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Equivalent Fractions Property
If , , and are numbers where and , then multiplying both the numerator and the denominator of a fraction by the same nonzero number produces an equivalent fraction: . This property also works in reverse, meaning that common factors can be divided out without changing the fraction's value: .
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References
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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Elementary Algebra @ OpenStax
Algebra
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Ch.6 Polynomials - Elementary Algebra @ OpenStax
Ch.8 Rational Expressions and Equations - Elementary Algebra @ OpenStax
Ch.9 Roots and Radicals - Elementary Algebra @ OpenStax
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
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Equivalent Decimals
A project manager is tracking task completion across different departments. Match each department's completion fraction on the left with its equivalent fraction on the right for the final report.
A retail manager is comparing sales data and notices that 2/5 of the morning shift's transactions were paid in cash, which is the same portion as 4/10 of the afternoon shift's transactions. What is the specific mathematical term for fractions that represent the same quantity or portion of a whole, even though they have different numerators and denominators?
During a company-wide resource review, a manager identifies two fractions as being 'equivalent.' True or False: This indicates that both fractions represent the same quantity or portion of the resources, despite having different numerators and denominators.
Defining Consistency in Financial Reporting
An instructional designer is drafting a glossary for a corporate 'Math in the Workplace' workshop. Arrange the following phrases in the correct order to form the complete, formal definition of 'Equivalent Fractions'.
In a corporate inventory audit, if one department reports that 2/5 of its supplies have been utilized and another department reports the same amount as 4/10, they are using different numbers to represent the same portion of resources. Fractions that represent the same quantity or value, even though they have different numerators and denominators, are formally known as ________ fractions.
Analyzing Fuel Efficiency Reports
Defining Equivalent Fractions in Workplace Documentation
In a corporate efficiency report, a manager notes that two different departments have the same task completion rate: Department A reported 2/5 and Department B reported 4/10. What is the fundamental property that makes these two fractions 'equivalent'?
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Equivalent Fractions Property
Learn After
Procedure for Simplifying a Fraction
How to Simplify a Rational Expression
A logistics manager is adjusting a fuel-to-distance ratio of a/b for a fleet of trucks. According to the Equivalent Fractions Property, which expression represents an equivalent ratio for any non-zero scaling factor c (where b is also non-zero)?
A logistics coordinator is scaling a fuel-to-weight ratio. According to the Equivalent Fractions Property, multiplying both the numerator and the denominator of a fraction by the same nonzero number produces an ____ fraction.
In a professional setting, if an analyst is working with a financial ratio represented by the fraction a/b, the Equivalent Fractions Property states that multiplying both the numerator (a) and the denominator (b) by the same non-zero number (c) will result in a fraction that is equivalent to the original ratio.
An operations analyst is documenting the mathematical standards for resizing data batches while maintaining consistent proportions. Match each component of the Equivalent Fractions Property with its correct description or mathematical representation.
Standardizing Performance Ratios
Data Standardization in Quality Assurance
A logistics coordinator needs to scale a shipping ratio to accommodate a larger cargo volume. According to the Equivalent Fractions Property, arrange the following steps in the correct order to transform the original ratio into an equivalent fraction using a non-zero scaling factor .
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A budget analyst is scaling a cost-to-revenue ratio to reflect a larger department size by multiplying both terms by a non-zero factor . According to the Equivalent Fractions Property, why does the new fraction maintain the exact same value as the original ratio?
A project manager is scaling a resource allocation ratio of (units per department) to accommodate a larger organizational structure. According to the Equivalent Fractions Property, which operation must be performed to ensure the new ratio remains equivalent to the original?
Example of Dividing
Simplifying a Fraction