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

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.

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