Lecture 9: Putting it all Together

Pediatric Medications

Most of the content of this section is the same as material that we have already covered, becuase when we give medications to children and infants, much of the procedure is the same as that for adults; however, with children and infants, there are specific concerns that must be addressed, so we will address these issues in this section.

Oral Medications

The main difference between oral medications given to children and those given to adults is that pediatric oral medications are usually liquid, whereas most adult oral medications come in pill form.

Below are photographs of some of the containers often used for dosage of liquid oral drugs:

an oral syringe
another kind of oral syringe
using an oral syringe
to dose an infant
a calibrated oral dropper
a calibrated medicine spoon
a calibrated medicine cup

Adults generally take liquid oral medication by using a calibrated medicine cup of some kind, but droppers, spoons, and oral syringes are often used for dosing small children and infants who may not be able to drink from a cup. It is also important to note that you should never use an oral syringe to give injectable medication, because oral syringes are not sterile. It is possible, however, to use a regular syringe as an oral syringe, as long as you remove the needle first.

Oral syringes and medicine droppers are generally used for infants since it can be difficult to get them to drink from a spoon or a cup; smaller children will often be dosed with a calibrated medicine spoon, and older children may be dosed with a medicine cup or be given pills to swallow like an adult. Sometimes pills may be crushed and mixed into a small amount of juice or a soft food, but this can only be done if the tablets or capsules do not have a special coating that is intended to extend the release time of the medicine or to protect the stomache from irritation, since any such coating would be destroyed if the pills were crushed.

With children it is especially important to make sure that they drink or swallow all of the medication; for example, it may be necessary to watch the child drink the liquid or swallow the pills and then to check their mouths to be sure that they have swallowed them.

Also, oral liquid medications come in different kinds of mixtures. If an oral liquid is labeled as a suspension, this means that it is a mixture of powder in a liquid that will settle out over time. So if we are giving a patient an oral suspension, we must be sure to shake the medication thoroughly before we measure it so that when we measure the liquid we can be sure that it contains the proper amount of medication (if we don't shake it, most of the medication may have settled to the bottom), and then we must be sure to administer the medication as soon as possible, because if it is allowed to sit for any period of time, the medication will settle to the bottom of the liquid, and the patient will not get the proper dose. If a medicine is a suspension, it will say so on the label.

Subcutaneous and Intramuscular Medications

When administering subQ or IM medications to children, we follow all of the same procedures as when we administer them to adults, with 2 noteworthy exceptions:

  1. Maximum safe dosage: 1 mL
    For children, the maximum safe dosage that can be injected is 1 mL (as opposed to the 3 mL which is the maximum safe dosage for adults).

  2. Syringe used: tuberculin syringe
    Since the maximum safe dosage for children is so small, we will always use a tuberculin syringe, which holds a maximum of 0.5 or 1 mL, to measure their IM or subQ medications.
    Because these syringes always have hundredths marked on them, we will always round our volumes to the nearest hundredth.
    (This is different from the procedure with adults, where the 3-cc syringe is the most commonly used.)

Also, since the muscles of children and infants are also less developed than those of adults, when giving an IM injection, the large muscle of the thigh is often used.

Calculating the volume needed to give a pediatric oral, subcutaneous or intramuscular injection is exactly the same as it was for adults. For example:

Example:

Calculate the number of mL needed to administer the dosage below:
Order: Vantin 70 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 70 mg, we need to figure out how many mL it takes to make 70 mg:

_____mL=70 mg

So, in order to do this, we must convert 70 mg into mL, and the only way to do this is to multiply by a fraction that

Where can we find a fraction like this? The concentration given on the label is 100 mg per 5 mL. This tells us that 5 mL is equal to 100 mg, so if we write this as a fraction, it becomes:

5 mL
100 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    5 mL
    100 mg
    and
    100 mg
    5 mL
    . Why did we choose
    5 mL
    100 mg
    ?
    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

70 mg
1
×
5 mL
100 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

70 mg×5 mL
1×100 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

70 mg×5 mL
1×100 mg

Now we simplify and multiply out the fraction:

We can divide both 5 and 100 by 5 to get:

_____mL=

70 mg×51 mL
10020 mg

We can divide both 70 and 20 by 10 to get:

_____mL=

707 mg×51 mL
100202 mg

Writing this out more neatly yields:

_____mL=

7×1 mL
1×2

There is nothing now in this fraction that can be simplified, so we multiply 7 by 1 to get 7. Then we divide 7 by 2 to get 3.5.

