Chapter 1 PowerPoint Dosages and Calculations

© 2012 The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 1 Fractions

PowerPoint® Presentation to accompany:

Math and Dosage Calculations for Healthcare ProfessionalsFourth Edition

Booth, Whaley, Sienkiewicz, and Palmunen

1-2


Learning Outcomes

1.1 Produce fractions and mixed numbers in the proper form.

1.2 Produce and identify equivalent fractions.

1.3 Determine the simplest form of a fraction.

1.4 Find the least common denominator.

1-3


Learning Outcomes (cont.)

1.5 Compare the values of fractions.

1.6 Add fractions.

1.7 Subtract fractions.

1.8 Multiply fractions.

1.9 Divide fractions.

1-4


Key Terms Complex fraction

Denominator

Equivalent fractions

Least common denominator

Mixed number

Numerator

Prime number

1-5


Introduction

Basic math skills are building blocks for accurate dosage calculations.

Healthcare professionals need confidence in math skills.

A minor mistake can mean major errors in the patient’s medication.

1-6


Producing Fractions and Mixed Numbers In the Proper Form

Fractions and mixed numbers measure a portion or part of a whole amount.

They are written in two ways: as common fractions as decimals

1-7


Common Fractions represent equal parts of a whole;

consist of two numbers and a fraction bar.

1-8


Common Fractions Common fractions are written in the form:

Numerator (top part of the fraction) = part of whole Denominator (bottom part of the fraction)

represents the whole

one part of the whole the whole 5

1

1-9


Common Fractions (cont.)

With a scored (marked) tablet for 2 parts, you:

administer 1 part of that tablet each day;

show this as 1 part of 2 wholes or ½;

read it as “one half.”

1-10


Fraction Rule

Rule 1-1 When the denominator is 1, the fraction equals the number in the numerator.

ExamplesExamples

Check these equations by treating each fraction as a division problem.

414 100

1100

1-11


Mixed Numbers

Mixed numbers combine a whole number with a fraction.

Example Example

Fractions with a value greater than 1 are written as mixed numbers.

2 (two and two-thirds)

32

1-12


Rule 1-2 1. If the numerator of the fraction is less than the

denominator, the fraction has a value of < 1.

¾ < 1

2. If the numerator of the fraction is equal to the denominator, the fraction has a value =1.

Mixed Numbers (cont.)

144

1-13



Rule 1-2 (cont.)

3. If the numerator of the fraction is greater than the denominator, the fraction has a value > 1.

14

5

1-14


Rule 1-3 To convert a fraction to a mixed number:

1. Divide the numerator by the denominator. The result will be a whole number plus a remainder.

2. Write the remainder as the number over the original denominator.


1-15



Rule 1-3 (cont.)

3. Combine the whole number and the fraction remainder. This mixed number equals the original fraction.

1-16


Mixed Numbers (con’t)

Convert to a mixed number:

1. Divide the numerator by the denominator.

2.

The result is the whole number 2 with a remainder of 3.

ExampleExample 411

3R2411

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3. Write the remainder over the whole = ¾

4. Combine the whole number and the fraction = 2¾

ExampleExample

1-18


Rule 1-4 To convert a mixed number ( ) to a fraction:

1. Multiply the whole number by the denominator of the fraction.

5x3 = 15

2. Add the product to the numerator of the fraction.

15+1 = 16

31

5


1-19


Rule 1-4 (cont.)

3. Write the sum from Step 2 over the original denominator.

4. The result is a fraction equal to original mixed number. Thus:

316

316

31

5


1-20


Practice

What is the numerator in ?

Answer = 17

Answer = 100

10017

What is the denominator in ?1004

1-21


Practice

Twelve patients are in the hospital unit. Four have type A blood. What fraction does not have type A blood?

Answer = 128

1-22


Producing and Identifying Equivalent Fractions

Rule 1-5

To find an equivalent fraction, multiply or divide both the numerator and denominator by the same number.

63

ExampleExample 84

42same as same as

1-23


Equivalent Fractions (con’t)

Find equivalent fractions for ExampleExample

62

22

31

X

31

Exception: The numerator and denominator cannot be multiplied or divided by zero.

1-24


Rule 1-6 To find the missing numerator in an equivalent fraction:

1. Multiply the original numerator by the denominator of the new fraction.

2. Divide the product from step 1 by the original denominator.

Equivalent Fractions (cont.)

1-25


Equivalent Fractions (cont.)

123

2 xExample 1Example 1

Answer : x = 8

24 3 = 82 x 12 = 24

1-26


Practice

1. Find 2 equivalent fractions for

2. Find the missing numerator:

Answer: 128

101

168

x

Answers: 404

,202

1-27


Simplifying Fractions

Rule 1-7 To reduce a fraction to its lowest terms, find the largest whole number that divides evenly into both the numerator and denominator.

1-28


Simplifying Fractions (cont.)

