Who can solve this question?

EricJRN, MSN, RN · Aug 17, 2007

You can do this! I think it's just the distractors that are tricking you.

Ultimately, you end up with 500 mg in 1.2 mL, but you only want to give half of that (250 mg), so how many mL would that be?

Daye · Aug 17, 2007

Desired dose devide the dose you have multiply the quanity will give you the dosage amount

250

500 = 0.5

0.5 X 1.2= 0.6

Daytonite, BSN, RN · Aug 17, 2007

ordered: ancef 250 mg im. the instructions: reconstitute with 2 ml of sterile water. after reconstitution each 1.2 ml yields ancef 500 mg. how many ml will you give?
can you show me your steps. i am getting problems, because normally the reconstituted amount is the same right. for e.g. 2 ml, not 2 ml and then 1.2 ml
please advice

mg is a measurement of weight; ml is a measurement of liquid. you have to keep them in their separate terms when you work the problem

the problem is telling you that after you reconstitute the powder you will have 500 mg of ancef in each 1.2 ml of liquid. the problem is basically asking you, "how much of this liquid are you going to give?" the 500mg of ancef is the weight measurement. the 1.2 ml is the liquid measurement. we aren't told how much liquid they are actually adding to the ancel powder to come up with the 1.2 ml. it actually isn't an important point for this problem. all you need to know is that this 500 mg in 1.2 ml now becomes your new "dose on hand" figure to plug into the equation of "dose desired divided by dose on hand". your dose desired is 250 mg. your dose on hand is 500 mg in 1.2 ml. now, i set up the calculation by dimensional analysis (factor label) method so i can get an answer that is going to give me an answer with a label of ml on it.

250mg/500mg/1.2

ml

(dose desired divided by dose on hand)

this simplifies to:

250 mg/1 x 1.2 ml/500 mg =

0.6 ml

you can also do this by a ratio (fraction) equivalency:

1.2 ml/500 mg = x ml/250 mg

, cross multiply and solve for

x

.

SA2BDOCTOR · Aug 17, 2007

oooooooooooohhhhhhhhhhhh 1.2/2=0.6:) That is all? was I reading to much into the question?

You can do this! I think it's just the distractors that are tricking you.
Ultimately, you end up with 500 mg in 1.2 mL, but you only want to give half of that (250 mg), so how many mL would that be?

elkpark · Aug 17, 2007

What is a little confusing is that all those molecules of Ancef in solution do expand the volume of the liquid. That's why the manufacturer tells you on the label that 500 mg = 1.2 ml after reconstitution and that's what you pay attention to. If you just drew up 1 ml because you put in 2 ml of liquid in the first place, you would be shorting the patient a little on the Ancef.

Always, the important number is what the label says the concentration is after you reconstitute.

Daye · Aug 17, 2007

Yes, but remember you will always need to know how to set up the question in the right formula so that you actually know you are getting the right answer. Daytonite set it up perfect and explained it clearly, worth memorizing

Music in My Heart · Aug 17, 2007

mg is a measurement of weight; ml is a measurement of liquid. you have to keep them in their separate terms when you work the problem
the problem is telling you that after you reconstitute the powder you will have 500 mg of ancef in each 1.2 ml of liquid. the problem is basically asking you, "how much of this liquid are you going to give?" the 500mg of ancef is the weight measurement. the 1.2 ml is the liquid measurement. we aren't told how much liquid they are actually adding to the ancel powder to come up with the 1.2 ml. it actually isn't an important point for this problem. all you need to know is that this 500 mg in 1.2 ml now becomes your new "dose on hand" figure to plug into the equation of "dose desired divided by dose on hand". your dose desired is 250 mg. your dose on hand is 500 mg in 1.2 ml. now, i set up the calculation by dimensional analysis (factor label) method so i can get an answer that is going to give me an answer with a label of ml on it.
250mg/500mg/1.2
ml
(dose desired divided by dose on hand)

this simplifies to:

250 mg/1 x 1.2 ml/500 mg =
0.6 ml
you can also do this by a ratio (fraction) equivalency:
1.2 ml/500 mg = x ml/250 mg
, cross multiply and solve for
x
.

this is very well stated and a clear explanation of how to solve these problems. however, i'd like to propose a modification just to avoid confusion for some folks:

following standard algebraic rules,

250mg/500mg/1.2

ml

does not simplify to

250 mg/1 x 1.2 ml/500 mg

.

equations are always processed left to right, starting with exponentiation followed by multiplication/division and then addition/subtraction.

if you type 250/500/1.2 into a calculator or spreadsheet, you'll get 0.41. this equation should be properly written as

250mg/(500mg/1.2

ml

)

which does simplify as stated.

because i also believe that students' confusion sometimes arises from a poor grasp of basic physics i'd like to point out that:

ml is not a measurement of liquid but rather is a unit of volume (solid, liquid, or gas).

strictly speaking, mg is not a unit of weight but instead a unit of mass; weight is a unit of force (mass multiplied by acceleration). this distinction is not too significant in chemistry and biology but i believe that it's preferable to use precise terms when learning new subjects. the distinction can become more significant when considering things like density and specific gravity.

SA2BDOCTOR · Aug 18, 2007

I would like thank each and everyone of you, for your assistance with this question.