So, our answer is 3.5 mL.

Example:

Calculate the number of mL needed to administer the dosage below:
Order: amoxicillin 10 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 10 mg, we need to figure out how many mL it takes to make 10 mg:

_____mL=10 mg

So, in order to do this, we must convert 10 mg into mL, and the only way to do this is to multiply by a fraction that

Where can we find a fraction like this? The concentration given on the label is 250 mg per 5 mL. This tells us that 5 mL is equal to 250 mg, so if we write this as a fraction, it becomes:

5 mL
250 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    5 mL
    250 mg
    and
    250 mg
    5 mL
    . Why did we choose
    5 mL
    250 mg
    ?
    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

10 mg
1
×
5 mL
250 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

10 mg×5 mL
1×250 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

10 mg×5 mL
1×250 mg

Now we simplify and multiply out the fraction:

We can divide both 5 and 250 by 5 to get:

_____mL=

10 mg×51 mL
25050 mg

We can divide both 10 and 50 by 10 to get:

_____mL=

101 mg×51 mL
250505 mg

Writing this out more neatly yields:

_____mL=

1×1 mL
1×5

There is nothing now in this fraction that can be simplified, so we multiply 1 by 1 to get 1. Then we divide 1 by 5 to get 0.2.

So, our answer is 0.2 mL.

Example:

Calculate the number of mL needed to administer the dosage below:
Order: Veetids 25 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 25 mg, we need to figure out how many mL it takes to make 25 mg:

_____mL=25 mg

So, in order to do this, we must convert 25 mg into mL, and the only way to do this is to multiply by a fraction that

Where can we find a fraction like this? The concentration given on the label is 125 mg per 5 mL. This tells us that 5 mL is equal to 125 mg, so if we write this as a fraction, it becomes:

5 mL
125 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    5 mL
    125 mg
    and
    125 mg
    5 mL
    . Why did we choose
    5 mL
    125 mg
    ?
    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

25 mg
1
×
5 mL
125 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

25 mg×5 mL
1×125 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

25 mg×5 mL
1×125 mg

Now we simplify and multiply out the fraction:

We can divide both 5 and 125 by 5 to get:

_____mL=

25 mg×51 mL
12525 mg

We can divide both 25 and 25 by 25 to get:

_____mL=

251 mg×51 mL
125251 mg

Writing this out more neatly yields:

_____mL=

1×1 mL
1×1

There is nothing now in this fraction that can be simplified, so we multiply 1 by 1 to get 1. Then we divide 1 by 1 to get 1.

So, our answer is 1 mL.

Example:

Calculate the number of mL needed to administer the dosage below:
Order: clindamycin 75 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 75 mg, we need to figure out how many mL it takes to make 75 mg:

_____mL=75 mg

So, in order to do this, we must convert 75 mg into mL, and the only way to do this is to multiply by a fraction that

Where can we find a fraction like this? The concentration given on the label is 150 mg per mL. This tells us that 1 mL is equal to 150 mg, so if we write this as a fraction, it becomes:

1 mL
150 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mL
    150 mg
    and
    150 mg
    1 mL
    . Why did we choose
    1 mL
    150 mg
    ?
    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

75 mg
1
×
1 mL
150 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

75 mg×1 mL
1×150 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

75 mg×1 mL
1×150 mg

Now we simplify and multiply out the fraction:

We can divide both 75 and 150 by 75 to get:

_____mL=

751 mg×1 mL
1502 mg

Writing this out more neatly yields:

_____mL=

1×1 mL
1×2

There is nothing now in this fraction that can be simplified, so we multiply 1 by 1 to get 1. Then we divide 1 by 2 to get 0.5.

So, our answer is 0.5 mL.

