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Distributive Property
The distributive property connects multiplication with addition and subtraction. For any real numbers , , and :
This property also works when the factor multiplies from the right, and when addition is replaced by subtraction:
In algebra, the distributive property is used to remove parentheses when simplifying expressions. When the terms inside parentheses are not like terms — for example, in where and cannot be added — the order of operations alone cannot simplify the expression further. The distributive property provides a way forward by multiplying the outside factor by each term inside the parentheses separately. A helpful visual technique is to draw arrows from the outside factor to each term inside the parentheses, reminding you which multiplications to perform.
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OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Elementary Algebra
OpenStax Intermediate Algebra
OpenStax Intermediate Algebra
OpenStax Intermediate Algebra
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Ch.3 Math Models - Elementary Algebra @ OpenStax
Ch.6 Polynomials - Elementary Algebra @ OpenStax
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Ch.9 Roots and Radicals - Elementary Algebra @ OpenStax
Ch.8 Rational Expressions and Equations - Elementary Algebra @ OpenStax
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
Related
Square Root of a Negative Number Is Not Real
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Additive Identity
Multiplicative Identity
Multiplication by Zero
Distributive Property
In a professional technical report, measurements may appear as whole numbers, fractions, or non-terminating decimals. Which term describes the set of all numbers that can be represented as a point on a continuous number line?
A logistics coordinator is organizing data types for a shipping database. Match each number classification with the definition that correctly identifies its role within the real number system.
When a surveyor is recording measurements for a land deed, any value that can be plotted on a continuous number line—such as a whole number of feet, a fraction of an inch, or a non-terminating decimal like the square root of 2—is classified as a real number.
Classification of Numerical Measurement Sets
Defining Data Parameters for Scientific Software
In professional engineering specifications, any measurement that can be represented as a point on a continuous number line—encompassing whole numbers, fractions, and non-repeating decimals—is classified as a(n) ________ number.
A database administrator is setting up data validation rules for a logistics platform to handle various types of measurement data. Arrange the following mathematical sets in order from the most specific (the category with the most restricted set of values) to the most inclusive (the category that encompasses all possible values on a continuous number line).
Numerical Classification Standards for Technical Documentation
A software developer is writing the documentation for a database field that is classified as a 'Real Number' type. According to mathematical standards, which two primary subsets of numbers must be included to ensure this field accounts for every possible point on a continuous number line?
A technical specification for a new scientific instrument states that all output values are recorded as 'Real Numbers.' According to the definition of this number system, what does this classification imply about the scope of the data the instrument can produce?
Nested Subsets of the Real Number System
Absolute Value
Learn After
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying by Distributing and Combining Like Terms
Simplifying by Distributing and Combining Like Terms
Solving by Distributing and Simplifying
Strategy for Solving Linear Equations
Multiplying a Polynomial by a Monomial
Multiplying Using the Distributive Property
Multiplying Using the Distributive Property
Multiplying Using the Distributive Property
A payroll specialist is calculating a standard 5 percent bonus for two different departments. The total bonus can be represented by the expression 0.05(S + M), where S is the total salary of the Sales department and M is the total salary of the Marketing department. Which mathematical property justifies rewriting this expression as 0.05S + 0.05M?
A contractor is calculating the total area of two rooms that have the same width 'w' but different lengths 'l1' and 'l2'. The total area is w(l1 + l2). The contractor calculates the area of each room separately as wl1 + wl2 and then adds them. The mathematical rule that justifies this is the ________ property.
A payroll administrator is expanding the expression 40(r + 2) to calculate total weekly pay including a 2 dollar hourly raise. Arrange the steps in the correct order to expand this expression using the Distributive Property.
An HR manager is simplifying payroll formulas for different departments. Match each initial cost expression on the left with its equivalent simplified form on the right using the distributive property.
A facilities manager is calculating the total cost of upgrading n standard workstations and 5 conference rooms, where the cost per upgrade is x dollars. The total cost is represented by the expression x(n + 5). True or False: According to the distributive property, this expression is equivalent to xn + 5.
Identifying Budgeting Properties in Procurement
Validating Budgeting Formulas in Logistics
Defining the Distributive Property in Administrative Budgeting
A retail manager is calculating the total revenue from selling 'k' holiday gift baskets. Each basket contains a bottle of sparkling cider (c) and a box of chocolates (h). The total revenue is represented by the expression k(c + h). According to the distributive property, which of the following is equivalent to this expression?
A project coordinator is calculating the total labor cost for two separate teams using the expression (Hours_Team_A + Hours_Team_B) × Hourly_Rate. To allocate expenses to different departments, the coordinator rewrites this as (Hours_Team_A × Hourly_Rate) + (Hours_Team_B × Hourly_Rate). Which mathematical property justifies this expansion?
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying 6\left( rac{5}{6}y + rac{1}{2} ight) Using the Distributive Property
Simplifying 12\left( rac{1}{3}n + rac{3}{4} ight) Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Strategy for Solving Equations with Fraction or Decimal Coefficients