3 Ratios, Proportions, and Dimensional Analysis Free Online FlashCards

Why does the order of quantities in a ratio matter?

Order matters: milligrams per milliliter and milliliters per milligram express different relationships.

How can you create an equivalent ratio?

Multiply or divide both terms by the same nonzero number.

Why is $\frac{1\ \mathrm{g}}{1{,}000\ \mathrm{mg}}$ a useful conversion factor?

$\frac{1\ \mathrm{g}}{1{,}000\ \mathrm{mg}}=1$, because $1\ \mathrm{g}=1{,}000\ \mathrm{mg}$. Orient the fraction so the unwanted unit cancels.

What does a proportion express?

A proportion states that two ratios are equal.

A liquid has $250\ \mathrm{mg}$ per $5\ \mathrm{mL}$. How much drug is in $7.5\ \mathrm{mL}$?

$375\ \mathrm{mg}$.

At $250\ \mathrm{mg}$ per $5\ \mathrm{mL}$, what volume contains $375\ \mathrm{mg}$?

$7.5\ \mathrm{mL}$.

What is a rate?

A rate is a ratio comparing quantities, often with different units, such as $\mathrm{mg}/\mathrm{mL}$ or $\mathrm{mL}/\mathrm{hr}$.

What relationship does a medication concentration describe?

A concentration relates the amount of drug to the volume or mass of the preparation.

What is dimensional analysis?

It multiplies labeled fractions arranged so unwanted units cancel and the requested unit remains.

What should the remaining unit be in a dimensional-analysis calculation?

The remaining unit should match the quantity requested in the answer.

An order is $0.75\ \mathrm{g}$, and each tablet contains $250\ \mathrm{mg}$. How many tablets are needed?

$3$ tablets.

A liquid contains $125\ \mathrm{mg}$ per $5\ \mathrm{mL}$. What volume provides $250\ \mathrm{mg}$?

$10\ \mathrm{mL}$.