”
The numbers that are added
together to get the sum.

10. “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.

11. “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.

12. “Inverse Property of Addition”
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?

13. “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?

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

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

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

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

18. Associative Property of Addition
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.

19. 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.

20. Commutative Property of Addition
Adding two numbers  doesn’t matter which number comes first. = =

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

22. 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

23. 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?

24. 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.

25. 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”

26. 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.

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

28. 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.

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

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

31. Polynomials
“Degree”
“Leading Coefficient”

32. 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

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

34. 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 !!!

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