Example:

Calculate the number of mL needed to administer the dosage below:
Order: morphine 2 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 2 mg, we need to figure out how many mL it takes to make 2 mg:

_____mL=2 mg

So, in order to do this, we must convert 2 mg into mL, and the only way to do this is to multiply by a fraction that

Where can we find a fraction like this? The concentration given on the label is 10 mg/mL. This tells us that 1 mL is equal to 10 mg, so if we write this as a fraction, it becomes:

1 mL
10 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mL
    10 mg
    and
    10 mg
    1 mL
    . Why did we choose
    1 mL
    10 mg
    ?
    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

2 mg
1
×
1 mL
10 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

2 mg×1 mL
1×10 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

2 mg×1 mL
1×10 mg

Now we simplify and multiply out the fraction:

We can divide both 2 and 10 by 2 to get:

_____mL=

21 mg×1 mL
105 mg

Writing this out more neatly yields:

_____mL=

1×1 mL
1×5

There is nothing now in this fraction that can be simplified, so we multiply 1 by 1 to get 1. Then we divide 1 by 5 to get 0.2.

So, our answer is 0.2 mL.

Example:

Calculate the number of mL needed to administer the dosage below:
Order: Dilantin 20 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 20 mg, we need to figure out how many mL it takes to make 20 mg:

_____mL=20 mg

So, in order to do this, we must convert 20 mg into mL, and the only way to do this is to multiply by a fraction that

Where can we find a fraction like this? The concentration given on the label is 250 mcg in 5 mL. This tells us that 5 mL is equal to 250 mg, so if we write this as a fraction, it becomes:

5 mL
250 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    5 mL
    250 mg
    and
    250 mg
    5 mL
    . Why did we choose
    5 mL
    250 mg
    ?
    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

20 mg
1
×
5 mL
250 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

20 mg×5 mL
1×250 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

20 mg×5 mL
1×250 mg

Now we simplify and multiply out the fraction:

We can divide both 5 and 250 by 5 to get:

_____mL=

20 mg×51 mL
25050 mg

We can divide both 20 and 50 by 10 to get:

_____mL=

202 mg×51 mL
250505 mg

Writing this out more neatly yields:

_____mL=

2×1 mL
1×5

There is nothing now in this fraction that can be simplified, so we multiply 2 by 1 to get 2. Then we divide 2 by 5 to get 0.4.

So, our answer is 0.4 mL.

Intravenous Medications

We give pediatric IV medications in much the same way that we give adult IV medications; however the volume of fluid administered is usually much smaller than that for an adult, flow rates are usually lower (for example, 200 mL/h would be find for an adult, but would be too high for a small child), and the safety of doses is often determined by a child's weight, so orders must be checked for safety.

Also, children and infants have smaller more fragile veins, so they are more likely to have IV infiltration occur during administration, and therefore the IV site should be checked regularly for the usual signs that the canula has become dislodged from the vein.

IVs for both children and adults also often require an IV flush. An IV flush is a small amount of NS, or sometimes a low concentration of heparin (100 units/mL), which is infused through the IV tubing. Often it is done to ensure that none of the medication is left in the tubing, because when giving an IV, after the IV has finished, some amount of the medication remains stuck to the sides of the tubing; so the longer the tubing is, the larger the volume of fluid needed in an IV flush to ensure that all the medication is flushed from the tubing and that therefore the patient receives the amount of medication prescribed. Saline is used for this type of flush. A saline IV flush might also be used before giving an IV push or bolus, to ensure that the line has not infiltrated and that the injection of the medication to follow will actually go into the patient's bloodstream. Also, an IV flush may be used with a heplock/saline port on an intermittent IV setup to periodically clear out any blood clots that might form in the cannula in the periods of time during which fluid is not infusing.

When an IV flush is given, the fluid used for the flush must also be tracked, since it adds to the total amount of fluid that is given to the patient. Also, a nurse must label an IV bag so that it is clear whether it is the medication that is infusing, or whether it is the flush that follows the medication administration.

One other consideration of IV medication administration that is relevant for both children and adults is how medication should be mixed with an ordered diluent. For example, an order may read: Vancomycin 50 mg in 20 mL D5W to infuse over 1 h. Let us suppose that the 50 mg of vancomycin takes us exactly 1 mL of volume. Then do we add 20 mL of D5W to the vancomycin to get a solution with a total volume of 21 mL, or do we add only 19 mL of D5W so that when it is combined with the 1 mL of vancomycin we get a solution with a total volume of 20 mL?

The answer to this question is: it depends on hospital policy. Some hospitals do it the first way, and some use the second convention instead. For the problems in the textbook and in this class, we will assume that we are working in a hospital where the volume given in the order is for the total volume of the final solution, and not the volume of the diluent. So for this class, the answer is that we would add 19 mL of D5W to the 1 mL of vancomycin to produce a final solution that is 20 mL.