Daytonite, BSN, RN · Aug 18, 2007

this is very well stated and a clear explanation of how to solve these problems. however i'd like to propose a modification just to avoid confusion for some folks:[indent']following standard algebraic rules, 250mg/500mg/1.2 ml does not simplify to 250 mg/1 x 1.2 ml/500 mg. [/indent]
equations are always processed left to right
, starting with exponentiation followed by multiplication/division and then addition/subtraction.

equations are processed left to right by order of operations.

i apologize for not presenting the solution correctly. i was having trouble typing the equation into the program. it should actually have read 250mg/1/500mg/1.2 ml. i was unable to correct my post because my internet connection dumped me off line. when i realized i had skipped a step i wanted to hurriedly get it posted and left out a part of the term.

in the problem you have:

dose desired

: 250 mg/1, divided by

dose on hand

: 500 mg/1.2 ml

which looks like this when you plug it into the forumula of

dose desired divided by dose on hand

:

250 mg/1

/

500 mg/1.2 ml

this is a complex fraction. in the world of mathematics is would also be written in this form with parentheses around it:

[

(250 mg/1)

/

(500 mg/1.2 ml)

]

.

all equations are processed in the

order of operations

as follows: parentheses-exponents-multiplication-division-addition-subtration. the mathematical computations must be done within the parentheses

first

before you can move on. you have division bars in these terms that you have to deal with. that is done by multiplying this complex fraction by a reciprocal complex fraction of

1.2 ml/500 mg/1.2 ml/500 mg

in order to clear the fraction,

500mg/1.2 ml

, out of the denominator and leave you with

250 mg/1

/

1 x 500 mg/1.2 ml

250/1/1

is an identity that can be re-written as

250 mg/1

but you still are left with the

500 mg/1.2 ml

reciprocal. it joins the equation which has now become a mathematical problem of two fractions that are going to be multiplied together.

(250 mg/1) x (1.2 ml/500 mg)

now, you cancel out the label of "mg" in the numerator of the first term and the denominator of the second term. this leaves you with two fractions to multiply together and only one remaining label. also, be aware that each fraction is understood to have parentheses around it and by order of operations the math (division) must be done on them first before performing the multiplication:

(250/1) x (1.2 ml/500)

the final answer is

0.6 ml

.

that is how the problem is done by dimensional analysis. it can also be done, as i pointed out by doing a ratio equivalency.

sa2bdoctor. . .i apologize for any confusion this is creating for you. to do this problem by dimensional analysis you have to have had some algebra as this complex fraction stuff is an intermediate level algebric manipulation if i remember correctly.

loricatus · Aug 18, 2007

Ordered: Ancef 250 mg IM. The instructions: Reconstitute with 2 ml of sterile water. After reconstitution each 1.2 ml yields Ancef 500 mg. How many ml will you give?
Can you show me your steps. I am getting problems, because normally the reconstituted amount is the same right. For e.g. 2 ml, not 2 ml and then 1.2 ml
Please advice

IMHO the easiest way to approach this would be:

250 mg is 1/2 of 500 mg.

and I have 1.2 mg that I need to have 1/2 of

so...

1/2 of 1 mg is .5mg & 1/2 of .2 mg is .1 mg

.5 mg + .1mg = .6 mg

No need to put equations on paper this way-it can be easily done in your head.

When it gets more complicated than 1/2 of a dosage, then use the formulas.

SA2BDOCTOR · Aug 18, 2007

daytonite~

thank you. i understand it the first time :) i guess i need to read my questions properly. my problem is that when i am doing questions and they pop a question that is different to the other question. i can't seem to figure it out as quickly.

i keep telling my self that a shoe is a shoe even though the have different shapes and colors:)

[/indent]equations are processed left to right by order of operations.
i apologize for not presenting the solution correctly. i was having trouble typing the equation into the program. it should actually have read 250mg/1/500mg/1.2 ml. i was unable to correct my post because my internet connection dumped me off line. when i realized i had skipped a step i wanted to hurriedly get it posted and left out a part of the term.
in the problem you have:
dose desired
: 250 mg/1, divided by
dose on hand
: 500 mg/1.2 ml
which looks like this when you plug it into the forumula of
dose desired divided by dose on hand
:
250 mg/1
/
500 mg/1.2 ml

this is a complex fraction. in the world of mathematics is would also be written in this form with parentheses around it:
[
(250 mg/1)
/
(500 mg/1.2 ml)
]
.
all equations are processed in the
order of operations
as follows: parentheses-exponents-multiplication-division-addition-subtration. the mathematical computations must be done within the parentheses
first
before you can move on. you have division bars in these terms that you have to deal with. that is done by multiplying this complex fraction by a reciprocal complex fraction of
1.2 ml/500 mg/1.2 ml/500 mg
in order to clear the fraction,
500mg/1.2 ml
, out of the denominator and leave you with
250 mg/1
/
1 x 500 mg/1.2 ml

250/1/1
is an identity that can be re-written as

250 mg/1
but you still are left with the
500 mg/1.2 ml
reciprocal. it joins the equation which has now become a mathematical problem of two fractions that are going to be multiplied together.

(250 mg/1) x (1.2 ml/500 mg)

now, you cancel out the label of "mg" in the numerator of the first term and the denominator of the second term. this leaves you with two fractions to multiply together and only one remaining label. also, be aware that each fraction is understood to have parentheses around it and by order of operations the math (division) must be done on them first before performing the multiplication:

(250/1) x (1.2 ml/500)

the final answer is
0.6 ml
.
that is how the problem is done by dimensional analysis. it can also be done, as i pointed out by doing a ratio equivalency.
sa2bdoctor. . .i apologize for any confusion this is creating for you. to do this problem by dimensional analysis you have to have had some algebra as this complex fraction stuff is an intermediate level algebric manipulation if i remember correctly.