calculating the amount of a drug needed to administer a particular dosage2

Calculating the Amount of a Drug Needed to Administer a Particular DosageWhen a patient is given an order for a particular drug, that order almost always requests the drug in dosage units such as milligrams, grams, micrograms, grains, Units and milliequivalents. However, to actually measure out the medicine and give it to the patient, we cannot measure milligrams, grams, micrograms, grains, Units and milliequivalents; instead we need to measure the drug by taking out the correct number of pills or the correct volume of the liquid to give to the patient. So, we need to convert dosage units to administration units before we can give a patient any medication. To see how we might calculate this, we look at several examples: Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: pentozifylline 600 mgFirst we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:_____tab=Since the ordered dosage is 600 mg, we need to figure out how many tab it takes to make 600 mg:_____tab=600 mgSo, in order to do this, we must convert 600 mg into tab, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 600 mg and which will also cancel out the mg units we don't want and introduce the tab units we do want.Where can we find a fraction like this? The concentration given on the label is 400 mg per tab. This tells us that 1 tab is equal to 400 mg, so if we write this as a fraction, it becomes:1 tab

400 mg

This fraction is equal to one because the top is equal to the bottom. There were actually 2 possibilities: 1 tab

400 mg

and 400 mg

1 tab

. Why did we choose 1 tab

400 mg

? It has mg on the bottom, which will cancel out the mg on the top. And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:_____tab=600 mg

1

1 tab

400 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=600 mg1 tab

1400 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____tab=600 mg1 tab

1400 mg

Now we simplify and multiply out the fraction:We can divide both 600 and 400 by 200 to get:_____tab=6003 mg1 tab

14002 mg

Writing this out more neatly yields:_____tab=31 tab

12

There is nothing now in this fraction that can be simplified, so we multiply 3 by 1 to get 3. Then we divide 3 by 2 to get 1.5.So, our answer is 1.5 tab.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: Cipro 0.75 gFirst we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:_____tab=Since the ordered dosage is 0.75 g, we need to figure out how many tab it takes to make 0.75 g:_____tab=0.75 gIf we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label. So, in order to do this, we must convert 0.75 g into mg, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.75 g and which will also cancel out the g units we don't want and introduce the mg units we do want.Where can we find a fraction like this?Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:1000 mg

1 g

This fraction is equal to one because the top is equal to the bottom. There were actually 2 possibilities: 1000 mg

1 g

and 1 g

1000 mg

. Why did we choose 1000 mg

1 g

? It has g on the bottom, which will cancel out the g on the top. And it has mg on the top, which will introduce the unit mg, which we need!

So, this yields:_____tab=0.75 g

1

1000 mg

1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=0.75 g1000 mg

11 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:_____tab=0.75 g1000 mg

11 g

So, now we must find a way to convert mg into tab. In order to do this, we must convert 0.75 g into tab, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.75 g and which will also cancel out the g units we don't want and introduce the tab units we do want.Where can we find a fraction like this? The concentration given on the label is 250 mg per tab. This tells us that 1 tab is equal to 250 mg, so if we write this as a fraction, it becomes:1 tab

250 mg


250 mg

and 250 mg

1 tab


250 mg

? It has g on the bottom, which will cancel out the g on the top. And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:_____tab=0.75 g1000 mg

11 g

1 tab

250 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=0.75 g1000 mg1 tab

11 g250 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____tab=0.75 g1000 mg1 tab

11 g250 mg

Now we simplify and multiply out the fraction:We can divide both 250 and 1000 by 250 to get:_____tab=0.75 g10004 mg1 tab

11 g2501 g

Writing this out more neatly yields:_____tab=0.7541 tab

111

There is nothing now in this fraction that can be simplified, so we multiply 0.75, 4 and 1 to get 3. And we multiply 1 and 1 to get 1. Then we divide 3 by 1 to get 3.So, our answer is 3 tab.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: Verelan 240 mgFirst we look at the label and see that this medication is administered in cap, so we are looking for our answer to be in cap:_____cap=Since the ordered dosage is 240 mg, we need to figure out how many cap it takes to make 240 mg:_____cap=240 mgSo, in order to do this, we must convert 240 mg into cap, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 240 mg and which will also cancel out the mg units we don't want and introduce the cap units we do want.Where can we find a fraction like this? The concentration given on the label is 120 mg cap. This tells us that 1 cap is equal to 120 mg, so if we write this as a fraction, it becomes:1 cap

120 mg

This fraction is equal to one because the top is equal to the bottom. There were actually 2 possibilities: 1 cap

120 mg

and 120 mg

1 cap

. Why did we choose 1 cap

120 mg

? It has mg on the bottom, which will cancel out the mg on the top. And it has cap on the top, which will introduce the unit cap, which we need!

