Foundational Math Skills
2 Ratios and Proportions
Lesson
Learning Outcomes
By the end of this chapter, learners will be able to:
- define the terms ratio and proportion,
- write ratios and proportions in numerical format using a colon and using fractions, and
- describe how to solve for an unknown amount in a proportion equation.
Ratios
You have likely used ratios in many ways in everyday life, but perhaps you are not sure how to define a ratio. A ratio is a numerical expression which shows the connection between two or more numbers. These numbers must be related in some way; we do not use ratios to compare unrelated numbers. Most often, you will see a ratio using just two whole numbers.
When writing a ratio, the numbers are written in a particular order. For instance, if I was writing a ratio of how many nursing students were in one clinical practice group, I would write [latex]8:1[/latex].
In healthcare, we use ratios in a variety of situations. For instance, when describing safe staffing levels, reviewing morbidity and mortality data, or while carrying out medication administration.
Examples of Ratios in Healthcare
When identifying staffing levels, a ratio is used to clearly indicate the number of patients a nurse can safely provide nursing care for on a particular unit:
- In an intensive care unit, you may see a ratio of one nurse for one intubated, acute patient. This is written in numerical form as [latex]1:1[/latex].
- In a surgical unit, you may see a ratio of one nurse for four patients. This is written as [latex]1:4[/latex].
- On a medical unit where care is provided by teams of two nurses (a licensed practical nurse and a registered nurse) for every ten patients, you may see a ratio written as [latex]2:10[/latex], or [latex]1:1:10[/latex] if they are separating the types of nurses within this example.
Mortality rates may also be expressed as ratios:
- An infant mortality rate of four deaths in every one thousand births is written as [latex]4:1000[/latex].
The quantity of medication in a unit measure can also be expressed as a ratio:
- A tablet of acetaminophen containing 325 mg of drug is written as [latex]1:325[/latex].
Sample Exercise 2.1
- How would you write the ratio of thirty two students in one classroom?
Answer:
[latex]32:1[/latex]
A ratio can also be expressed as a fraction, with the two numbers acting as the numerator and denominator. The numerator is always from the left of the colon, the denominator is from the right. For example, an infant mortality rate of [latex]4:1000[/latex] can be expressed as:
[latex]\dfrac{4}{1000}[/latex]
Sample Exercise 2.2
- How would you write the ratio of the amount of one tablet contains 325 mg of acetaminophen, or [latex]1:325[/latex] as a fraction?
Answer:
[latex]\dfrac{1}{325}[/latex]
Proportions
A proportion is an equation of two ratios of equivalent amounts. The terms of the first ratio are related to the terms of the second ratio. This means you should ensure the numbers of each ratio ar