## Simple Conversions

Posted by Laura on August 17, 2009

This is how I have set up my calculations.

Starting with conversions. Using a simple one we all know the answer to, I will set up my formula.

Question 1. 2000 mL = ____ L

First put what we want to know on the top of the equivalent line, or in the place of the numerator. We are going to use the algebraic X for the unknown. X L

Then, for the denominator we put what we have. 2000 mL. So our equation will now look like this.

X L

_______ =

2000 mL

Next we put all our equivalents on the other side of the equal sign. So we know 1 L = 1000 mL. When we put our equivalent or conversion factor up, make sure the same units are on the numerator or denominator side. Now the equation will look like this:

X L 1 L

_______ = _________

2000 mL 1000 mL

When you have a ratio like this, you must cross multiply to get your answer. Starting with the top left you will get :

X times 1000 = 2000 (1) then, 1000 X = 2000 then, X = 2000/1000 then, X = 2

or X = 2 Liter

This is the same way I set up my dosage calculations. Putting the question on the left of the equation, and then conversions on the right. Remember the first conversion or equivalent must line up with the left side’s units. All conversion factors after (on the left of the equation will have units opposite). On the right of the equation we will multiply straight across. Then we will cross multiply with the left side to solve for X.

So, a little harder conversion.

Question 2: 2 qt = _________ mL

X mL 2 pt 500 mL

_____ = ______ x _____

2 qt 1 qt 1 pt

Above we have the unknown in our 1st spot. Our known quantity (what we have) below it. Next on the opposite of the equal side (or our conversion side) we put our conversions to get there. We know 2 pints equal one quart. So we place this so the units are on same side. As we do this we see only one unit is the same – the quarts. We place it on the bottom and the unmatched one on top. Since we know we need to match up to mls, we find the equivalent for pts to mls.

Now any extra conversions on the right of our equation **must have equal units opposite**. This is different than the first fraction, and if I am going to mess up – this is it.

So we placed the 500 ml above 1 pt.

Now we solve for X. Starting with the problem on the right of the equal sign. Here we cross out any equal units. So I would cancel the pt ‘s. Multiply straight across to get 1000 mL above 1 qt.

X mL 2 pt 500 mL

_____ = _____ x ______

2 qt 1 qt 1 pt

X mL 1000 mL

_____ = _______

2 qt 1 qt

Now that we have just one fraction on either side, with like units, we can cross-multiply to solve for X.

1 X = 2 (1000) or, X = 2 (1000) or, X = 2000

So our answer is 2000 mL

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