So, this yields:_____cap=240 mg

1

1 cap

120 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____cap=240 mg1 cap

1120 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____cap=240 mg1 cap

1120 mg

Now we simplify and multiply out the fraction:We can divide both 240 and 120 by 120 to get:_____cap=2402 mg1 cap

11201 mg

Writing this out more neatly yields:_____cap=21 cap

11

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 1 to get 2.So, our answer is 2 cap.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: Augmentin 150 mgFirst 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 150 mg, we need to figure out how many mL it takes to make 150 mg:_____mL=150 mgSo, in order to do this, we must convert 150 mg into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 150 mg and which will also cancel out the mg units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 125 mg/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=150 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=150 mg5 mL

1125 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____mL=150 mg5 mL

1125 mg

Now we simplify and multiply out the fraction:We can divide both 5 and 125 by 5 to get:_____mL=150 mg51 mL

112525 mg

We can divide both 150 and 25 by 25 to get:_____mL=1506 mg51 mL

1125251 mg

Writing this out more neatly yields:_____mL=61 mL

11

There is nothing now in this fraction that can be simplified, so we multiply 6 by 1 to get 6. Then we divide 6 by 1 to get 6.So, our answer is 6 mL.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: phenobarbital 30 mgFirst we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:_____tab=Since the ordered dosage is 30 mg, we need to figure out how many tab it takes to make 30 mg:_____tab=30 mgSo, in order to do this, we must convert 30 mg into tab, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 30 mg and which will also cancel out the mg units we don't want and introduce the tab units we do want.Where can we find a fraction like this? The concentration given on the label is 15 mg tab. This tells us that 1 tab is equal to 15 mg, so if we write this as a fraction, it becomes:1 tab

15 mg


15 mg

and 15 mg

1 tab


15 mg


So, this yields:_____tab=30 mg

1

1 tab

15 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=30 mg1 tab

115 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____tab=30 mg1 tab

115 mg

Now we simplify and multiply out the fraction:We can divide both 30 and 15 by 15 to get:_____tab=302 mg1 tab

1151 mg

Writing this out more neatly yields:_____tab=21 tab

11

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 1 to get 2.So, our answer is 2 tab.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: Synthroid 0.3 mgFirst we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:_____tab=Since the ordered dosage is 0.3 mg, we need to figure out how many tab it takes to make 0.3 mg:_____tab=0.3 mgIf we look closely, we notice that while the order is written in mg, the label actually uses mcg. We we need to convert mg into mcg if we want to be able to do any calculations that use the information given on the label. So, in order to do this, we must convert 0.3 mg into mcg, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.3 mg and which will also cancel out the mg units we don't want and introduce the mcg units we do want.Where can we find a fraction like this?Well, we know that 1 mg=1000 mcg. If we write this as a fraction, it becomes:1000 mcg

1 mg

This fraction is equal to one because the top is equal to the bottom. There were actually 2 possibilities: 1000 mcg

1 mg

and 1 mg

1000 mcg

. Why did we choose 1000 mcg

1 mg

? It has mg on the bottom, which will cancel out the mg on the top. And it has mcg on the top, which will introduce the unit mcg, which we need!

So, this yields:_____tab=0.3 mg

1

1000 mcg

1 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=0.3 mg1000 mcg

11 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____tab=0.3 mg1000 mcg

11 mg

So, now we must find a way to convert mcg into tab. In order to do this, we must convert 0.3 mg into tab, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.3 mg and which will also cancel out the mg units we don't want and introduce the tab units we do want.Where can we find a fraction like this? The concentration given on the label is 150 mcg tab. This tells us that 1 tab is equal to 150 mcg, so if we write this as a fraction, it becomes:1 tab

150 mcg


150 mcg

and 150 mcg

1 tab


150 mcg


So, this yields:_____tab=0.3 mg1000 mcg

11 mg

1 tab

150 mcg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=0.3 mg1000 mcg1 tab

11 mg150 mcg

We can then cancel the mcg which appears in both the top and the bottom of the fraction on the right:_____tab=0.3 mg1000 mcg1 tab

