Example of Evaluating $3ab^2$ when a=-rac{2}{3} and b=-rac{1}{2}

Example of Evaluating $4c^3d$ when c=-rac{1}{2} and d=-rac{4}{3}

A pharmacy technician uses the expression $\frac{1}{10}w + \frac{1}{2}$ to determine the dosage (in milliliters) for a specialized medication, where $w$ represents the patient's weight in kilograms. If a patient weighs $\frac{3}{4}$ of a kilogram, what is the correct first step to evaluate this expression?

A small business owner uses the expression $\frac{3}{5}w + \frac{1}{4}$ to calculate the shipping cost (in dollars) for a lightweight package, where $w$ represents the weight in pounds. Arrange the following steps in the correct order to evaluate the shipping cost for a package weighing $\frac{1}{2}$ pound.

A quality control inspector uses the expression $\frac{7}{8}v$ to check the volume of a liquid container. Match each component of the evaluation process with its correct description for the case where $v = \frac{4}{5}$.

In a corporate resource management system, when evaluating a variable expression that involves a fractional value, the standard procedure is to first substitute the fractional value for the variable and then simplify the resulting expression according to the order of operations.

Standard Procedure for Evaluating Variable Expressions with Fractions

A logistics coordinator at a freight delivery company uses the variable expression $\frac{2}{3}d + \frac{1}{4}$ to estimate delivery times (in hours), where $d$ is the distance in miles. To evaluate this expression for a courier trip of $d = \frac{1}{2}$ mile, the coordinator must first ____ the fractional value $\frac{1}{2}$ for the variable $d$ in the expression, and then simplify according to the order of operations.

Training Guide for Freight Rate Calculation