Requirement to Multiply Every Term by the LCD
When solving an equation by clearing fractions or decimals, it is critical to multiply both sides of the equation by the least common denominator (LCD). Because of the Distributive Property, this means that every single term in the equation must be multiplied by the LCD, including any terms that are integers and do not contain a fraction. Failing to multiply every term by the LCD alters the underlying equality and will lead to an incorrect solution.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
Solving by Clearing Fractions
Solving by Clearing Fractions
Strategy to Solve Equations with Rational Expressions
A logistics coordinator is simplifying a shipping cost formula that contains several fractions. To use the method of clearing fractions from the equation, in what order should the coordinator perform the following steps?
A financial analyst is clearing fractions from a revenue equation to make the algebra simpler. According to the standard strategy, what is the primary goal of multiplying every term in the equation by the least common denominator (LCD)?
A project coordinator is simplifying a budget allocation formula that contains several fractions. Match each step of the 'clearing fractions' strategy with the correct action the coordinator should take to transform the equation into one with only integer coefficients.
A production planner is simplifying a resource allocation formula that contains several fractional coefficients. To begin the process of 'clearing the fractions,' the planner must first identify the ________ ________ ________ (LCD) of every fraction in the equation.
A budget analyst is simplifying a departmental expense formula that contains both whole numbers and fractions. True or False: To 'clear the fractions' from the equation while maintaining equality, the analyst must multiply every term on both sides of the equation by the Least Common Denominator (LCD), including the terms that do not have fractions.
Standard Procedure for Clearing Fractional Coefficients
Assisting a Colleague with Complex Financial Formulas
Standard Procedure for Clearing Fractional Coefficients in Equations
A project coordinator is simplifying a budget formula that contains several fractional coefficients. To make the calculations easier, the coordinator multiplies every term on both sides of the equation by a common multiple of all the denominators. Which of the following is true regarding the solution to this new equation?
A construction foreman is using a resource allocation formula that contains several fractional coefficients. To simplify his calculations, he applies the strategy of 'clearing the fractions' by multiplying both sides of the equation by the Least Common Denominator (LCD). What is the primary characteristic of the coefficients and constants in the resulting equivalent equation?
Solving rac{4q+3}{2} + 6 = rac{3q+5}{4} by Clearing Fractions
Solving rac{3r+5}{6} + 1 = rac{4r+3}{3} by Clearing Fractions
Solving rac{2s+3}{2} + 1 = rac{3s+2}{4} by Clearing Fractions
Solving by Clearing Fractions
Solving by Clearing Fractions
Solving by Clearing Fractions
Solving by Clearing Fractions
Solving by Clearing Fractions
Requirement to Multiply Every Term by the LCD
Learn After
When solving an equation by clearing fractions, such as , what is the mandatory requirement regarding the integer terms (10 and 50) when multiplying both sides of the equation by the Least Common Denominator (5)?
True or False: When clearing decimals from a logistics formula—such as —by multiplying both sides by 10, the Distributive Property requires that every single term in the equation, including the integers 100 and 500, must be multiplied by 10.
Clearing Fractions and the Distributive Property
A payroll specialist uses the equation to calculate a company's salary structure. To clear the fraction, the specialist multiplies both sides of the equation by the least common denominator (10). According to the Distributive Property, the specialist must multiply ____ term in the equation by 10 to ensure the equation remains balanced.
In your role as an inventory analyst, you often use algebraic formulas with fractions to calculate storage capacity. When clearing fractions from these equations to simplify your work, you must remember the rules of algebraic operations. Match each concept related to clearing fractions with its correct description based on the requirement to multiply every term.