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Convert a Fraction to a DecimalDivide the numerator of the fraction by the denominator. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Square Root Notationmmis read âthe square root ofm.â Ifm=n2,m=n2,thenm=n,m=n,fornâ¥0.nâ¥0. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Order DecimalsStep 1.Write the numbers one under the other, lining up the decimal points.Step 2.Check to see if both numbers have the same number of digits. If not, write zeros at the end of the one with fewer digits to make them match.Step 3.Compare the numbers as if they were whole numbers.Step 4.Order the numbers us... | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Step 1.Write the numbers one under the other, lining up the decimal points. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Step 2.Check to see if both numbers have the same number of digits. If not, write zeros at the end of the one with fewer digits to make them match. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Step 3.Compare the numbers as if they were whole numbers. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Step 4.Order the numbers using the appropriate inequality sign. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Commutative Property ofAddition:Ifa,ba,bare real numbers, thena+b=b+a.a+b=b+a.Multiplication:Ifa,ba,bare real numbers, thena·b=b·a.a·b=b·a.When adding or multiplying, changing theordergives the same result. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Addition:Ifa,ba,bare real numbers, thena+b=b+a.a+b=b+a. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Multiplication:Ifa,ba,bare real numbers, thena·b=b·a.a·b=b·a.When adding or multiplying, changing theordergives the same result. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Associative Property ofAddition:Ifa,b,ca,b,care real numbers, then(a+b)+c=a+(b+c).(a+b)+c=a+(b+c).Multiplication:Ifa,b,ca,b,care real numbers, then(a·b)·c=a·(b·c).(a·b)·c=a·(b·c).When adding or multiplying, changing thegroupinggives the same result. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Addition:Ifa,b,ca,b,care real numbers, then(a+b)+c=a+(b+c).(a+b)+c=a+(b+c). | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Multiplication:Ifa,b,ca,b,care real numbers, then(a·b)·c=a·(b·c).(a·b)·c=a·(b·c).When adding or multiplying, changing thegroupinggives the same result. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Distributive Property:Ifa,b,ca,b,care real numbers, thena(b+c)=ab+aca(b+c)=ab+ac(b+c)a=ba+ca(b+c)a=ba+caa(bâc)=abâaca(bâc)=abâac(bâc)a=baâca(bâc)a=baâca | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
a(b+c)=ab+aca(b+c)=ab+ac | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
(b+c)a=ba+ca(b+c)a=ba+ca | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
a(bâc)=abâaca(bâc)=abâac | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
(bâc)a=baâca(bâc)a=baâca | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Identity Propertyof Addition:For any real numbera:a+0=a0+a=aa:a+0=a0+a=a0is theadditive identityof Multiplication:For any real numbera:a·1=a1·a=aa:a·1=a1·a=a11is themultiplicative identity | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
of Addition:For any real numbera:a+0=a0+a=aa:a+0=a0+a=a0is theadditive identity | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
of Multiplication:For any real numbera:a·1=a1·a=aa:a·1=a1·a=a11is themultiplicative identity | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Inverse Propertyof Addition:For any real numbera,a+(âa)=0.a,a+(âa)=0.A number and itsoppositeadd to zero.âaâais theadditive inverseofa.a.of Multiplication:For any real numbera,(aâ0)a·1a=1.a,(aâ0)a·1a=1.A number and itsreciprocalmultiply to one.1a1ais themultiplicative inverseofa.a. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
of Addition:For any real numbera,a+(âa)=0.a,a+(âa)=0.A number and itsoppositeadd to zero.âaâais theadditive inverseofa.a. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
of Multiplication:For any real numbera,(aâ0)a·1a=1.a,(aâ0)a·1a=1.A number and itsreciprocalmultiply to one.1a1ais themultiplicative inverseofa.a. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Properties of ZeroFor any real numbera,a,a·0=00·a=0a·0=00·a=0â The product of any real number and 0 is 0.0a=00a=0foraâ0aâ0â Zero divided by any real number except zero is zero.a0a0is undefined â Division by zero is undefined. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
For any real numbera,a,a·0=00·a=0a·0=00·a=0â The product of any real number and 0 is 0. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
0a=00a=0foraâ0aâ0â Zero divided by any real number except zero is zero. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
a0a0is undefined â Division by zero is undefined. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Metric System of MeasurementLength1 kilometer (km)=1,000 m1 hectometer (hm)=100 m1 dekameter (dam)=10 m1 meter (m)=1 m1 decimeter (dm)=0.1 m1 centimeter (cm)=0.01 m1 millimeter (mm)=0.001 m1 meter=100 centimeters1 meter=1,000 millimeters1 kilometer (km)=1,000 m1 hectometer (hm)=100 m1 dekameter (dam)=10 m1 meter (m)=1 ... | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Length1 kilometer (km)=1,000 m1 hectometer (hm)=100 m1 dekameter (dam)=10 m1 meter (m)=1 m1 decimeter (dm)=0.1 m1 centimeter (cm)=0.01 m1 millimeter (mm)=0.001 m1 meter=100 centimeters1 meter=1,000 millimeters1 kilometer (km)=1,000 m1 hectometer (hm)=100 m1 dekameter (dam)=10 m1 meter (m)=1 m1 decimeter (dm)=0.1 m1 cen... | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Mass1 kilogram (kg)=1,000 g1 hectogram (hg)=100 g1 dekagram (dag)=10 g1 gram (g)=1 g1 decigram (dg)=0.1 g1 centigram (cg)=0.01 g1 milligram (mg)=0.001 g1 gram=100 centigrams1 gram=1,000 milligrams1 kilogram (kg)=1,000 g1 hectogram (hg)=100 g1 dekagram (dag)=10 g1 gram (g)=1 g1 decigram (dg)=0.1 g1 centigram (cg)=0.01 g... | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Capacity1 kiloliter (kL)=1,000 L1 hectoliter (hL)=100 L1 dekaliter (daL)=10 L1 liter (L)=1 L1 deciliter (dL)=0.1 L1 centiliter (cL)=0.01 L1 milliliter (mL)=0.001 L1 liter=100 centiliters1 liter=1,000 milliliters1 kiloliter (kL)=1,000 L1 hectoliter (hL)=100 L1 dekaliter (daL)=10 L1 liter (L)=1 L1 deciliter (dL)=0.1 L1 c... | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
