#### 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.

very good

Thank you for the comment. I will be posting IV calculations in the next day or two.

My school teaches another method. Namely the 10, 50, 20 method. Have u heard of it? We had a brief review at our school during clinical simulation lab…but the content was reviewed so briefly, most of us did not understand it and we have our first exam in two weeks and we must score 100% in order to pass the exam.

this was part of a "crash pediatric math review" for a nurse who has not done pediatric care for a long time!! very helpful.. thanks so much!