PHARMACEUTICAL MATH I PHRA 1209

Basic algebra can be used to solve for an unknown amount if the other amounts are known.  Proportions to calculate doses (to be covered later) are just another variation of the algebraic technique.

Remember that the "letters" used in algebra just represent some number (for example x = 2).  The letter is used in place of the number.

For example:   A = 3     B = 6    C = 2

Instead of using  3 = 6 / 2 , we could write A = B / C

Some simple math concepts must first be remembered in order to do algebra.

• anything divided by itself = 1

  3 / 3 = 1        5 / 5 = 1        apple / apple = 1        A / A = 1

   

• anything multiplied by one is the anything

  1 x 5 = 5        1 x 10 = 10    1 x apple = apple    1 x A = A

   

• an equal sign "=" means that everything to the left is equal to everything to the right

  5 = 5            2 x 5 = 10        10 / 5 = 6 / 3

   

• both sides will remain equal if one does the EXACT same thing to BOTH sides

  for example, given 5 = 5

  if we multiple one side by 2, to keep it equal, we must immediately multiple the other side by 2.

  2 x 5 = 2 x 5

An easy way to solve a basic algebra problem is to break it down into two steps:

1. is the unknown on top of the line
   
2. is the unknown by itself on its side of the equal sign

Each question has two possible answers:  yes or no

Let's start with the first question.

• Is the unknown on top of the line:

  if yes - go to step 2

  if no - put the unknown on top of BOTH lines on each side of the equal sign

  For example in the equation  

  

First place a line under the A

If we were solving for B, the question would be "is B on top of the line?" notice that B is already on top of the line so the answer would be "yes" and we would go to step 2.

If we were solving for C, the question would be "is C on top of the line?" notice that C is not on top of the line. Therefore, we would place C on top of BOTH lines.

Next notice the right side of the equal sign. We now have a C on top of the line and a C on the both of the line.  C divided by C is equal to 1 and 1 x B = B.  The two C's simply cancel each other out leaving

Now ask once again  "is C on top of the line?"  The answer is "yes" therefore go to step two.

Step two asks "is the unknown C by itself on its side of the equal sign?"

Looking at the equation, we see an "A" on the same side as the "C" (disregard any 1s).

We must therefore get rid of any other letters or numbers by canceling them out.

Canceling mean if the letter or number we want to get rid of is on the top with the unknown we would divide BOTH sides by the letter or number.  If the letter or number we want to get rid of is on the bottom of the line, we would put that number or letter on the top of BOTH lines.

In our example, since A is on the same side as C and is on top of the line, we would divide BOTH sides by A

We now have on the left side an A / A.  This would cancel out leaving

If we now ask "is the unknown C by itself on its side of the equal sign?", the answer would be "yes" and if the answer is "yes", we are finished.

We would then replace B and C with whatever numbers they represent and it is now a simple arithmetic problem.

To expand on this process:

Question 1:    Is the unknown on top of the line?

if "yes" then go to Question 2

if "no" then put the unknown on top of BOTH lines on each side of the equal sign and then go to Question 2

Question 2:    "Is the unknown by itself on its side of the equal sign?"

if "yes" then you are done

if "no" then get rid of any other letters or numbers by canceling them out.

Example:  Solve for X

Solution:

Example:  Solve for X

Solution:

Example:  Solve for X

Solution:

Other examples:

If a valium injection is available in a concentration of 12 mg per 3 ml, how many mgs of valium would be in a 5 ml injection?

Solve for X mg

mg valium in 5 ml = 20 mg