Ratios and Proportions



Ratios and Proportions



Chapter objectives


Upon completion of this chapter, the learner will be able to:


1. Define the key terms that relate to the chapter.


2. Identify the proper way to set up ratios with 100% accuracy.


3. List proportions found in the health care field.


4. Demonstrate how to set up a proportion with 100% accuracy.


5. Solve for “X” with 100% accuracy.


6. Use medication formulas with 100% accuracy to solve word problems.



Objective 1




Objective 2


Most people do not become excited when they hear the words ratio and proportion. Moans, groans, and looks of defeat quickly spread across the room. I once asked some students, “What is it about ratios and proportions that is so intimidating?” Answers included, “I never can set the problem up correctly,” “I’m not sure if I am supposed to reduce the ratio prior to cross multiplying or if I have the problem set up correctly,” and “I never remember how to get ‘X’ by itself in order to solve the problem.” Do you have the same concerns? In this chapter, we will discuss different ways to set up and solve ratio and proportion problems. I hope that you will find a strategy that reinforces your knowledge level and allows you to be confident in these basic algebra equations.



Objectives 2, 3, 4


Ratio


By nature, human beings love to compare objects. Take a minute and list different activities in your daily life that involve comparisons.



imageMATH IN THE REAL WORLD 5-1
Comparisons of Daily Living




When you think about it, a ratio is simply a comparison between two objects or amounts.


Health care uses ratios in determining medication dosages and additives to IV solutions and in reporting laboratory values and disease statistics. Once a ratio has been identified, it is easy to write a proportion to find a solution or the answer to a question.


Ratios can be written either as a fraction or with a colon to separate the items being compared. In word problems, you will commonly see the word to between the two items of comparison.












Example:
The shelter houses 15 dogs to every 7 cats.
15:7, 157image, or 15 to 7









Example:
There are 7 boys and 12 girls in the class.
7:12, 712image, or 7 to 12


image


Look at the medication labels in Figures 5-1, 5-2, and 5-3. What are the examples in these three figures comparing? If you said medication per milliliter, you are correct. Each of the labels compares the medication dose to a specified amount of liquid, expressed in milliliters (ml).


image
Figure 5-1 Erythromycin label. (From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.)

image
Figure 5-2 KAON-CL label. (From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.)

image
Figure 5-3 Robinul Injectable label. (From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.)

Now look at the labels of medications that are dispensed as tablets (Figures 5-4, 5-5, and 5-6). The labels express the dosage per tablet.


image
Figure 5-4 Pravachol label. (From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.)

image
Figure 5-5 Voltaren label. (From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.)

image
Figure 5-6 Glucophage label. (From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.)


imageMATH ETIQUETTE 5-1


When dealing with ratios, always reduce fractions to their lowest form before multiplying. This will reduce computation errors.



imagePRACTICE THE SKILL 5-1


Write the ratio for the medication amounts shown in Figures 5-1, 5-2, and 5-3








Objective 4


Proportion


A proportion is a mathematical equation that compares two equal ratios. Proportions can be written as fractions with an equal sign (=) between the two ratios or can be expressed by the use of double colons (::) between the ratios.












Examples:
12=36image or 1:2 :: 3:6


image


The key to solving a proportion problem is how you set up your problem. Refer to the box Strategy 5-1 for steps in setting up a proportion.



imageSTRATEGY 5-1
Writing Proportions






Example


In Mrs. Smith’s second grade class, there is one boy for every two girls. Mrs. Cheryl’s second grade class has three boys for every six girls. Are these proportions equal?



1. Read the problem.


    In Mrs. Smith’s second grade class, there is one boy for every two girls. Mrs. Cheryl’s second grade class has three boys for every six girls. Are these proportions equal?


2. Identify the known information.


    In Mrs. Smith’s second grade class, there is one boy for every two girls. Mrs. Cheryl’s second grade class has three boys for every six girls. Are these proportions equal?


3. Write the proportion so that the same units appear in the same location for each proportion.


    1boy2girls=3boys6girlsimage    1 boy : 2 girls :: 3 boys : 6 girls


4. Solve the problem using cross multiplication if your proportion is written as a fraction.


5. If your problem is written in linear fashion, multiply the means (“inside” numbers) together and the extremes (“outside” numbers) together.

















12=36image 1:2 :: 3:6
1 × 6 = 2 × 3 1 × 6 :: 2 × 3
6 = 6 6 :: 6
Yes, this is a true proportion. Yes, this is a true proportion.


image


Is there a different way to solve this problem? You might think it would have been easier and just as accurate to reduce your fractions before multiplying. As previously stated, there is more than one way to solve a math problem. Yes, you would have come up with the same answer if you had reduced 36image to 12image; then your answer would have been 12image = 12image. Again, the answer to the problem would be, “Yes, this is a true proportion.”



Objective 5


Solving for “X”


In the real world, we encounter proportion problems when we try to compare similar measurements but do not have all the information. Most common proportions involve the distribution of medication, laboratory result measurements, and concentration of medication in fluids.


The key to solving these problems is to set up the problem so the same measurements are in the same location on both sides of the equation. It is common to use the letter “X” to represent the unknown.



imageSTRATEGY 5-2
Writing Proportions as a Fraction





imageSTRATEGY 5-3
Cross Multiplication




23=X4image




imageHUMAN ERROR 5-1


Many times, errors occur because we have entered the sequence of numbers incorrectly into the calculator. With division, enter in the dividend first, select the division button, then enter the divisor, and press the equal button to obtain your answer.



imageSTRATEGY 5-4
Checking Your Work



Related posts:

  1. U.S. Customary Units and the Apothecary System
  2. Application of Measurement and Dose Conversion
  3. The Metric System
  4. Power of 10

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Apr 17, 2017 | Posted by in NURSING | Comments Off on Ratios and Proportions

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