42 terms

# Combining Like Terms, Algebraic Expressions, and Simple Equations

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mathematics
According to the Merriam-Webster dictionary, a component of mathematics is the science of numbers and their operations.
factor
Numbers that are multiplied together to form a product. A number that divides evenly into another without leaving a reminder.
multiple
The product of a given number and the counting numbers (1, 2, 3, 4, 5, 6, etc)
product
A product is the result of multiplying factors together. It is the answer to a multiplication problem.
base
In the expression ax, a represents the base. For example, given 25, 2 is referred to as the base
exponent (power)
The number that indicates how many times the base is used as a factor.
Scientific notation
a way of expressing numbers of different capacities - either extremely small numbers or extremely large numbers. Scientific notation is the product of two factors: (1) a number greater than or equal to one, but less than 10, and (2) a power of 10.
standard notation or standard form
The standard (or typical) form for representing numbers in everyday life.
evaluate
to find the value or answer.
numerical expression
a math sentence containing only numbers and operational symbols
operation(s)
the four basic operations in mathematics are addition, subtraction, multiplication, and division
order of operations
a rule for evaluating expressions: first perform the operations in parentheses, then compute powers and roots, then perform all multiplication and division from left to right, and then perform all addition and subtraction from left to right.
composite number
a number with more than two factors
prime factorization
a way in which every composite number can be written as the product of prime numbers
prime number
a number with exactly two factors - 1 and itself
factor or divisor
Numbers that are multiplied together to form a product. A number that divides evenly into another without leaving a remainder
Greatest Common Factor (GCF) or Greatest Common Divisor (GCD)
(1) The largest common factor (or divisor) amongst two or more numbers.(2) The largest number that divides evenly into two or more numbers without leaving a remainder.
Least Common Multiple (LCM) or Least Common Denominator (LCD)
The smallest common multiple amongst two or more numbers.
multiple
The product of a given number and the counting numbers (1, 2, 3, 4, 5, etc)
Venn Diagram
A graphic organizer or drawing that provides a visual representation for groups of "things," such as numbers. A Venn diagram is a useful way of understanding similarities and differences amongst the given groups.
constant
a number that does not change
evaluate
to find the value or answer using order of operations
numerical expression
a math sentence containing only numbers and operational symbols. (ie. 3 + 2, 5 • 4)
operation(s)
The four basic operations in mathematics are addition, subtraction, multiplication, and division.
order of operations
a rule for evaluating expressions: first perform the operations in parentheses, then compute powers and roots, then perform all multiplication and division from left to right, and then perform all addition and subtraction from left to right.
substitute
to replace a variable with a number
variable
a variable is a letter that represents a value that can change
variable expression
a math sentence containing only numbers, operational symbols, and variables. (ie. 3 + x and 5y)
Addition keywords: add, plus, increased by, the sum, total, added to (switch), more than (switch), greater than (switch)
operation(s) or operational symbols
The four basic operations in mathematics are addition, subtraction, multiplication, and division.
division
Division keywords: divided by, the quotient, ratio, shared equally
muliplication
Multiplication keywords: multiplied by, times, of, the product, per, double, twice, triple
subtraction
Subtraction keywords: subtract, minus, decreased by, the difference, less, subtracted from (switch), less than (switch), fewer than (switch)
coefficient
Within a term, the coefficient is the number that multiplies the variable.
like terms
Like terms have identical variables; that is, they have the same variable to the same power. Constants are classified as like terms as well.
term
A term is a number (constant), variable, or the product of a number and a variable.
equation
A math sentence with an equal sign. An equation states that two math expressions are equal.
equivalent
equal to.
expression
is formed using only numbers, only variables, or a combination of both numbers and variables. Examples include, 8, 23, x, y, 5 + 7, 2x, x/6, 4x + 8, etc.
formula
equations that state a rule or fact for relating two or more variables.
inverse operations
undo, or reverse, each other. For example, addition and subtraction are inverse operations since 2 + 3 = 5 and 5 - 3 = 2. Additionally, multiplication and division are inverse operations since 2 • 3 = 6 and 6 ÷ 3 = 2.
solution
any value (or number) for a variable that makes an equation true.