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- https://math.libretexts.org/Courses/Nova_Scotia_Community_College/MATH_1043/02%3A_Algebra/2.02%3A_The_Fundamentals_of_Algebra/2.2.04%3A_Simplifying_Algebraic_ExpressionsThe commutative property allows us to change the order of multiplication without affecting the product or answer. The associative property allows us to regroup without affecting the product or answer.
- https://math.libretexts.org/Courses/Las_Positas_College/Book%3A_College_Algebra/01%3A_Prerequisites/1.02%3A_Real_Numbers_-_Algebra_EssentialsIn this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
- https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/06%3A_The_Fundamentals_of_Algebra/6.03%3A_Simplifying_Algebraic_Expressions\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -1...\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -15y.} \\ = - 18t - 63 ~ & \textcolor{red}{ \text{ Write the answer in simpler form.}} \\ ~ & \textcolor{red}{ \text{ Subtracting } -15y \text{ is the same as adding } 15y.} \end{aligned}\nonumber \]
- https://math.libretexts.org/Courses/Mt._San_Jacinto_College/Ideas_of_Mathematics/01%3A_Number_Sense/1.03%3A_Algebra_EssentialsIf we carefully placed more rocks of equal weight on both sides of this formation, it would still balance. Similarly, the expressions in an equation remain balanced when we add the same quantity to bo...If we carefully placed more rocks of equal weight on both sides of this formation, it would still balance. Similarly, the expressions in an equation remain balanced when we add the same quantity to both sides of the equation. In this section, we will solve equations, remembering that what we do to one side of the equation, we must also do to the other side.
- https://math.libretexts.org/Under_Construction/Stalled_Project_(Not_under_Active_Development)/Book%3A_Beginning_Algebra_(Feiner)/2%3A_The_Commutative%2C_Associative%2C_and_Distributive_Laws%2F%2FProperties/2.3%3A_The_Associative_Property_of_Addition_and_MultiplicationThe picture illustrates the Associative property of addition. In general \[\fbox{\Large \boldmath a+(b+c)=(a+b)+c}\] The general property (using \(a\), \(b\) and \(c\)) does not exist. The picture ill...The picture illustrates the Associative property of addition. In general \[\fbox{\Large \boldmath a+(b+c)=(a+b)+c}\] The general property (using \(a\), \(b\) and \(c\)) does not exist. The picture illustrates the Associative Property of Multiplication. For the automatic number to work, you need to add the "AutoNum" template (preferably at the end) to the page. Division is not associative, the general property (using \(a\), \(b\), and \(c\)) does not exist.
- https://math.libretexts.org/Courses/Mission_College/Math_001%3A_College_Algebra_(Kravets)/01%3A_Prerequisites/1.01%3A_Real_Numbers_-_Algebra_EssentialsIt is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East ...It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Because of the evolution of number systems, we can now perform complex calculations using these and other categories of real numbers. In this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
- https://math.libretexts.org/Courses/Hope_College/Math_125%3A_Hope_College/01%3A_Algebra_Essentials/1.01%3A_Real_Numbers_-_Algebra_EssentialsIn this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/01%3A_Prerequisites/1.01%3A_Real_Numbers_-_Algebra_EssentialsIn this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
- https://math.libretexts.org/Courses/Las_Positas_College/Foundational_Mathematics/02%3A_Integers/2.13%3A_Simplifying_(Still_Not_Solving)_Algebraic_Expressions)/2.13.01%3A_Simplifying_Algebraic_Expressions\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -1...\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -15y.} \\ = - 18t - 63 ~ & \textcolor{red}{ \text{ Write the answer in simpler form.}} \\ ~ & \textcolor{red}{ \text{ Subtracting } -15y \text{ is the same as adding } 15y.} \end{aligned}\nonumber \]
- https://math.libretexts.org/Courses/Palo_Alto_College/College_Algebra/01%3A_Prerequisites/1.02%3A_Real_Numbers_-_Algebra_EssentialsIt is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East ...It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Because of the evolution of number systems, we can now perform complex calculations using these and other categories of real numbers. In this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
- https://math.libretexts.org/Courses/Santiago_Canyon_College/HiSet_Mathematica_(Lopez)/05%3A_Multiplicacion_y_division_de_numeros_enteros/5.05%3A_Propiedades_de_la_MultiplicacionSi se multiplican tres números enteros, el producto será el mismo si los dos primeros se multiplican primero y luego ese producto se multiplica por el tercero, o si los dos segundos se multiplican pri...Si se multiplican tres números enteros, el producto será el mismo si los dos primeros se multiplican primero y luego ese producto se multiplica por el tercero, o si los dos segundos se multiplican primero y ese producto se multiplica por el primero. El hecho de que\(1 \cdot \text{ any number} = \text{that particular number}\) sea un ejemplo de la propiedad de la multiplicación.
