{"id":156,"date":"2024-10-16T18:56:01","date_gmt":"2024-10-16T18:56:01","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/?post_type=chapter&p=156"},"modified":"2024-10-21T13:50:24","modified_gmt":"2024-10-21T13:50:24","slug":"glossary-of-terms","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/glossary-of-terms\/","title":{"raw":"Glossary of Terms","rendered":"Glossary of Terms"},"content":{"raw":"
\r\n \t
algebraic expression<\/strong><\/dt>\r\n \t
constants and variables combined using addition, subtraction, multiplication, and division<\/dd>\r\n<\/dl>\r\n
\r\n \t
associative property of addition<\/strong><\/dt>\r\n \t
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]<\/dd>\r\n<\/dl>\r\n
\r\n \t
associative property of multiplication<\/strong><\/dt>\r\n \t
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]<\/dd>\r\n<\/dl>\r\n
\r\n \t
base<\/strong><\/dt>\r\n \t
in exponential notation, the expression that is being multiplied<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
binomial<\/strong><\/dt>\r\n \t
a polynomial containing two terms<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n \t
commutative property of addition<\/strong><\/dt>\r\n \t
two numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
commutative property of multiplication<\/strong><\/dt>\r\n \t
two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\\cdot b=b\\cdot a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
constant<\/strong><\/dt>\r\n \t
a quantity that does not change value<\/dd>\r\n<\/dl>\r\n
\r\n \t
distributive property<\/strong><\/dt>\r\n \t
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]<\/dd>\r\n<\/dl>\r\n
\r\n \t
equation<\/strong><\/dt>\r\n \t
a mathematical statement indicating that two expressions are equal<\/dd>\r\n<\/dl>\r\n
\r\n \t
exponent<\/strong><\/dt>\r\n \t
in exponential notation, the raised number or variable that indicates how many times the base is being multiplied<\/dd>\r\n<\/dl>\r\n
\r\n \t
exponential notation<\/strong><\/dt>\r\n \t
a shorthand method of writing products of the same factor<\/dd>\r\n<\/dl>\r\n
\r\n \t
formula<\/strong><\/dt>\r\n \t
an equation expressing a relationship between constant and variable quantities<\/dd>\r\n<\/dl>\r\n
\r\n \t
identity property of addition<\/strong><\/dt>\r\n \t
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]<\/dd>\r\n<\/dl>\r\n
\r\n \t
identity property of multiplication<\/strong><\/dt>\r\n \t
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]<\/dd>\r\n<\/dl>\r\n
\r\n \t
index<\/strong><\/dt>\r\n \t
the number above the radical sign indicating the n<\/em>th root<\/dd>\r\n<\/dl>\r\n
\r\n \t
integers<\/strong><\/dt>\r\n \t
the set consisting of the natural numbers, their opposites, and 0: [latex]\\{\\dots ,-3,-2,-1,0,1,2,3,\\dots \\}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
inverse property of addition<\/strong><\/dt>\r\n \t
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]<\/dd>\r\n<\/dl>\r\n
\r\n \t
inverse property of multiplication<\/strong><\/dt>\r\n \t
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]<\/dd>\r\n<\/dl>\r\n
\r\n \t
irrational numbers<\/strong><\/dt>\r\n \t
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<\/dd>\r\n<\/dl>\r\n
\r\n \t
natural numbers<\/strong><\/dt>\r\n \t
the set of counting numbers: [latex]\\{1,2,3,\\dots \\}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
order of operations<\/strong><\/dt>\r\n \t
a set of rules governing how mathematical expressions are to be evaluated, assigning priorities to operations<\/dd>\r\n<\/dl>\r\n
\r\n \t
principal n<\/em>th root<\/strong><\/dt>\r\n \t
the number with the same sign as [latex]a[\/latex] that when raised to the n<\/em>th power equals [latex]a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
principal square root<\/strong><\/dt>\r\n \t
the nonnegative square root of a number [latex]a[\/latex] that, when multiplied by itself, equals [latex]a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
radical<\/strong><\/dt>\r\n \t
the symbol used to indicate a root<\/dd>\r\n<\/dl>\r\n
\r\n \t
radical expression<\/strong><\/dt>\r\n \t
an expression containing a radical symbol<\/dd>\r\n<\/dl>\r\n
\r\n \t
radicand<\/strong><\/dt>\r\n \t
the number under the radical symbol<\/dd>\r\n<\/dl>\r\n
\r\n \t
rational numbers<\/strong><\/dt>\r\n \t
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.<\/dd>\r\n<\/dl>\r\n
\r\n \t
real number line<\/strong><\/dt>\r\n \t
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.<\/dd>\r\n<\/dl>\r\n
\r\n \t
real numbers<\/strong><\/dt>\r\n \t
the sets of rational numbers and irrational numbers taken together<\/dd>\r\n<\/dl>\r\n
\r\n \t
scientific notation<\/strong><\/dt>\r\n \t
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<\/dd>\r\n<\/dl>\r\n
\r\n \t
variable<\/strong><\/dt>\r\n \t
a quantity that may change value<\/dd>\r\n<\/dl>\r\n
\r\n \t
whole numbers<\/strong><\/dt>\r\n \t
the set consisting of [latex]0[\/latex] plus the natural numbers: [latex]\\{0,1,2,3,\\dots \\}[\/latex]<\/dd>\r\n<\/dl>","rendered":"