11 mg150 mcg

Now we simplify and multiply out the fraction:We can divide both 150 and 1000 by 50 to get:_____tab=0.3 mg100020 mcg1 tab

11 mg1503 mg


113

There is nothing now in this fraction that can be simplified, so we multiply 0.3, 20 and 1 to get 6. And we multiply 1 and 3 to get 3. Then we divide 6 by 3 to get 2.So, our answer is 2 tab.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: Procan 1.5 gFirst we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:_____tab=Since the ordered dosage is 1.5 g, we need to figure out how many tab it takes to make 1.5 g:_____tab=1.5 gIf we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label. So, in order to do this, we must convert 1.5 g into mg, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 1.5 g and which will also cancel out the g units we don't want and introduce the mg units we do want.Where can we find a fraction like this?Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:1000 mg

1 g


1 g

and 1 g

1000 mg


1 g


So, this yields:_____tab=1.5 g

1

1000 mg

1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=1.5 g1000 mg

11 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:_____tab=1.5 g1000 mg

11 g

So, now we must find a way to convert mg into tab. In order to do this, we must convert 1.5 g into tab, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 1.5 g and which will also cancel out the g units we don't want and introduce the tab units we do want.Where can we find a fraction like this? The concentration given on the label is 750 mg tab. This tells us that 1 tab is equal to 750 mg, so if we write this as a fraction, it becomes:1 tab

750 mg


750 mg

and 750 mg

1 tab


750 mg

? It has g on the bottom, which will cancel out the g on the top. And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:_____tab=1.5 g1000 mg

11 g

1 tab

750 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____tab=1.5 g1000 mg1 tab

11 g750 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____tab=1.5 g1000 mg1 tab

11 g750 mg

Now we simplify and multiply out the fraction:We can divide both 750 and 1000 by 250 to get:_____tab=1.5 g10004 mg1 tab

11 g7503 g


113

There is nothing now in this fraction that can be simplified, so we multiply 1.5, 4 and 1 to get 6. And we multiply 1 and 3 to get 3. Then we divide 6 by 3 to get 2.So, our answer is 2 tab.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: cefaclor 0.5 gFirst 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 0.5 g, we need to figure out how many mL it takes to make 0.5 g:_____mL=0.5 gIf we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label. So, in order to do this, we must convert 0.5 g into mg, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.5 g and which will also cancel out the g units we don't want and introduce the mg units we do want.Where can we find a fraction like this?Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:1000 mg

1 g


1 g

and 1 g

1000 mg


1 g


So, this yields:_____mL=0.5 g

1

1000 mg

1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=0.5 g1000 mg

11 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:_____mL=0.5 g1000 mg

11 g

So, now we must find a way to convert mg into mL. In order to do this, we must convert 0.5 g into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.5 g and which will also cancel out the g units we don't want and introduce the mL units we do want.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


250 mg

and 250 mg

5 mL


250 mg

? It has g on the bottom, which will cancel out the g on the top. And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:_____mL=0.5 g1000 mg

11 g

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=0.5 g1000 mg5 mL

11 g250 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____mL=0.5 g1000 mg5 mL

11 g250 mg

Now we simplify and multiply out the fraction:We can divide both 5 and 250 by 5 to get:_____mL=0.5 g1000 mg51 mL

11 g25050 g

We can divide both 50 and 1000 by 50 to get:_____mL=0.5 g100020 mg51 mL

11 g501 g

Writing this out more neatly yields:_____mL=0.5201 mL

111

There is nothing now in this fraction that can be simplified, so we multiply 0.5, 20 and 1 to get 10. And we multiply 1 and 1 to get 1. Then we divide 10 by 1 to get 10.So, our answer is 10 mL.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: heparin 3000 UFirst 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 3000 U, we need to figure out how many mL it takes to make 3000 U:_____mL=3000 USo, in order to do this, we must convert 3000 U into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 3000 U and which will also cancel out the U units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 5000 U/mL. This tells us that 1 mL is equal to 5000 U, so if we write this as a fraction, it becomes:1 mL

5000 U


5000 U

and 5000 U

1 mL


5000 U

? It has U on the bottom, which will cancel out the U on the top. And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:_____mL=3000 U

1

1 mL

5000 U

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=3000 U1 mL

15000 U

We can then cancel the U which appears in both the top and the bottom of the fraction on the right:_____mL=3000 U1 mL

15000 U

Now we simplify and multiply out the fraction:We can divide both 3000 and 5000 by 1000 to get:_____mL=30003 U1 mL

