Oral Solids

Let’s use a real example to illustrate the four different methods of calculation:

EXAMPLE

When you’re solving any problem, first check that the order and the supply are in the same weight measure. If they are not, you must convert one or the other amount to its equivalent. With dimensional analysis, you would use a conversion factor. In this example, no equivalent is needed; both the order and the supply are in milligrams.

EXAMPLE

Proportions Expressed as Two Fractions

Using fractions, set up proportions so that like units are across from each other (the units and the numerator match and the units and denominators match). The first fraction is the known equivalent.

EXAMPLE

The second fraction is the unknown, or the desired (ordered) dose.

EXAMPLE

The completed proportion would be presented as follows:

Next, solve for x. (For a review of how to solve proportions, refer to Chapter 1.)

In our current example, solving for x follows this process:

1.

1 × 6.25 = 12.5x

2.

3.

Answer: ½ tablet = x

Proportions Expressed as Two Ratios

You can set up a ratio by using colons. Double colons separate the two ratios. The first ratio is the known equivalent; the second ratio is the desired (ordered) dose, or the unknown. The ratio must always follow the same sequence.

The ratio will look like this:

Supply: Have:: x: Desire

1 tablet: 12.5 mg:: x: 6.25 mg

Next, solve for x. (For a review of how to solve ratios, refer to Chapter 1.)

In our current example, solving for x follows this process:

1.

2. 1 × 6.25 = 12.5x

3.

4.

5.

Answer: ½ tablet = x

Formula Method

The formula method is simpler than either of the above methods. Using a formula eliminates the need for cross-multiplying, a potential source of error in calculation. When you use this method with oral solids, the supply is typically either 1 tablet or 1 capsule.

Here’s how the formula method is set up:

½ tablet = x

Dimensional Analysis

A fourth method of dosage calculation is called dimensional analysis. This method is used extensively in mathematics and science, especially chemistry calculations. Students often say that once you master dimensional analysis, you tend to use it all the time because it is simpler and more accurate than the other methods.

The dimensional analysis method uses terminology similar to that of other calculation methods. There are several ways to set up the dimensional analysis equation. One way is to set up the equation starting with what unit of measurement you are solving for and how the dose is supplied. Add to this what you have. Then add the desired (ordered) dose. Solve the equation. The equation is set up like a fraction with the appropriate numerators and denominators but looks slightly different.

You can set up the problem using the same terms as above:

In this example, we are solving for how many tablets of Coreg to administer. Place tablets first in the equation:

tablets

The dose supplied is tablets, and the dose we have is 12.5 mg (per tablet).

So, add to the equation:

Then add the desired dose of 6.25 mg:

According to the basic rules of reducing fractions (review Chapter 1 if necessary), the two “mg” designations cancel each other:

The setup should now look like this:

Multiply the numerators, multiply the denominators, and then divide the product of the numerators by the product of the denominators. In this example, the numbers in the numerator are 1 × 6.25 = 6.25. The only number in the denominator is 12.5. Divide 6.25 by 12.5 to get ½ tablet. The answer is ½ tablet.

In this example, it would look like this:

Note: When using dimensional analysis, you could also set up the equation starting with the desired dose, then adding the dose supplied and the dose you have. For example, in the problem above, the equation would look like this:

You would solve the same way, cancelling like units of measurement, reducing if possible, and you will have the same answer:

Either way of setting up the dimensional analysis equation will work. This text will use the first way of setting up the problem.

For the purposes of this book, we’ll use these four methods—the formula method, the proportion method expressed as two ratios, the proportion method expressed as two fractions, and the dimensional analysis. You just need to see which method makes the most sense to you, then learn it thoroughly and use it. Answers for the self-and proficiency tests in each chapter will include all four methods.

Let’s use another example to show all four methods:

EXAMPLE

Because the supply is scored, you can administer 1 ½ tablets.

You can also reduce the numbers in the numerator and denominator, using the rules of reducing fractions (see Chapter 1). For this example in the formula and dimensional analysis methods, we could reduce the fraction by dividing 7.5 in the numerator by 5 and then dividing 5 in the denominator by 5.

EXAMPLE

Converting Order and Supply to the Same Weight Measure

If the order and supply are in a differing weight measure, then you must convert one or the other amount to its equivalent. For example, if the order states 1 g and the drug is supplied in milligrams, then a conversion is needed from either grams to milligrams or milligrams to grams. Let’s take another real-life example to explain this.

Order: Amoxil (amoxicillin) 1 g po q6h

Supply: Read the label.

Desired dose: 1 g

Supply: tablets

Have: 500 mg

In this example, let’s use the equivalent: 1 g = 1000 mg. Here’s how the problem is set up:

EXAMPLE

For dimensional analysis, we include the conversion as an additional step, known as a conversion factor. A conversion factor is a ratio of units that equals 1. In this example, it will be: .

So the dimensional analysis equation will look like this:

Cancel out like units of measurement, in this case, “g” and “mg.” Reduce the fraction if possible.

Solve by multiplying the numerators, 1 × 1 × 2 = 2; multiply the denominators, in this case, it is 1; divide the product of the numerators by the product of the denominators 2 ÷ 1 = 2 tablets.

How do you know which conversion factor to use? In the above example, would you use or .?

You use the conversion factor that has the same unit of measurement in the denominator as the ordered unit of measurement. In this example, 1 g is ordered, so you would put 1 g in the denominator and the equivalent, 1000 mg, in the numerator: .

This is so the same units of measurement “cancel” each other out; in this case, the “g’s” cancel each other and the “mg’s” cancel each other. You are left with “capsules,” and that is what you are solving for.

Clearing Decimals When Using the Formula Method

When the numerator and denominator are decimals, add zeros to make the number of decimal places the same. Then drop the decimal points. This short arithmetic operation replaces long division:

In division, you must clear the denominator (divisor) of decimal points before you can carry out the arithmetic. Then you move the decimal point in the numerator the same number of places. (For further help in dividing decimals, refer to Chapter 1.)

EXAMPLE

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