Question

use dimensional analysis to convert.
how many ounces (oz) are in 46 quarts (qt)? (1 qt = 4 cups, 1 cup = 8 oz)
to convert 46 qt to ounces, you must first convert 46 qt to cups.
which expression correctly shows the measurement multiplied by the conversion factor?
\\(\frac{46\text{ qt}}{1} \cdot \frac{1\text{ qt}}{4\text{ cups}}\\)
\\(\frac{46\text{ qt}}{1} \cdot \frac{4\text{ cups}}{1\text{ qt}}\\)
\\(\frac{1}{46\text{ qt}} \cdot \frac{1\text{ qt}}{4\text{ cups}}\\)
\\(\frac{1}{46\text{ qt}} \cdot \frac{1\text{ cup}}{1\text{ qt}}\\)

Explanation:

Step1: Identify conversion direction

We need to convert quarts (qt) to cups, using the given conversion factor $1\ \text{qt} = 4\ \text{cups}$. To cancel the unit "qt", the conversion factor should have cups in the numerator and qt in the denominator.

Step2: Match to correct expression

Start with the given measurement $\frac{46\ \text{qt}}{1}$, then multiply by the conversion factor $\frac{4\ \text{cups}}{1\ \text{qt}}$ so that the "qt" units cancel out, leaving cups.

Answer:

$\boldsymbol{\frac{46\ \text{qt}}{1} \cdot \frac{4\ \text{cups}}{1\ \text{qt}}}$ (the second option)