\n
algebraic expression<\/strong><\/dt>\n
constants and variables combined using addition, subtraction, multiplication, and division<\/dd>\n<\/dl>\n
\n
associative property of addition<\/strong><\/dt>\n
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]<\/dd>\n<\/dl>\n
\n
associative property of multiplication<\/strong><\/dt>\n
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]<\/dd>\n<\/dl>\n
\n
base<\/strong><\/dt>\n
in exponential notation, the expression that is being multiplied<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
binomial<\/strong><\/dt>\n
a polynomial containing two terms<\/dd>\n<\/dl>\n

\tcommutative property of addition<\/strong>
\n \ttwo numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[\/latex]<\/p>\n

\n
commutative property of multiplication<\/strong><\/dt>\n
two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\\cdot b=b\\cdot a[\/latex]<\/dd>\n<\/dl>\n
\n
constant<\/strong><\/dt>\n
a quantity that does not change value<\/dd>\n<\/dl>\n
\n
distributive property<\/strong><\/dt>\n
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]<\/dd>\n<\/dl>\n
\n
equation<\/strong><\/dt>\n
a mathematical statement indicating that two expressions are equal<\/dd>\n<\/dl>\n
\n
exponent<\/strong><\/dt>\n
in exponential notation, the raised number or variable that indicates how many times the base is being multiplied<\/dd>\n<\/dl>\n
\n
exponential notation<\/strong><\/dt>\n
a shorthand method of writing products of the same factor<\/dd>\n<\/dl>\n
\n
formula<\/strong><\/dt>\n
an equation expressing a relationship between constant and variable quantities<\/dd>\n<\/dl>\n
\n
identity property of addition<\/strong><\/dt>\n
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]<\/dd>\n<\/dl>\n
\n
identity property of multiplication<\/strong><\/dt>\n
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]<\/dd>\n<\/dl>\n
\n
index<\/strong><\/dt>\n
the number above the radical sign indicating the n<\/em>th root<\/dd>\n<\/dl>\n
\n
integers<\/strong><\/dt>\n
the set consisting of the natural numbers, their opposites, and 0: [latex]\\{\\dots ,-3,-2,-1,0,1,2,3,\\dots \\}[\/latex]<\/dd>\n<\/dl>\n
\n
inverse property of addition<\/strong><\/dt>\n
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]<\/dd>\n<\/dl>\n
\n
inverse property of multiplication<\/strong><\/dt>\n
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]<\/dd>\n<\/dl>\n
\n
irrational numbers<\/strong><\/dt>\n
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<\/dd>\n<\/dl>\n
\n
natural numbers<\/strong><\/dt>\n
the set of counting numbers: [latex]\\{1,2,3,\\dots \\}[\/latex]<\/dd>\n<\/dl>\n
\n
order of operations<\/strong><\/dt>\n
a set of rules governing how mathematical expressions are to be evaluated, assigning priorities to operations<\/dd>\n<\/dl>\n
\n
principal n<\/em>th root<\/strong><\/dt>\n
the number with the same sign as [latex]a[\/latex] that when raised to the n<\/em>th power equals [latex]a[\/latex]<\/dd>\n<\/dl>\n
\n
principal square root<\/strong><\/dt>\n
the nonnegative square root of a number [latex]a[\/latex] that, when multiplied by itself, equals [latex]a[\/latex]<\/dd>\n<\/dl>\n
\n
radical<\/strong><\/dt>\n
the symbol used to indicate a root<\/dd>\n<\/dl>\n
\n
radical expression<\/strong><\/dt>\n
an expression containing a radical symbol<\/dd>\n<\/dl>\n
\n
radicand<\/strong><\/dt>\n
the number under the radical symbol<\/dd>\n<\/dl>\n
\n
rational numbers<\/strong><\/dt>\n
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.<\/dd>\n<\/dl>\n
\n
real number line<\/strong><\/dt>\n
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.<\/dd>\n<\/dl>\n
\n
real numbers<\/strong><\/dt>\n
the sets of rational numbers and irrational numbers taken together<\/dd>\n<\/dl>\n
\n
scientific notation<\/strong><\/dt>\n
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<\/dd>\n<\/dl>\n
\n
variable<\/strong><\/dt>\n
a quantity that may change value<\/dd>\n<\/dl>\n
\n
whole numbers<\/strong><\/dt>\n
the set consisting of [latex]0[\/latex] plus the natural numbers: [latex]\\{0,1,2,3,\\dots \\}[\/latex]<\/dd>\n<\/dl>\n","protected":false},"author":15,"menu_order":2,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":22,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/156"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":2,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/156\/revisions"}],"predecessor-version":[{"id":161,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/156\/revisions\/161"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/parts\/22"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/156\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/media?parent=156"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapter-type?post=156"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/contributor?post=156"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/license?post=156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}