Med-Math Basics

1. Changing fractions to decimals and decimals to fractions

a) In order to change decimals to fractions, you must know the units.  Here is a trick for knowing your units.

1000

100

10

Decimal

1/10

1/100

1/1000

e.g. convert these decimals into fractions

1) 0.25

- We see that there are 2 numbers after the decimal.  If we look at our chart at the centre (where our decimal is), we notice that two spaces to the right is Therefore, our fraction will be:  

2) 0.004

- We see that there are 3 numbers after the decimal (0, 0 and 4).  If we look at our chart, 3 spaces after the decimal is .  Therefore, our fraction will be

3) 136.75

- We see that we have 3 whole numbers to the left of our decimal and 2 numbers to the right of our decimal.  Using our chart, we see that the whole numbers remain as they are.  On the right hand side, we see that 2 numbers to the right of the decimal is .  Therefore, our fraction will be:

b) In order to convert fractions into decimals, we divide the numerator by the denominator

e.g.

Then,

c) Dividing decimals

When we divide decimals, we must first get rid of the decimal on the left hand number.

e.g.

To get rid of the decimal in 4.3, we must move the decimal one spot to the right to give us 43.0.  Since we moved this decimal one place to the right, we must move the decimal in 5.427 one place to the right.

Then we simply follow normal division.

2. Percentages

Percent means parts per hundred.  Percents can be written as fractions or decimals.

e.g. change 4% to a fraction:  Since percents are per hundred, then our fraction is:

 4% = 

e.g. change 4% to a decimal: Since percent are per hundred, we can either do two things: divide the number by 100 to get the decimal, or simply move the decimal point TWO PLACES TO THE LEFT.

Then, 4.0% becomes 0.04 as a decimal.

Or, 0.2% becomes 0.002 as a decimal

3. Ratio and Proportion

A ratio indicates a relationship between two numbers.  Ratios can be written as a fraction, i.e. 1 apple to 2 oranges = ½ or it can be written as two numbers separated by a colon, such as 1:2.

A proportion is a relationship between two ratios.  Proportions can also be written as fractions or as colons.  E.g. or 2:8 :: 10:40

To solve proportions with a variable, we cross multiply.

e.g.

(x)(0.125) = (1)(0.25)

0.125x = 0.25

x = 0.25 / 0.125

4. Metric conversions

In order to do calculations with medicine, the dosages must be in the same metric unit.  Therefore, we must sometimes convert them to be the same.  Here is a table that will help you with these conversions:

Mega (M)

Kilo (K)

Hecto (H)

Deca (Da)

Meters (M) Liters (L) Grams (G)

Deci (d)

Centi (c )

Milli (m)

Micro (mc) or (µ)

E.g Convert 100 mg into g

To do this, look at the chart.  Mg, or milli is on the right hand side.  To move to g, we have to move 3 boxes to the left.  Therefore, we move our decimal three spaces to the left.

Then, 100.0 mg = 0.10 g

E.g. Convert 100 mcg into mg

We see that mcg is the furthest box on the left.  To move to milli, we have to move three boxes to the left.  Therefore, we move our decimal three spaces to the left.

Then, 100.0 mcg = 0.10 mg

E.g. Convert 30 mL into L

We see that milli is on the right hand side of the box.  To move to L, we have to move three boxes to the left.  Therefore, we move our decimal three spaces to the left.

Then, 30.0mL = 0.030 L

5. Medicine Calculations – Tablets

Use this formula when calculating tablets. 

Desire = physician’s order

Have = what you have on hand

Amount = total amount you will give

E.g.  Order is levothyroxine sodium 37.5 mcg po qd

         Stock is stored tablets of 0.025 mg

To solve this, first we must change the units to be the same.  Let’s change mcg to mg.

To do this, we see that mcg, or micro is on the very right.  To get to mg, we have to move three boxes to the left.  Then, 37.5 mcg becomes 0.0375 mg.

Then we can substitute the numbers into the formula:

Order is 0.0375 mg (Desire)                      

Stock is 0.025 mg                                     

6. Medicine Calculations – Liquids

Use this formula when calculating liquid amounts:

Stock = amount of liquid you have

E.g. Order is amoxicillin oral suspension 500 mg po q8h

        Stock is 250 mg per 5 mL.

We notice that the units are already the same (mg and mg), therefore no conversions are needed.  Then,

Order is 500 mg                         

Have is 250 mg                         

Stock is 5 mL

7. Medicine Calculations with IV Drip rates

To calculate IV drip rates, we use two formulas:

1) (read as ml per hour)

2) (Where TF = tubing drip factor and gtt/min is drops per minute)

E.g.  Order is 500ml D5N5 IV 12 N – 4pm

        Available: microdrip at 60 gtt/mL, macrodrip at 20 gtt/mL

Solution: we know that the order is 500 ml from 12 noon – 4pm which is 4 hours.  We must calculate this for both the micro and macrodrips

Step one:

Step two:  Let’s start with micro, and then do macro

micro:

macro :

From doing both, we can pick which one we want to use, label the IV and then set the drip rate. 

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