- algebraic expression
- constants and variables combined using addition, subtraction, multiplication, and division
- associative property of addition
- the sum of three numbers may be grouped differently without affecting the result; in symbols, [latex]a+\left(b+c\right)=\left(a+b\right)+c[/latex]
- associative property of multiplication
- the product of three numbers may be grouped differently without affecting the result; in symbols, [latex]a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c[/latex]
- base
- in exponential notation, the expression that is being multiplied
- binomial
- a polynomial containing two terms
commutative property of addition
two numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[/latex]
- commutative property of multiplication
- two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\cdot b=b\cdot a[/latex]
- constant
- a quantity that does not change value
- distributive property
- the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, [latex]a\cdot \left(b+c\right)=a\cdot b+a\cdot c[/latex]
- equation
- a mathematical statement indicating that two expressions are equal
- exponent
- in exponential notation, the raised number or variable that indicates how many times the base is being multiplied
- exponential notation
- a shorthand method of writing products of the same factor
- formula
- an equation expressing a relationship between constant and variable quantities
- identity property of addition
- there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, [latex]a+0=a[/latex]
- identity property of multiplication
- there is a unique number, called the multiplicative identity, 1, which, when multiplied by a number, results in the original number; in symbols, [latex]a\cdot 1=a[/latex]
- index
- the number above the radical sign indicating the nth root
- integers
- the set consisting of the natural numbers, their opposites, and 0: [latex]\{\dots ,-3,-2,-1,0,1,2,3,\dots \}[/latex]
- inverse property of addition
- for every real number [latex]a[/latex], there is a unique number, called the additive inverse (or opposite), denoted [latex]-a[/latex], which, when added to the original number, results in the additive identity, 0; in symbols, [latex]a+\left(-a\right)=0[/latex]
- inverse property of multiplication
- for every non-zero real number [latex]a[/latex], there is a unique number, called the multiplicative inverse (or reciprocal), denoted [latex]\dfrac{1}{a}[/latex], which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, [latex]a\cdot \dfrac{1}{a}=1[/latex]
- irrational numbers
- the set of all numbers that are not rational; they cannot be written as either a terminating or repeating decimal; they cannot be expressed as a fraction of two integers
- natural numbers
- the set of counting numbers: [latex]\{1,2,3,\dots \}[/latex]
- order of operations
- a set of rules governing how mathematical expressions are to be evaluated, assigning priorities to operations
- principal nth root
- the number with the same sign as [latex]a[/latex] that when raised to the nth power equals [latex]a[/latex]
- principal square root
- the nonnegative square root of a number [latex]a[/latex] that, when multiplied by itself, equals [latex]a[/latex]
- radical
- the symbol used to indicate a root
- radical expression
- an expression containing a radical symbol
- radicand
- the number under the radical symbol
- rational numbers
- the set of all numbers of the form [latex]\dfrac{m}{n}[/latex], where [latex]m[/latex] and [latex]n[/latex] are integers and [latex]n\ne 0[/latex]. Any rational number may be written as a fraction or a terminating or repeating decimal.
- real number line
- a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.
- real numbers
- the sets of rational numbers and irrational numbers taken together
- scientific notation
- a shorthand notation for writing very large or very small numbers in the form [latex]a\times {10}^{n}[/latex] where [latex]1\le |a|<10[/latex] and [latex]n[/latex] is an integer
- variable
- a quantity that may change value
- whole numbers
- the set consisting of [latex]0[/latex] plus the natural numbers: [latex]\{0,1,2,3,\dots \}[/latex]