In a corporate accounting department, a specialist needs to calculate the unit cost of an item by dividing the total expense of 15.75 dollars by a quantity of 0.25. To simplify the long division, the specialist shifts the decimal points in both numbers two places to the right to divide 1575 by 25. Which mathematical property justifies that this action does not change the resulting unit cost?

A logistics coordinator is calculating the number of shipping units by dividing a total weight of {}42.5 tons by a unit weight of {}0.25 tons. To simplify the long division, the coordinator shifts the decimal points in both numbers two places to the right to divide ${}4250$ by ${}25$. This action is mathematically justified by the ____ Fractions Property, which states that multiplying both the dividend and the divisor by the same nonzero number does not change the quotient.

An inventory manager is calculating the number of individual units in a shipment by dividing the total weight of {}15.6 kilograms by the weight per unit of {}0.12 kilograms. To simplify the long division, they shift the decimal points in both numbers to divide ${}1560$ by ${}12$. True or False: This simplification is mathematically justified by the Equivalent Fractions Property, which states that multiplying both the dividend and the divisor by the same power of ${}10$ (in this case, ${}100$) does not change the quotient.

In professional accounting and inventory management, specialists often shift decimal points to simplify division calculations, such as when determining unit costs or logistics weights. Match each term below with its correct mathematical definition or its specific role in justifying why this simplification does not change the final result.

Payroll Calculation and Decimal Division

Explaining Decimal Operations in Financial Training

An estimator at a manufacturing firm is calculating the unit cost of a specialized metal part by dividing the total batch invoice of 148.50 dollars by a production quantity of 1.2 thousand units (represented by the division expression ${}148.50 \div 1.2$). To simplify the long division, the estimator shifts the decimal points to divide 1485 by 12 instead.

To recall how this standard decimal-shifting procedure is mathematically justified, arrange the logical progression of steps in the correct order, starting with the initial representation of the problem and finishing with the application of the Equivalent Fractions Property.