Mathematics Skills for Health Care Providers Lesson 7 of 7 Introduction to Ratio/Proportions

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Kimberly Williams
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1 Mathematics Skills for Health Care Providers Lesson 7 of 7 Introduction to Ratio/Proportions Learning Objectives At the end of this lesson, you will be able to: 1. Apply what you have learned to identify and change the way ratios and proportions are written. 2. Apply ratio and proportion steps for solving math problems in your job. This lesson includes ratio and proportion computations. This is one of the most useful tools you will learn in mathematics. The skills you develop in this lesson will be useful on many different types of math problems that you may encounter. Vocabulary and Key Terms Ratio - A ratio is a pair of numbers used to describe a relationship or make a comparison between two quantities. A ratio can be written three ways. Like fractions, ratios should be reduced. Notice that each form has been reduced. 1. Using the word to 48 to 8 = 6 to 1 2. Using a colon 48:8 = 6:1 3. Expressed in fraction form 48/8 = 6/1 Proportion - A part considered in relation to the whole. Thee relationship between things or parts of things with respect to the total magnitude or quantity. Unit 2 - Mathematics Lesson 7 143

2 Prescription for Understanding There will always be a need to compare numbers in mathematics. Subtracting and division are methods of comparing. A ratio is a comparison of numbers by division. In a ratio, unlike a fraction, you keep a 1 in the denominator. This is because you are comparing the numbers. Remember: numbers in a ratio must always be written in the order that the problem asks. Review the examples below: Example 1. Let s suppose you earn $200 a week. Your house rent is $40 weekly. What is the ratio of your rent to your income? Answer: Make a ratio with the rent on top (numerator) and the weekly income on the bottom (denominator). Then reduce. Rent = 40 = 1/5 or 1:5 Income 200 Example 2. Simplify the ratio 1/3:1/2. Answer: Ratio is a comparison of numbers by division. Rewrite the above example as a division problem and solve. 1/3:1/2 = 1/3 1/2 = 1/3 2/1 = 2/3 or 2:3 Example 3. On a workplace mathematics test of 20 questions, you missed 2 questions. What is the ratio of the number you answered correctly to the number you missed? Step 1: Subtract the number of questions you missed from the total number of questions. Total questions - 20 Number missed - 2 Number correct - 18 Step 2: Make a ratio with the number you answered correctly on top (numerator) and the number you missed on the bottom (denominator). Then reduce if necessary. Number correct 18 = 9 or 9:1 Number missed 2 1 Unit 2 - Mathematics Lesson 7 144

3 Skill Check 1. Let s assume there are 150 employees at your facility and 105 employees belong to some type of recreation club. What is the ratio of the number of employees who do not belong to a recreation club to the total number of employees? 2. In a workplace mathematics class with 20 students, there are 12 women. What is the ratio of the number of women to the total number of students? 3. Simplify the ratio 1/4:2/3. 4. Out of a total weekly budget of $180.00, $30.00 is spent for food. What is the ratio of the amount spent for food to the amount not spent on food? 5. In the class in problem 2 above, what is the ratio of the number of men to the total number of women? Now select your area of work and then turn to the appropriate page for Let s Apply to Your Workplace questions: Nursing Assistant Page Dietary Services Page Environmental Services Page Unit 2 - Mathematics Lesson 7 145

4 Unit 2 - Mathematics Lesson 7 146

5 Let s Apply to Nurse Assistant Mathematics Lesson 7 of 7 Nursing assistants use ratios and proportions in many different places. One example is in determining how many nurse assistants will be required to care for the residents. Example If one nursing assistant can care for 8 residents, 1/8 or 1:8, then for every 8 residents you have 1 nurse assistant that cares for them. Therefore, if a facility has 160 residents, how many nurse assistants are required to maintain an 8 to 1 ratio? One nurse to care for 8 residents each. Step 1: Determine the total number of residents, in this example 160. Step 2: Divide the total number of residents by the requirement ratio of 8 residents per 1 nurse assistant or 8 / 160 = 20 Step 3: The answer of 20 is the total number of nurse assistants required for 160 residents. Therefore, in a facility with 160 residents, the ratio will be 20:160 or 20 to 160. Unit 2 - Mathematics Lesson 7 147