150005 U


15

There is nothing now in this fraction that can be simplified, so we multiply 3 by 1 to get 3. Then we divide 3 by 5 to get 0.6.So, our answer is 0.6 mL.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: furosemide 5 mgFirst 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 5 mg, we need to figure out how many mL it takes to make 5 mg:_____mL=5 mgSo, in order to do this, we must convert 5 mg into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 5 mg and which will also cancel out the mg units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 20 mg/2 mL. This tells us that 2 mL is equal to 20 mg, so if we write this as a fraction, it becomes:2 mL

20 mg


20 mg

and 20 mg

2 mL


20 mg



1

2 mL

20 mg


120 mg


120 mg


12010 mg


120102 mg


12

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 tab, cap, or mL needed to administer the dosage below:Order: Cleocin Phosphate 450 mgFirst 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 450 mg, we need to figure out how many mL it takes to make 450 mg:_____mL=450 mgSo, in order to do this, we must convert 450 mg into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 450 mg and which will also cancel out the mg units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 900 mg in 6 mL. This tells us that 6 mL is equal to 900 mg, so if we write this as a fraction, it becomes:6 mL

900 mg


900 mg

and 900 mg

6 mL


900 mg



1

6 mL

900 mg


1900 mg


1900 mg


1900150 mg


19001501 mg


11

There is nothing now in this fraction that can be simplified, so we multiply 3 by 1 to get 3. Then we divide 3 by 1 to get 3.So, our answer is 3 mL.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: Atropine 0.5 mgFirst 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 0.5 mg, we need to figure out how many mL it takes to make 0.5 mg:_____mL=0.5 mgIf we look closely, we notice that while the order is written in mg, the label actually uses mcg. We we need to convert mg into mcg if we want to be able to do any calculations that use the information given on the label. So, in order to do this, we must convert 0.5 mg into mcg, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.5 mg and which will also cancel out the mg units we don't want and introduce the mcg units we do want.Where can we find a fraction like this?Well, we know that 1 mg=1000 mcg. If we write this as a fraction, it becomes:1000 mcg

1 mg

This fraction is equal to one because the top is equal to the bottom. There were actually 2 possibilities: 1000 mcg

1 mg

and 1 mg

1000 mcg

. Why did we choose 1000 mcg

1 mg

? It has mg on the bottom, which will cancel out the mg on the top. And it has mcg on the top, which will introduce the unit mcg, which we need!

So, this yields:_____mL=0.5 mg

1

1000 mcg

1 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=0.5 mg1000 mcg

11 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____mL=0.5 mg1000 mcg

11 mg

So, now we must find a way to convert mcg into mL. In order to do this, we must convert 0.5 mg into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.5 mg and which will also cancel out the mg units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 400 mcg/mL. This tells us that 1 mL is equal to 400 mcg, so if we write this as a fraction, it becomes:1 mL

400 mcg


400 mcg

and 400 mcg

1 mL


400 mcg


So, this yields:_____mL=0.5 mg1000 mcg

11 mg

1 mL

400 mcg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=0.5 mg1000 mcg1 mL

11 mg400 mcg

We can then cancel the mcg which appears in both the top and the bottom of the fraction on the right:_____mL=0.5 mg1000 mcg1 mL

11 mg400 mcg

Now we simplify and multiply out the fraction:We can divide both 400 and 1000 by 200 to get:_____mL=0.5 mg10005 mcg1 mL

11 mg4002 mg


112

There is nothing now in this fraction that can be simplified, so we multiply 0.5, 5 and 1 to get 2.5. And we multiply 1 and 2 to get 2. Then we divide 2.5 by 2 to get 1.25.So, our answer is 1.25 mL.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: cyanocobalamin 600 mcgmcgis mcgFirst 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 600 mcg, we need to figure out how many mL it takes to make 600 mcg:_____mL=600 mcgIf we look closely, we notice that while the order is written in mcg, the label actually uses mg. We we need to convert mcg into mg if we want to be able to do any calculations that use the information given on the label. So, in order to do this, we must convert 600 mcg into mg, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 600 mcg and which will also cancel out the mcg units we don't want and introduce the mg units we do want.Where can we find a fraction like this?Well, we know that 1000 mcg=1 mg. If we write this as a fraction, it becomes:1 mg

1000 mcg


1000 mcg

and 1000 mcg

1 mg


1000 mcg

? It has mcg on the bottom, which will cancel out the mcg on the top. And it has mg on the top, which will introduce the unit mg, which we need!