Temperature ConversionTo convert from Fahrenheit temperature, F, to Celsius temperature, C, use the formulaC=59(Fâ32)C=59(Fâ32)To convert from Celsius temperature, C, to Fahrenheit temperature, F, use the formulaF=95C+32F=95C+32 | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
To convert from Fahrenheit temperature, F, to Celsius temperature, C, use the formulaC=59(Fâ32)C=59(Fâ32) | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
To convert from Celsius temperature, C, to Fahrenheit temperature, F, use the formulaF=95C+32F=95C+32 | https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts |
absolute value : The absolute value of a number is its distance from 0 on the number line. The absolute value of a numbernnis written as|n||n|. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
additive identity : The additive identity is the number 0; adding 0 to any number does not change its value. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
additive inverse : The opposite of a number is its additive inverse. A number and its additive inverse add to 0. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
coefficient : The coefficient of a term is the constant that multiplies the variable in a term. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
complex fraction : A complex fraction is a fraction in which the numerator or the denominator contains a fraction. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
composite number : A composite number is a counting number that is not prime. A composite number has factors other than 1 and itself. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
constant : A constant is a number whose value always stays the same. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
counting numbers : The counting numbers are the numbers 1, 2, 3, ⦠| https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
decimal : A decimal is another way of writing a fraction whose denominator is a power of ten. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
denominator : The denominator is the value on the bottom part of the fraction that indicates the number of equal parts into which the whole has been divided. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
divisible by a number : If a numbermmis a multiple ofnn, thenmmis divisible bynn. (If 6 is a multiple of 3, then 6 is divisible by 3.) | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
equality symbol : The symbol â==â is called the equal sign. We reada=ba=bas âaais equal tobb.â | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
equation : An equation is two expressions connected by an equal sign. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
equivalent decimals : Two decimals are equivalent if they convert to equivalent fractions. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
equivalent fractions : Equivalent fractions are fractions that have the same value. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
evaluate an expression : To evaluate an expression means to find the value of the expression when the variable is replaced by a given number. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
expression : An expression is a number, a variable, or a combination of numbers and variables using operation symbols. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
factors : Ifa·b=ma·b=m, thenaandbaandbare factors ofmm. Since 3 · 4 = 12, then 3 and 4 are factors of 12. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
fraction : A fraction is writtenabab, wherebâ0bâ0aais the numerator andbbis the denominator. A fraction represents parts of a whole. The denominatorbbis the number of equal parts the whole has been divided into, and the numeratoraaindicates how many parts are included. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
integers : The whole numbers and their opposites are called the integers: ...â3, â2, â1, 0, 1, 2, 3... | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
irrational number : An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
least common denominator : The least common denominator (LCD) of two fractions is the Least common multiple (LCM) of their denominators. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
least common multiple : The least common multiple of two numbers is the smallest number that is a multiple of both numbers. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
like terms : Terms that are either constants or have the same variables raised to the same powers are called like terms. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
multiple of a number : A number is a multiple ofnif it is the product of a counting number andn. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
multiplicative identity : The multiplicative identity is the number 1; multiplying 1 by any number does not change the value of the number. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
multiplicative inverse : The reciprocal of a number is its multiplicative inverse. A number and its multiplicative inverse multiply to one. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
number line : A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
