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Solving the Proportion
Solve the proportion .
Step 1 — Multiply both sides by the LCD. The denominators are and . Since , the LCD is . Multiply both sides by :
Step 2 — Simplify. On the left, cancels with the denominator , leaving . On the right, , so the product is :
Step 3 — Check. Substitute back into the original proportion: This matches the original right side, confirming the solution is .
This example illustrates the basic technique for solving a proportion when the variable appears in a numerator: multiply both sides by the LCD to clear fractions, divide out common factors, and verify by substituting the result into the original equation.
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In workplace applications such as scaling a blueprint or adjusting a budget, what is the specific term for an equation that states two ratios are equal?
In a professional setting, when a team lead needs to scale a known ratio to a larger context by creating an equation that asserts two ratios are equal, this equation is known as a ____.
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In a proportion used for scaling professional ratios, such as , the values in the denominators ( and ) must not be equal to zero.
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Suppose you are a logistics manager who needs to scale a fuel-to-mileage ratio for a larger vehicle fleet. To find an unknown value using a proportion, arrange the following steps in the correct order to solve the equation using the method of clearing fractions.
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In a manufacturing facility, a quality control technician uses the proportion to demonstrate that the ratio of defective parts remains consistent as production scales. According to the formal definition of a proportion, how should the technician read this equation during a shift report?
A logistics coordinator is comparing the fuel efficiency of two different delivery trucks by documenting their miles-per-gallon ratios. If the coordinator records these rates as a proportion, what does this mathematical equation specifically assert about the two ratios?
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Learn After
A retail manager is analyzing sales data and sets up the proportion x/63 = 4/7 to predict the number of customers (x) who will purchase a premium membership out of a group of 63. To solve for x by clearing the fractions, which value represents the Least Common Denominator (LCD) that both sides of the equation should be multiplied by?
A store manager uses the proportion x/63 = 4/7 to predict inventory needs. Match each component of the solving process with its correct numerical value based on the standard procedure for clearing denominators.
A logistics coordinator uses the proportion x/63 = 4/7 to determine the number of units (x) that should be loaded into a shipping container with a capacity of 63. According to the solution for this proportion, the value of x is ____.
A retail manager is solving the equation x/63 = 4/7 to determine the inventory needed for a large order. True or False: According to the standard solving procedure, the final step after calculating the value of x is to verify the solution by substituting it back into the original equation.
An operations analyst is using the proportion to determine the required quantity of a component for a production run of 63 units. Arrange the following steps in the correct order to solve for the unknown quantity using the standard algebraic method.
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A quality control auditor is performing the 'Check' step to verify the solution for the production proportion . To confirm the result is correct, the auditor simplifies the fraction to see if it equals . According to the standard verification process, which common factor is divided out of both the numerator and denominator to complete this simplification?
A financial analyst is solving the proportion to determine a project's success rate. According to the standard procedural guide, the method of 'multiplying both sides by the LCD' is the primary technique used because the unknown variable () is located in which position?