Let's look at some example orders where we determine how much diluent is to be added, and then practice calculating the flow rate needed, just as we did with adults:

Example:

The order is for 125 mg of Prostaphlin diluted to 50 mL of D5W to infuse over 90 min.
125 mg of Prostaphlin has a volume of 2.5.

How many mL of diluent must be added to the drug to produce the ordered solution?

What flow rate will we need to set on a manual IV in order to correctly give this dosage over the specified time?

First we will calculate the number of mL of D5W that we must add to the drug to get the ordered solution. The ordered solution has be ordered "diluted to 50 mL of D5W". This means that we need a total of 50 mL once the diluent is added. Since the medicine itself takes up a volume of 2.5 mL, this means that the amount of D5W we need to add is:

_____mL=50 mL - 2.5 mL =47.5 mL of D5W

Now we will calculate the flow rate.
We want our answer to be in

mL
h
, because all the problems in this chapter involve a manual IV setup, so the speed must be in gtt/min, because the way we measure the flow rate on a manual IV is to count the number of drops which fall in the drip chamber per minute.

_____

mL
h
=

Now since we are looking for a rate, which is volume over time, we need to find something to put on the right side of the equation that will be a rate which expresses volume over time. Well, since we know that we must infuse 50 mL over 90 min, we can put this total volume over total time to get a rate expressed in volume over time.

_____

mL
h
=
50 mL
90 min

Now, since we want to cancel out the min at the bottom right of our equation, we need to multiply by a fraction which is equal to one and also has min in the top, to cancel out the min which appears in the bottom of the right of our equation. Because we know that 60 min = 1 h, we can use the fraction

60 min
1 h
, because this fraction is equal to one and has min in the top, which we will need to cancel out the min in the bottom of our fraction in the right side of the equation.

So our equation becomes:

_____

mL
h
=
50 mL
90 min
×
60 min
1 h

Now we need to cancel out all units that appear in both the top and the bottom of the equation:

_____

mL
h
=
50 mL
90 min
×
60 min
1 h
=
50 mL
90
×
60
1 h
=
50
90
×
60
1
mL
h

Now we need to cancel as much as possible by dividing the top and bottom of the fractions by any factors they have in common:

We can divide both 60 and 90 by 30. So, dividing these numbers, which we can do because one is on the bottom of the fractions and one is on the top, yields:

_____

mL
h
=
50
903
×
602
1
=
50
3
×
2
1
mL
h

Now we have nothing left to simplify, so we multiply across the top and multiply across the bottom to get:

_____

mL
h
=
50
3
×
2
1
=
100
3
mL
h

Dividing the top by the bottom and then rounding to the nearest whole drop yields:

100
3
mL
h
= 33.333333333333
mL
h
= 33
mL
h

So the correct flow rate is 33

mL
h
.

Example:

The order is for 800 mg of Vancocin diluted to 75 mL of D5W to infuse over 60 min.
800 mg of Vancocin has a volume of 16.

How many mL of diluent must be added to the drug to produce the ordered solution?

What flow rate will we need to set on a manual IV in order to correctly give this dosage over the specified time?

First we will calculate the number of mL of D5W that we must add to the drug to get the ordered solution. The ordered solution has be ordered "diluted to 75 mL of D5W". This means that we need a total of 75 mL once the diluent is added. Since the medicine itself takes up a volume of 16 mL, this means that the amount of D5W we need to add is:

_____mL=75 mL - 16 mL =59 mL of D5W

Now we will calculate the flow rate.
We want our answer to be in

mL
h
, because all the problems in this chapter involve a manual IV setup, so the speed must be in gtt/min, because the way we measure the flow rate on a manual IV is to count the number of drops which fall in the drip chamber per minute.

_____

mL
h
=

Now since we are looking for a rate, which is volume over time, we need to find something to put on the right side of the equation that will be a rate which expresses volume over time. Well, since we know that we must infuse 75 mL over 60 min, we can put this total volume over total time to get a rate expressed in volume over time.

_____

mL
h
=
75 mL
60 min

Now, since we want to cancel out the min at the bottom right of our equation, we need to multiply by a fraction which is equal to one and also has min in the top, to cancel out the min which appears in the bottom of the right of our equation. Because we know that 60 min = 1 h, we can use the fraction

60 min
1 h
, because this fraction is equal to one and has min in the top, which we will need to cancel out the min in the bottom of our fraction in the right side of the equation.

