A logistics coordinator for a shipping company uses the proportion $\frac{n}{10} = \frac{3}{5}$ to determine the number of delivery trucks ($n$) needed for 10 regional routes. According to the method of cross-multiplication, which equation represents the correct first step to obtain a fraction-free equation?

A logistics manager uses the proportion $\frac{T}{24} = \frac{5}{8}$ to determine the number of trailers ($T$) required for a shipment. Match each component of the cross-multiplication process to its correct partner or function in creating a fraction-free equation.

A logistics coordinator is scaling a shipping plan using the proportion $\frac{r}{12} = \frac{5}{3}$, where $r$ represents the required number of regional hubs. Arrange the steps of the cross-multiplication process in the correct order to convert this proportion into a fraction-free equation.

Inventory Management and Proportion Scaling

A facility manager uses the proportion $\frac{A}{B} = \frac{C}{D}$ to determine the ratio of staff members to office square footage. True or False: According to the cross-multiplication method, the correct equation to obtain a fraction-free result is $AC = BD$.

Solving Proportions via Cross-Multiplication

An assistant pastry chef scaling a bakery recipe uses the proportion $\frac{f}{12} = \frac{5}{6}$, where $f$ represents the required cups of flour. To remove the fractions using the cross-multiplication method, the chef multiplies the numerator of each fraction by the denominator of the other and sets the products equal. This process yields the fraction-free equation ${}6f =$ ____.