#### 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.