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Calculating rates and scaling rates. Drops per mL and drops per minute questions unit rate to equivalent rate.

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Write the following question down on paper and evaluate it without using a calculator.

If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

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A certain IV drip delivers $\\var{dpml}$ drops per mL. This is equivalent to [[0]] drops per $\\var{volume}$ mL.

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We can approach these questions like equivalent fractions by replacing the word 'per' with the operation of division.

The following are all equivalent ways of writing the same rate:

$\\var{dpml}$ drops per mL = $\\var{dpml}$ drops/mL = $\\var{dpml}$ drops / $1$ mL = $\\dfrac{\\var{dpml} \\text{ drops}}{1 \\text{ mL}}$.

We can multiply the top and bottom by any number other than zero and keep the rate the same. Since we are asked about $\\var{volume}$ mL, we multiply the top and bottom by $\\var{volume}$ so the bottom of the fraction is $\\var{volume}$.

$\\dfrac{\\var{dpml} \\text{ drops}}{1 \\text{ mL}}\\times\\dfrac{\\var{volume}}{\\var{volume}}=\\dfrac{\\var{ans1} \\text{ drops}}{\\var{volume}\\text{ mL}}$

In other words, the rate is equivalent to $\\var{ans1}$ drops per $\\var{volume}$ mL.

We can also approach these questions like ratios.

Think of $\\var{dpml}$ drops per mL as the ratio $\\var{dpml}$ drops : $1$ mL.

We can multiply both sides of this ratio by any non-zero number to get an equivalent ratio. Since we want to know about $\\var{volume}$ mL, we multiply both sides by $\\var{volume}$.

$\\var{dpml} \\text{ drops} \\,:\\, 1 \\text{ mL} = \\var{dpml}\\times \\var{volume}\\text{ drops}\\, :\\, 1 \\times \\var{volume} \\text{ mL} = \\var{ans1} \\text{ drops}\\,:\\, \\var{volume}\\text{ mL}$.

In other words, there are $\\var{ans1}$ drops in $\\var{volume}$ mL.

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A patient requires $\\var{dpm}$ drops per minute from an IV. How many drops will they need over $\\var{duration}$ minutes?

[[0]] drops.

We can approach these questions like equivalent fractions by replacing the word 'per' with the operation of division.

The following are all equivalent ways of writing the same rate:

$\\var{dpm}$ drops per minute = $\\var{dpm}$ drops/min = $\\var{dpm}$ drops / $1$ min = $\\dfrac{\\var{dpm} \\text{ drops}}{1 \\text{ min}}$.

We can multiply the top and bottom by any number other than zero and keep the rate the same. Since we are asked about $\\var{duration}$ minutes, we multiply the top and bottom by $\\var{duration}$ so the bottom of the fraction is $\\var{duration}$.

$\\dfrac{\\var{dpm} \\text{ drops}}{1 \\text{ min}}\\times\\dfrac{\\var{duration}}{\\var{duration}}=\\dfrac{\\var{ans2} \\text{ drops}}{\\var{duration}\\text{ min}}$

In other words the rate is equivalent to $\\var{ans2}$ drops per $\\var{duration}$ minutes.

We can also approach these questions like ratios.

Think of $\\var{dpm}$ drops per minute as the ratio $\\var{dpm}$ drops : $1$ minute.

We can multiply both sides of this ratio by any non-zero number to get an equivalent ratio. Since we want to know about $\\var{duration}$ minutes, we multiply both sides by $\\var{duration}$.

$\\var{dpm} \\text{ drops} \\,:\\, 1 \\text{ min} = \\var{dpm}\\times \\var{duration}\\text{ drops}\\, :\\, 1 \\times \\var{duration} \\text{ min} = \\var{ans2} \\text{ drops}\\,:\\, \\var{duration}\\text{ min}$.

In other words there are $\\var{ans2}$ drops in $\\var{duration}$ minutes.

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