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### Course: Algebra 1>Unit 3

Lesson 3: Word problems with multiple units

# Using units to solve problems: Drug dosage

Future doctors and nurses out there, take note. This unit conversion word problem deals with converting drug dosage units, something that is commonly done in hospitals. Give it a try with us. Created by Sal Khan.

## Want to join the conversation?

• is there any way that you can post more problems like this im a pharmacy student and I am having a difficult time with conversions for some reason. I get confused on setting up the problems. Can you also cover other methods of conversions such as this example problem that I have in my book.

You receive a prescription for amoxicillin 75mg 4times a day (QID) for ten days. How many mL of amoxicillin 250mg/5ml do you need to fill this prescription to last a full 10 days.
• SuSu,
The secret to conversions is that words can cancel out each other just like numbers.

You have a ratio of 250mg to 5ml. The ratio can be used either as
250mg/5ml or
5ml/250 mg.

If you know the mg and you want your answer is ml, you want to multiply
mg * ml/mg = ml
Notice that the mg/mg on the left cancel out leaving you an answer in ml.
If you know ml and want to find mg you use
ml * mg/ml = mg
Notice that the ml/ml on the left cancel out leaving you an answer in mg.

75 mg/dose * 4 dose/day * 10days = 3000 mg
Again notice that the words mg*dose*day are in you numerator and
dose*day are in you demoniator. The dose/dose and day/day cancel out leaving your answer in mg.

75mg/dose * 4doses/day*10days*5ml/250mg.

The words dose*day*mg in both the numerator and denominator cancel out giving the answer in ml
and the numbers 75*4*10*5/250 = 15000/250=60

I hope that helps make it click for you.
It is important for a pharmasist to never mess up on conversions.
• Why is it essential to include the zero when writing decimals?
• If you are dealing with medications you ALWAYS include the zero in front of the decimal point. This not so much a math rule as it is a rule for patient care. In math, it is acceptable to write .4 mg. If you are dealing with medications you must write 0.4 mg. This prevents accidental dosing errors which could hurt or kill the patient. Without the zero in front of the decimal, someone may read .4 mg as 4 mg and give 10 times the intended dose.
• Is there a list of basic useful conversions every one should know and have memorized?
• I don't think so, unless I do not know the unwritten rule too.. but I've noticed that older people know 1yd=3ft, 3tsp =1 tb (got that one from who wants to be a millionaire), 12 inches in 1 ft, 1 mile= 5280 ft, quart = 4 cups, pint= 2 cups, 2.2 lbs= kg, 2.54 cm to inch..
• I don't really get how to convert decimals of inches into big thins like miles. All the numbers and equations get jumbled up in my head.
• so as not to get confused in converting units, i use the unitary method. first i try to find the value for 1unit and then multiply with the said number of units
• that goofy looking calculator
• Windows 7 calculator. This video is 13 years old.
• I thought you couldn't make pounds into kilograms. Is it really 0.45 KG.= 1 lb.?
• Yes. Any units of measurement that measure the same thing (weight, mass, volume, distance etc.) can be converted into and from one-another.

I can make up a completely new unit of measurement and if I give it some parameters, you could convert any other unit into it and vice-versa.

A pound is a measurement of weight, a kilogram is a measurement of weight. It is also completely reasonable that both have fixed values based on something, which means there will also be a RATIO of pounds to kilograms that will not change as long as their values remain fixed. In this case 2.2 : 1

However in the case of pounds to kilograms, the actual number has too many decimal places, so usually, the conversion rate is approximated to some degree. For everyday use, this is completely fine.
• is it right to do this way
72.7 kg = 160 lbs (approx)
160lbs*5mg/lbs=800mg or 0.8 g
0.8g * 1ml/0.9g= 0.88ml dosage per patient