#### Ex: Pediatric Medication Dosage Calculation – Four Steps

You receive a medication order of 40 mg/kg of body weight. The available medication is 100 mg/ml. How many milliliters should
you give to an 8 lb 4 oz infant? To solve this problem
we’ll be using proportions which we see here below,
if the units of a and c are the same and units
of b and d are the same then a times d must equal b times c. To set up the first proportion we’ll use the rate 40 milligrams per
kilogram of body weight. So we’ll have 40 milligrams, per one kilogram must equal
the number of milligrams for the infant which
we’ll call x milligrams. Per the weight, which is given
as eight pounds four ounces. Notice in this case we can
not cross multiply and solve for x because we do not have
the same units on the bottom. Here we have kilograms, and
here we have pounds and ounces. So we’ll first have to
get a common unit here, we’ll convert ounces to
pounds and then we’ll convert the pounds to kilograms
to finally solve for x. So we first want to convert
four ounces to pounds. You may recognize this as
0.25 pounds, but if we don’t, we can use the conversion
16 ounces equals one pound, set up another proportion to
convert four ounces to pounds. We can say that 16 ounces is to one pound as 4 ounces is to an
unknown number of pounds, we’ll call it y pounds. Notice in this case, the units on top and on the bottom are the
same, so we can cross multiply and solve for y. When cross multiplying
we’ll leave off the units so 16 times y must equal one
times four or 16 y equals four. We divide both sides by 16, we have y equals 4/16ths
which does simplify to 1/4th which would be 0.25. Remember to convert a
fraction to a decimal, we divide. Notice one divided four equals 0.25 and so does four divided by 16. Which means we can now
write this as 8.25 pounds instead of eight pounds four ounces. But notice how we still have
different units on the bottom so now we’ll convert pounds to kilogram. So for the next proportion
we’ll use the conversion 2.2 pounds is approximately one kilogram. This will give us the first
rate or ratio in our proportion we can say that 2.2
pounds is to one kilogram as 8.25 pounds, is to an unknown number of kilograms, we’ll call it z kilograms. Again notice how we have
the same units on top same units on the bottom, so we can cross multiply and solve for z. 2.2 times z must equal one times 8.25. So 2.2 z equals 8.25
divide both sides by 2.2, z is equal to this quotient here. 8.25 divided by 2.2 is 3.75. Which means 8.25 pounds,
is equal to 3.75 kilograms. So we finally can solve for
x to determine the number of milligrams the infant needs and then from there we
can determine the number of milliliters the infant needs. So we can say 40 milligrams is to one kilogram as x
milligrams is to 3.75 kilograms. So we notice finally we
do have the same units on the top and on the bottom
so now we can cross multiply and solve for x. We would have one times
x equals 40 times 3.75. One times x would be x. And then we have 40 times 3.75 which would give us the
number of milligrams the infant needs. So the infant needs 150 milligrams. And now we can use this
information to determine the number of milliliters the infant
needs, the medication comes in 100 milligrams per milliliter. So this will be one of the
rates for our last proportion. We’ll have 100 milligrams, to one milliliter, must equal the rate of 150 milligrams to an unknown number of milliliters. So if 150 milligrams to,
let’s call it q number of milliliters. Notice in this last proportion
we do have the same units on top and the same units on the bottom so we can cross multiply and solve for q to answer the final question. Q times 100, must equal one times 150. Well 100 q equals 150, divide both sides by 100, we would have q equals, this would be 1.5 which means you give the infant 1.5 milliliters of medication. I hope you found this helpful.