Ex: Pediatric Medication Dosage Calculation – Three Steps

Welcome to an example of a Pediatric Medication Calculation, they’ll be determined using proportions. Proportion is made when we set two ratios or rates equal to each
other as we see here, where as long as the units of a and c are the same and the units
of b and d are the same, then a times d must equal b times c. These are called cross products. So if we have one unknown, we can solve for the unknown
using the cross products. Here we’re given a 20
pound, six ounce child is to receive medication
ordered at 20 micrograms per kilogram of body weight. How many micrograms
should the child receive? To set up the proportion we’ll begin with a known rate of 20 micrograms
per kilogram, so we can write this as 20 micrograms per one kilogram must equal to the second rate would deal with the given weight of the child. Since kilograms is weight,
the 20 pounds, six ounces must go on the bottom. the numerator would be
the number of micrograms which is unknown, so
we’ll say x micrograms. Notice in this form we
cannot cross multiply because our denominator
contains different units. Here we have kilograms and
here we have both pounds and ounces. So first convert these
two to a common unit will convert the six ounces to pounds, and then we’ll have to convert the pounds to kilograms. So again for the first
step we’re going to convert six ounces to pounds, and
we’ll use the conversion 16 ounces equals one pound. So these two will give us our first ratio for the proportion. We’ll have 16 ounces is to one pound as six ounces would be
to an unknown number of pounds, which we’ll call y pounds. Notice we do have the same units on the top, and on the bottom, so we can go ahead and cross
multiply and solve for y. When cross multiplying, we
will leave off the units. So we’ll have 16 times
y equals one times six. 16 times y is 16y. Equals one times six of course is six. Divide both sides by 16. So we have y equals 6/16
or 3/8, that simplifies. And we do want to convert
this to a decimal, and then we’ll round
to two decimal places. So we convert this to a decimal, we’ll divide three by eight. Three divided by eight is 0.375. Do a round to the hundredth
or two decimal places, notice how this five
here’s our decision maker. Five or more, we round up, four or less we round down. Because we have a five here. Round up by changing this to 0.38. Which means six ounces is
approximately 0.38 pounds, so now we can rewrite
this as 20.38 pounds. Notice how we still have
different units on the bottom. Here we have kilograms,
and here we have pounds. So now we’ll convert
20.38 pounds to kilograms using another proportion. The conversion we’ll use is 2.2 pounds is approximately one kilogram. So this will give us our first ratio, 2.2 pounds is to one kilogram as 20.38 pounds is to an
unknown number of kilograms, we’ll call it z kilograms. We have the same units on top, and on the bottom, so
we can cross multiply and solve for the unknown, so we have 2.2 times z
must equal one times 20.38. So we have 2.2z equals 20.38, divide both sides by 2.2. So z will be equal to this quotient here, which we’ll have to round. So 20.38 divided by 2.2 is
going to be approximately 9.26 if you round this
to two decimal places. Again here we have a three to the right, keeping this a six, so 9.26. So finally we have the
proportion that we need to solve this problem. We can replace 20.38
pounds with 9.26 kilograms. So 20 micrograms is to one kilogram as x micrograms is to 9.26 kilograms. So because we have the same units on top and on the bottom, we
can now cross multiply and solve for x. One times x must equal 20 times 9.26. Well one times x is just x, and 20 times 9.26 will give us the number of micrograms
needed for this child. 185.2 micrograms. I hope you found this helpful.