Question

1. complete the following.

part a. complete the statement.
\\(\dfrac{72\text{ in.}}{\text{min}} = \dfrac{120\\ \boldsymbol{\textcircled{1}}}{\boldsymbol{\textcircled{2}}}\\)
options: in., ft, yd, sec

Explanation:

Step1: Convert 72 inches to feet

Since $1\ \text{ft} = 12\ \text{in}$, calculate $\frac{72}{12} = 6\ \text{ft}$. So 72 in. is equivalent to 6 ft, but 120 is 20×6, so we scale: $120\ \text{in.} = \frac{120}{12} = 10\ \text{ft}$. Wait, correct: match the numerator unit first. The left numerator is inches, so right numerator should be same unit? No, wait, 72 in. to 120 in. is a scale, but units: wait, 1 min = 60 sec, so convert denominator to seconds.

Step2: Convert minutes to seconds

$1\ \text{min} = 60\ \text{sec}$. The ratio $\frac{72\ \text{in.}}{1\ \text{min}} = \frac{72\ \text{in.}}{60\ \text{sec}}$. Scale numerator to 120 in.: find scale factor $\frac{120}{72} = \frac{5}{3}$. Multiply denominator by $\frac{5}{3}$: $60 \times \frac{5}{3} = 100\ \text{sec}$. Wait no, simpler: set up equivalent ratio $\frac{72}{60} = \frac{120}{x}$, solve $x = \frac{120 \times 60}{72} = 100$.

Step3: Assign units

Left numerator is inches, so right numerator (①) is inches? No, wait 72 in. = 6 ft, 120 in. = 10 ft, but 72 in./min = 120 in./(100 sec). Wait, no: 72 inches per minute is equal to 120 inches per $\frac{120}{72} \times 60 = 100$ seconds. Or 72 in./min = 1.2 in./sec, 120 in. / 1.2 in./sec = 100 sec.

Answer:

①: in.
②: sec
The completed ratio is $\frac{72\ \text{in.}}{1\ \text{min}} = \frac{120\ \text{in.}}{100\ \text{sec}}$