So our equation becomes:

_____

mL
h
=
75 mL
60 min
×
60 min
1 h

Now we need to cancel out all units that appear in both the top and the bottom of the equation:

_____

mL
h
=
75 mL
60 min
×
60 min
1 h
=
75 mL
60
×
60
1 h
=
75
60
×
60
1
mL
h

Now we need to cancel as much as possible by dividing the top and bottom of the fractions by any factors they have in common:

We can divide both 60 and 60 by 60. So, dividing these numbers, which we can do because one is on the bottom of the fractions and one is on the top, yields:

_____

mL
h
=
75
601
×
601
1
=
75
1
×
1
1
mL
h

Now we have nothing left to simplify, so we multiply across the top and multiply across the bottom to get:

_____

mL
h
=
75
1
×
1
1
=
75
1
mL
h

Dividing the top by the bottom and then rounding to the nearest whole drop yields:

75
1
mL
h
= 75
mL
h
= 75
mL
h

So the correct flow rate is 75

mL
h
.

Example:

The order is for 625 mg of methylpredisolone diluted to 20 mL of D5W to infuse over 30 min.
625 mg of methylpredisolone has a volume of 10.

How many mL of diluent must be added to the drug to produce the ordered solution?

What flow rate will we need to set on a manual IV in order to correctly give this dosage over the specified time?

First we will calculate the number of mL of D5W that we must add to the drug to get the ordered solution. The ordered solution has be ordered "diluted to 20 mL of D5W". This means that we need a total of 20 mL once the diluent is added. Since the medicine itself takes up a volume of 10 mL, this means that the amount of D5W we need to add is:

_____mL=20 mL - 10 mL =10 mL of D5W

Now we will calculate the flow rate.
We want our answer to be in

mL
h
, because all the problems in this chapter involve a manual IV setup, so the speed must be in gtt/min, because the way we measure the flow rate on a manual IV is to count the number of drops which fall in the drip chamber per minute.

_____

mL
h
=

Now since we are looking for a rate, which is volume over time, we need to find something to put on the right side of the equation that will be a rate which expresses volume over time. Well, since we know that we must infuse 20 mL over 30 min, we can put this total volume over total time to get a rate expressed in volume over time.

_____

mL
h
=
20 mL
30 min

Now, since we want to cancel out the min at the bottom right of our equation, we need to multiply by a fraction which is equal to one and also has min in the top, to cancel out the min which appears in the bottom of the right of our equation. Because we know that 60 min = 1 h, we can use the fraction

60 min
1 h
, because this fraction is equal to one and has min in the top, which we will need to cancel out the min in the bottom of our fraction in the right side of the equation.

So our equation becomes:

_____

mL
h
=
20 mL
30 min
×
60 min
1 h

Now we need to cancel out all units that appear in both the top and the bottom of the equation:

_____

mL
h
=
20 mL
30 min
×
60 min
1 h
=
20 mL
30
×
60
1 h
=
20
30
×
60
1
mL
h

Now we need to cancel as much as possible by dividing the top and bottom of the fractions by any factors they have in common:

We can divide both 60 and 30 by 30. So, dividing these numbers, which we can do because one is on the bottom of the fractions and one is on the top, yields:

_____

mL
h
=
20
301
×
602
1
=
20
1
×
2
1
mL
h

Now we have nothing left to simplify, so we multiply across the top and multiply across the bottom to get:

_____

mL
h
=
20
1
×
2
1
=
40
1
mL
h

Dividing the top by the bottom and then rounding to the nearest whole drop yields:

40
1
mL
h
= 40
mL
h
= 40
mL
h

So the correct flow rate is 40

mL
h
.

Often when giving IVs to children and infants the dosage will be determined by their body weight. So, just as in previous sections, we may need to check the safety of a given dosage by comparing it to a normal or safe range.

Let's look at a few examples where we might do this:

Example:

Is the following order safe for a 10.5 kg child?
Order: morphine 1 mg IV q.4.h.

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's weight, we begin by putting 10.5 kg to the right of the equals sign, because we need to find the number of mg we need for a 10.5 kg patient:

_____ mg=10.5 kg

We can put 10.5 kg over 1 without changing it:

10.5 kg
1

If we look at the label, we see that it says that the safe dosage is 0.1 to 0.3 mg per kg per dose.