numerator : The numerator is the value on the top part of the fraction that indicates how many parts of the whole are included. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
opposite : The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero:âaâameans the opposite of the number. The notationâaâais read âthe opposite ofaa.â | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
origin : The origin is the point labeled 0 on a number line. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
percent : A percent is a ratio whose denominator is 100. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
prime factorization : The prime factorization of a number is the product of prime numbers that equals the number. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
prime number : A prime number is a counting number greater than 1, whose only factors are 1 and itself. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
radical sign : A radical sign is the symbolmmthat denotes the positive square root. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
rational number : A rational number is a number of the formpqpq, wherepandqare integers andqâ0qâ0. A rational number can be written as the ratio of two integers. Its decimal form stops or repeats. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
real number : A real number is a number that is either rational or irrational. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
reciprocal : The reciprocal ofababisbaba. A number and its reciprocal multiply to one:ab·ba=1ab·ba=1. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
repeating decimal : A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
simplified fraction : A fraction is considered simplified if there are no common factors in its numerator and denominator. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
simplify an expression : To simplify an expression, do all operations in the expression. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
square and square root : Ifn2=mn2=m, thenmmis the square ofnnandnnis a square root ofmm. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
term : A term is a constant or the product of a constant and one or more variables. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
variable : A variable is a letter that represents a number whose value may change. | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
whole numbers : The whole numbers are the numbers 0, 1, 2, 3, .... | https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms |
To Determine Whether a Number is a Solution to an EquationStep 1.Substitute the number in for the variable in the equation.Step 2.Simplify the expressions on both sides of the equation.Step 3.Determine whether the resulting statement is true.If it is true, the number is a solution.If it is not true, the number is not a... | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 1.Substitute the number in for the variable in the equation. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 2.Simplify the expressions on both sides of the equation. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 3.Determine whether the resulting statement is true.If it is true, the number is a solution.If it is not true, the number is not a solution. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
If it is true, the number is a solution. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
If it is not true, the number is not a solution. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Addition Property of EqualityFor any numbersa,b, andc, ifa=ba=b, thena+c=b+ca+c=b+c. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
For any numbersa,b, andc, ifa=ba=b, thena+c=b+ca+c=b+c. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Subtraction Property of EqualityFor any numbersa,b, andc, ifa=ba=b, thenaâc=bâcaâc=bâc. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
For any numbersa,b, andc, ifa=ba=b, thenaâc=bâcaâc=bâc. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
To Translate a Sentence to an EquationStep 1.Locate the âequalsâ word(s). Translate to an equal sign (=).Step 2.Translate the words to the left of the âequalsâ word(s) into an algebraic expression.Step 3.Translate the words to the right of the âequalsâ word(s) into an algebraic expression. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 1.Locate the âequalsâ word(s). Translate to an equal sign (=). | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 2.Translate the words to the left of the âequalsâ word(s) into an algebraic expression. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 3.Translate the words to the right of the âequalsâ word(s) into an algebraic expression. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
To Solve an ApplicationStep 1.Read the problem. Make sure all the words and ideas are understood.Step 2.Identify what we are looking for.Step 3.Name what we are looking for. Choose a variable to represent that quantity.Step 4.Translate into an equation. It may be helpful to restate the problem in one sentence with the ... | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 1.Read the problem. Make sure all the words and ideas are understood. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 2.Identify what we are looking for. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 3.Name what we are looking for. Choose a variable to represent that quantity. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 4.Translate into an equation. It may be helpful to restate the problem in one sentence with the important information. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
Step 5.Solve the equation using good algebra techniques. | https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts |
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