So, this yields:_____mL=600 mcg

1

1 mg

1000 mcg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=600 mcg1 mg

11000 mcg

We can then cancel the mcg which appears in both the top and the bottom of the fraction on the right:_____mL=600 mcg1 mg

11000 mcg

So, now we must find a way to convert mg into mL. In order to do this, we must convert 600 mcg into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 600 mcg and which will also cancel out the mcg units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 1 mg/mL. This tells us that 1 mL is equal to 1 mg, so if we write this as a fraction, it becomes:1 mL

1 mg


1 mg

and 1 mg

1 mL


1 mg

? It has mcg on the bottom, which will cancel out the mcg on the top. And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:_____mL=600 mcg1 mg

11000 mcg

1 mL

1 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=600 mcg1 mg1 mL

11000 mcg1 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____mL=600 mcg1 mg1 mL

11000 mcg1 mg

Now we simplify and multiply out the fraction:We can divide both 600 and 1000 by 200 to get:_____mL=6003 mcg1 mg1 mL

110005 mcg1 mcg


151

There is nothing now in this fraction that can be simplified, so we multiply 3, 1 and 1 to get 3. And we multiply 5 and 1 to get 5. Then we divide 3 by 5 to get 0.6.So, our answer is 0.6 mL.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: calcium gluconate 1.86 mEqFirst 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 1.86 mEq, we need to figure out how many mL it takes to make 1.86 mEq:_____mL=1.86 mEqSo, in order to do this, we must convert 1.86 mEq into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 1.86 mEq and which will also cancel out the mEq units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 0.465 mEq/mL. This tells us that 1 mL is equal to 0.465 mEq, so if we write this as a fraction, it becomes:1 mL

0.465 mEq


0.465 mEq

and 0.465 mEq

1 mL


0.465 mEq

? It has mEq on the bottom, which will cancel out the mEq on the top. And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:_____mL=1.86 mEq

1

1 mL

0.465 mEq

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=1.86 mEq1 mL

10.465 mEq

We can then cancel the mEq which appears in both the top and the bottom of the fraction on the right:_____mL=1.86 mEq1 mL

10.465 mEq

Now we simplify and multiply out the fraction:Writing this out more neatly yields:_____mL=1.861 mL

10.465

There is nothing now in this fraction that can be simplified, so we multiply 1.86 by 1 to get 1.86. Then we divide 1.86 by 0.465 to get 4.So, our answer is 4 mL.Example:Calculate the number of tab, cap, or mL needed to administer the dosage below:Order: medroxyprogesterone 0.1 gFirst 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 0.1 g, we need to figure out how many mL it takes to make 0.1 g:_____mL=0.1 gIf we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label. So, in order to do this, we must convert 0.1 g into mg, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.1 g and which will also cancel out the g units we don't want and introduce the mg units we do want.Where can we find a fraction like this?Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:1000 mg

1 g


1 g

and 1 g

1000 mg


1 g


So, this yields:_____mL=0.1 g

1

1000 mg

1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=0.1 g1000 mg

11 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:_____mL=0.1 g1000 mg

11 g

So, now we must find a way to convert mg into mL. In order to do this, we must convert 0.1 g into mL, and the only way to do this is to multiply by a fraction that is actually equal to one, so it does not change the value of 0.1 g and which will also cancel out the g units we don't want and introduce the mL units we do want.Where can we find a fraction like this? The concentration given on the label is 400 mg per mL. This tells us that 1 mL is equal to 400 mg, so if we write this as a fraction, it becomes:1 mL

400 mg


400 mg

and 400 mg

1 mL


400 mg

? It has g on the bottom, which will cancel out the g on the top. And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:_____mL=0.1 g1000 mg

11 g

1 mL

400 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:_____mL=0.1 g1000 mg1 mL

11 g400 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:_____mL=0.1 g1000 mg1 mL

11 g400 mg

Now we simplify and multiply out the fraction:We can divide both 400 and 1000 by 200 to get:_____mL=0.1 g10005 mg1 mL

11 g4002 g


112

There is nothing now in this fraction that can be simplified, so we multiply 0.1, 5 and 1 to get 0.5. And we multiply 1 and 2 to get 2. Then we divide 0.5 by 2 to get 0.25.So, our answer is 0.25 mL.

calculating the amount of a drug needed to administer a particular dosage2

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