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Multiplication Property of Equality
The Multiplication Property of Equality states that multiplying both sides of an equation by the same number preserves the equality. For any numbers , , and :
If , then
This property is used to solve equations in which the variable is divided by a number or has a fractional coefficient. Multiplying both sides by the appropriate value "undoes" the division or fraction. For example, to solve , multiply both sides by to obtain . Similarly, when the coefficient is a fraction such as , multiplying both sides by the reciprocal isolates the variable: . This technique leverages the inverse property of multiplication, since a number multiplied by its reciprocal equals .
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OpenStax
Elementary Algebra @ OpenStax
Ch.3 Math Models - Elementary Algebra @ OpenStax
Algebra
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Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
Ch.8 Rational Expressions and Equations - Elementary Algebra @ OpenStax
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When an office manager uses a formula to calculate a missing expense, the primary mathematical goal is to ____ the unknown variable by itself on one side of the equation.
In a professional context, such as determining the unit price needed to meet a specific revenue goal, which of the following best describes the process of 'solving' the resulting algebraic equation?
An administrative assistant is using an algebraic equation to find a missing value in a supply order. Match the following terms related to 'solving an equation' with their correct descriptions.
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In a workplace scenario, such as calculating the number of hours an employee worked based on their total earnings, the ultimate mathematical purpose of solving the resulting equation is to find a specific value for the variable that creates a true statement.
A project manager is solving an algebraic equation to determine the number of additional staff members needed for a new contract. Arrange the following conceptual stages of 'solving an equation' in the correct logical order, according to the standard mathematical definition.
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A laboratory technician is solving an equation to determine the exact amount of a catalyst needed for a chemical reaction. According to the definition of solving an equation, what is the defining characteristic of the specific value (the solution) the technician is searching for?
A project coordinator is reviewing the process of finding unknown values in a budget report. Match each aspect of the mathematical process of 'solving an equation' with its correct description according to the standard definition.
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Solving Using the Multiplication Property
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Translating and Solving ' divided by is '
Translating and Solving 'The quotient of and is '
Translating and Solving 'Three-fourths of is '
A logistics coordinator is calculating total inventory. If one-fourth of the total shipment (represented as x/4) is equal to 50 units, which mathematical property justifies multiplying both sides of the equation x/4 = 50 by 4 to solve for the total shipment x?
A warehouse supervisor is calculating total stock. If the equation states that one-fifth of the total stock (s/5) equals 200 units, the supervisor can multiply both sides of the equation by 5 to solve for 's'. This rule, which states that multiplying both sides of an equation by the same number preserves the equality, is known as the ____ Property of Equality.
A sales representative calculates that their commission is one-fifteenth of their total sales, represented by the equation s/15 = 2000. According to the Multiplication Property of Equality, the representative can multiply both sides of the equation by 15 to solve for the total sales 's' while maintaining the equality.
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An operations manager is training a new team on how to scale project resource equations while maintaining mathematical 'balance.' Match each algebraic term or concept related to the Multiplication Property of Equality with its correct description.
A logistics coordinator is calculating the total number of shipment crates (C) ordered for the month. They know that when the total is divided equally among 4 regional warehouses, each warehouse receives 150 crates (C/4 = 150). Arrange the steps in the correct logical order to solve this equation using the Multiplication Property of Equality.
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A warehouse manager is scaling an inventory order. The manager starts with an equality where the unit cost of Item A () is equal to the unit cost of Item B (). To prepare for a holiday rush, the manager triples the order for both (). Which mathematical property ensures that the total costs of the two orders remain equal?
A financial analyst is solving the equation &frac{3}{4}B = 1200& to find the total departmental budget (B). To isolate the variable using the Multiplication Property of Equality, the analyst multiplies both sides of the equation by &frac{4}{3}&. What is the mathematical term for the relationship of &frac{4}{3}& to the original coefficient &frac{3}{4}&?
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