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Subtracting
Subtract two fractions with unlike denominators by finding the LCD and converting to equivalent fractions:
Step 1 — Find the LCD and rewrite: Factor each denominator: and . The LCD is . The denominator 15 is missing three factors of 2 (i.e., 8), and the denominator 24 is missing the factor 5. Multiply accordingly:
Step 2 — Subtract: Combine the numerators: .
Step 3 — Simplify: Both 39 and 120 share the factor 3. Dividing each by 3 gives , which is written as . When the first numerator is smaller than the second after conversion, the result is negative. As with addition, never simplify the equivalent fractions before subtracting — that would destroy the common denominator.
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A logistics coordinator is combining two partial shipments of industrial solvent. One container is 1/4 full and the other is 2/5 full. To find the total amount, which of the following is the correct first step in the standard strategy for adding these fractions?
A logistics coordinator is combining two partial shipments of industrial solvent. One container is 1/4 full and the other is 2/5 full. To find the total amount, which of the following is the correct first step in the standard strategy for adding these fractions?
A logistics coordinator is combining two partial shipments of industrial solvent. One container is 1/4 full and the other is 2/5 full. To find the total amount, which of the following is the correct first step in the standard strategy for adding these fractions?
A quality control specialist is calculating the remaining amount of an alloy after a production cycle. The inventory record shows that of a metric ton was available, and of a metric ton was consumed. To determine the remaining amount using the standard strategy for subtracting fractions, arrange the following steps in the correct order.
A project coordinator is aggregating fractional budget allocations from different departments. To determine the total usage, they must follow the standard strategy for adding or subtracting fractions. Match each step of the strategy with its correct procedural action.
A warehouse supervisor is tracking production progress and notes that one team completed of a task while another team completed of the same task. True or False: According to the standard strategy for adding fractions, the supervisor should add both the numerators and the denominators to find the total portion completed, resulting in .
Fraction Strategy in Cargo Logistics
Requirement for Common Denominators in Operations
A research assistant is combining fractional volume measurements in a lab report. After adding the numerators and placing the result over the common denominator, the final step in the standard strategy is to ____ the resulting fraction if any common factors can be divided out.
Standard Operating Procedure for Fractional Inventory Reconciliation
Subtracting
Learn After
A logistics coordinator is comparing the remaining capacity of two storage containers. Container A is 7/15 full, and Container B is 19/24 full. To calculate the difference in capacity (7/15 - 19/24), what is the first step the coordinator should take?
An inventory analyst is calculating the difference in stock levels between two warehouse bins. Bin A is 7/15 full and Bin B is 19/24 full. To calculate the difference (7/15 - 19/24) using the standard subtraction method, place the following steps in the correct order.
A facility manager is comparing the resource consumption of two production lines. Line A uses of its daily allocation by noon, while Line B uses . To calculate the difference in their consumption (), the manager must convert both fractions to a common denominator. The Least Common Denominator (LCD) for these two fractions is ____.
A project coordinator is comparing the resource utilization of two different departments. Department A has utilized of its allocation, and Department B has utilized . To find the difference in utilization (Department A - Department B), the coordinator calculates . Match each numerical value from the standard calculation process with its corresponding role.
A project analyst is comparing the completion rates of two phases of a construction project. Phase 1 is complete and Phase 2 is complete. To determine the difference in progress, the analyst calculates using a common denominator of 120. True or False: The resulting fraction for this difference is negative because the first numerator (56) is smaller than the second numerator (95) after conversion.
Fuel Capacity Variance Analysis
Procedural Analysis of Fractional Subtraction
A logistics technician is calculating the variance in shipment volumes using the expression . According to the standard mathematical procedure, why is it essential that the technician performs the subtraction before attempting to simplify these fractions?
An inventory analyst is calculating the variance in stock levels between two warehouse bins, expressed as the difference . After identifying the Least Common Denominator (LCD) as 120, the analyst converts into an equivalent fraction. According to the standard calculation procedure, what is the numerator of this equivalent fraction?
Simplifying the Difference of Two Fractions