6 Exercise 1. If it requires 30 minutes for a nurse assistant to bathe two residents, how many minutes will be required to bathe 5 residents? a. 45 b. 90 c. 75 d If it requires 24 minutes to change the linens on three resident beds, how many beds can a nurse assistant change in 40 minutes? a. 5 b. 6 c. 7 d When gathering vital sign information on residents, it usually takes 20 minutes to complete the forms for 5 residents. How many residents will the nurse assistant be able to gather vital signs on in 48 minutes? a. 9 b. 12 c. 10 d. 15 Unit 2 - Mathematics Lesson 7 148

7 Let s Apply to Dietary Services Mathematics Lesson 7 of 7 Dietary Services workers use ratios and proportions in many different places. One example includes the preparation of recipes. Example You must mix four ounces of milk powder with one quart (32 ounces) of water to produce one quart of liquid milk. 4 oz. : 32 oz. or 4 to 32 Therefore, if you needed to mix one gallon of liquid milk (one quart will equal 32 ounces so 4 quarts 32 ounces will equal a total of 128 ounces), you would use 16 oz. : 128 oz. or 16 to 128 powder to water. Step 1: Determine the total amount of liquid milk needed. One gallon / 4 quarts / 128 ounces Step 2: Divide by the amount of milk powder used per quart 4 / 128 or Step 3: The answer is 16, which is the total amount of milk powder to produce one gallon / 4 quarts / 128 ounces of liquid milk. Therefore, the ratio will be 16 ounces : 128 ounces or 16 to 128 powder to water. Unit 2 - Mathematics Lesson 7 149

8 Exercise 1. How much rice is needed to mix with one gallon of water if the ratio is 1 to 2, rice to liquid? a. 2 gallons b. 1 gallon c. 1/2 gallon d. 1/4 gallon 2. How much water is needed to prepare orange juice using 1/2 quart of concentrate with a ratio of 1 to 4, concentrate to water? a. 4 quarts b. 1/2 quart c. 2 quarts d. 8 quarts 3. How much water will be required to soak 3/4 of a gallon of navy beans if a ratio of 3 to 1, water to beans, is required? a. 2 gallons b. 1 3/4 gallons c. 2 1/4 gallons d. 1 1/2 gallons Unit 2 - Mathematics Lesson 7 150

9 Let s Apply to Environmental Services Mathematics Lesson 7 of 7 Environmental Services workers use ratios and proportions in many different places. One example includes the preparation of floor wax. Example You must mix four ounces of wax concentrate with one quart (32 ounces) of water to produce one quart of liquid wax. 4 oz. : 32 oz. or 4 to 32 Therefore, if you needed to mix one gallon of liquid wax (one quart will equal 32 ounces so 4 quarts 32 ounces will equal a total of 128 ounces), you would use 16 oz. : 128 oz. or 16 to 128 wax concentrate to water. Step 1: Determine the total amount of liquid wax needed. One gallon / 4 quarts / 128 ounces Step 2: Divide by the amount of concentrate wax used per quart 4 / 128 or Step 3: The answer is 16, which is the total amount concentrate wax to produce one gallon / 4 quarts / 128 ounces of liquid wax. Therefore, the ratio will be 16 ounces : 128 ounces or 16 to 128 concentrate to water. Unit 2 - Mathematics Lesson 7 151

10 Exercise 1. To mix a disinfecting solution, how much bleach is needed to mix with one gallon (128 ounces) of water if the ratio is 1 to 16, bleach to water? a. 2 ounces b. 6 ounces c. 8 ounces d. 16 ounces 2. How much water is needed to prepare a floor striping solution using 1/2 quart of striping concentrate with a ratio of 1 to 8, concentrate to water? a. 2 quarts b. 4 quarts c. 8 quarts d. 16 quarts 3. How much concentrated liquid laundry detergent will be required to make up 50 gallons of liquid laundry soap if a ratio of 19 to 1, water to concentrate, is required? a. 1 gallon b. 1 1/2 gallons c. 2 gallons d. 2 1/2 gallons Unit 2 - Mathematics Lesson 7 152

PERCENTS. Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% =

PERCENTS. Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% = PERCENTS Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% = Percents are really fractions (or ratios) with a denominator of 100. Any