Because this safe dosage is given per dose, we should label our calculations "Safe dosage per dose", and because the safe dosage given is a range, our answer must be a range, too, with a minimum safe amount, and a maximum safe amount:

Now we want to get rid of the kg on the top of the right side of the equation, and we notice that we can write 0.1-0.3 mg per kg as two different fractions:

0.1 mg
1 kg
and
0.3 mg
1 kg
. In a minimum safe dosage, 0.1 mg and 1 kg should be equal and in a maximum safe dosage, 0.3 mg and 1 kg should be equal; we can multiply our equation for the minimum by
0.1 mg
1 kg
and our equation for the maximum by
0.3 mg
1 kg
, because:

Minimum safe dose per dose: _____ mg=

10.5 kg
1
×
0.1 mg
1 kg

Maximum safe dose per dose: _____ mg=

10.5 kg
1
×
0.3 mg
1 kg

Now all we need to do is to simplify our fractions:

None of the numbers will cancel, but we can cancel units that appear on both the top and the bottom to get:

Minimum safe dosage per dose: _____mg=

10.5 kg
1
×
0.1 mg
1 kg

Maximum safe dosage per dose: _____mg=

10.5 kg
1
×
0.3 mg
1 kg

Now we can multiply across to get:

Minimum safe dosage per dose: _____mg=

10.5
1
×
0.1 mg
1
=
1.05
1
mg

Maximum safe dosage per dose: _____mg=

10.5
1
×
0.3 mg
1
=
3.15
1
mg

So our safe dosage range per dose is:

1.05-3.15 mg

This is our safe amount per dose, so we can compare it with the ordered dose1 mg.

The ordered amount is unsafe, and we should check with the physician who wrote the order and should not give the patient this dose, because the ordered amount of 1 mg is not within the safe range per dose 1.05-3.15 mg.

Example:

Is the following order safe for a 26 kg child?
Order: Dilantin 40 mg IV b.i.d.

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's weight, we begin by putting 26 kg to the right of the equals sign, because we need to find the number of mg we need for a 26 kg patient:

_____ mg=26 kg

We can put 26 kg over 1 without changing it:

26 kg
1

If we look at the label, we see that it says that the safe dosage is 4 to 6 mg per kg per day.

Because this safe dosage is given per day, we should label our calculations "Safe dosage per day", and because the safe dosage given is a range, our answer must be a range, too, with a minimum safe amount, and a maximum safe amount:

Now we want to get rid of the kg on the top of the right side of the equation, and we notice that we can write 4-6 mg per kg as two different fractions:

4 mg
1 kg
and
6 mg
1 kg
. In a minimum safe dosage, 4 mg and 1 kg should be equal and in a maximum safe dosage, 6 mg and 1 kg should be equal; we can multiply our equation for the minimum by
4 mg
1 kg
and our equation for the maximum by
6 mg
1 kg
, because:

Minimum safe dose per day: _____ mg=

26 kg
1
×
4 mg
1 kg

Maximum safe dose per day: _____ mg=

26 kg
1
×
6 mg
1 kg

Now all we need to do is to simplify our fractions:

None of the numbers will cancel, but we can cancel units that appear on both the top and the bottom to get:

Minimum safe dosage per day: _____mg=

26 kg
1
×
4 mg
1 kg

Maximum safe dosage per day: _____mg=

26 kg
1
×
6 mg
1 kg

Now we can multiply across to get:

Minimum safe dosage per day: _____mg=

26
1
×
4 mg
1
=
104
1
mg

Maximum safe dosage per day: _____mg=

26
1
×
6 mg
1
=
156
1
mg

So our safe dosage range per day is:

104-156 mg

Because this range is the safe range per day, we must break this minimum and maximum down to the safe range per dose. The order says the frequency should be b.i.d., which means twice a daySo in order to go from the safe dosage range per day, 104-156 mg, to the safe dosage per dose, we must break the minimum daily dosage and the maximum daily dosage up into 2 equal sized pieces.

So, we divide 104 mg by 2 to get the minimum safe dosage per dose:

Minimum safe amount per dose: 52

And then we divide 156 mg by 2 to get the maximum safe dosage per dose:

Maximum safe amount per dose: 78

The ordered amount is unsafe, and we should check with the physician who wrote the order and should not give the patient this dose, because the ordered amount of 40 mg is not within the safe range per dose 52-78 mg.