Note: When 1 is the only number that divides evenly into the numerator and denominator, the fraction is reduced to its lowest terms.

1-29


Error Alert!

Reducing a fraction does not automatically mean it is simplified to its lowest terms.

1-30


Both 10 and 15 are divisible by 5:

Example Example

1510

32

55

1510

Reduce

Simplifying Fractions (cont.)

1-31


Practice

Reduce the following fractions:

Answer108

54

22

108

93

99

8127

8127

Answer31

33

93

then,

1-32


Finding Common Denominators

Rule 1-8 To find the least common denominator (LCD):

1. List the multiples of each denominator.

2. Compare the list for common denominators.

3. The smallest number on all lists is the LCD.

1-33


Finding Common Denominators (cont.)

Rule 1-9 To convert fractions with large denominators to equivalent fractions with a common denominator:

1. List the denominators of all the fractions.

2. Multiply the denominators. (The product is a common denominator.)

1-34



Rule 1-9 (cont.)

3. Convert each fraction to an equivalent with the common denominator.

1-35



Convert and to equivalent fractions with a common denominator.

1.

2. and

3. Equivalent fractions are and

Example Example 71

191

13319x7

1337

7x197x1

13319

19x719x1

1337

13319

1-36


Practice

Find the least common denominator for:

7

1

3

1and

Answer = 21

12

7

48

5and

Answer = 48

1-37


Comparing Fractions

Rule 1-10 To compare fractions:1. Write all fractions as equivalent fractions with a

common denominator.

2. Write the fraction in order by size of the numerator.

3. Restate the comparisons with the original fractions.

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1. Write as equivalent fractions with a common denominator. LCD = 10.

Comparing of Fractions (cont.)

10

2

2

2

5

1

10

?

5

1

10

8

2

2

5

4

10

?

5

4

10

3

10

3

5

4

5

1

10

3Example Example Order from smallest to largest:

1-39


Comparing the Value of Fractions

Example (cont.) Example (cont.)

2. Order fractions by size of numerator:

10

8

10

3

10

2

1-40


Practice Order from smallest to largest.

Order from largest to smallest.

Answer: they are in the correct order 8

7,

43

,32

5

31

4

31

5

21 ,, Answer:

5

21

5

31

4

31

1-41


Adding Fractions

Rule 1-11 To add fractions:

1. Rewrite any mixed numbers as fractions.

2. Write equivalent fractions with common denominators. The LCD will be the denominator of your

answer.

1-42


Adding Fractions

Rule 1-11 To add fractions:

3. Add the numerators. The sum will be the numerator of your answer.

1-43


Adding Fractions

2

5

4

13

2

12

4

13

4

35

4

23

4

10

4

13

Example Addition

Example Addition 2

12

4

13 Add:

4

10

4

13

2

5

4

13LCD is 4.

1-44


Rule 1-12 To subtract fractions:

1. Rewrite any mixed numbers as fractions.

2. Write equivalent fractions with common denominators. The LCD will be the denominator of

your answer.

Subtracting Fractions

1-45


Subtracting Fractions

Rule 1-12 To subtract fractions:

3. Subtract the numerators. The difference will be the numerator of your answer.

1-46


Adding and Subtracting Fractions

12

3

6

2Example

Subtraction

ExampleSubtraction

Subtract:

LCD is 12.

12

1

12

3

12

4

12

3

6

2

1-47


Rule 1-13 To multiply fractions:

1. Convert any mixed numbers or whole numbers to fractions.

2. Multiply the numerators and then the denominators.

3. Reduce the product to its lowest terms.

Multiplying Fractions

1-48


Multiplying Fractions (cont.)

To multiply multiply the numerators and multiply the denominators:

167

x218

61

33656

33656

16 x 217 x 8

167

x218

Example Example

1-49


Rule 1-14 To cancel terms when multiplying fractions, divide

both the numerator and denominator by the same number, if they can be divided evenly.

Cancel terms to solve:

16

7x

21

81 1

3 2

6

1Answer =

Multiplying Fractions (cont.)

1-50


Error Alert!

Avoid canceling too many terms.

Each time you cancel a term, you must cancel

it from one numerator AND one denominator.

1-51


Practice

Find the following products:

9

4x

8

3

Answer6

1

5

47 x

6

51

Answer10

314

1-52


Practice

A bottle of liquid medication contains 24 doses. The hospital has 9 ¾ bottles of medication. How many doses are available?

43

9 x 24 Answer 234

1-53


Rule 1-151. Convert any mixed or whole number to fractions.

2. Invert (flip) the divisor to find its reciprocal.

3. Multiply the dividend by the reciprocal of the divisor and reduce.

Dividing Fractions

1-54


You have bottle of liquid medication available, and you must give of this to your patient. How many doses are available in this bottle?

43

161

161

43 4

3161

by the reciprocal ofMultiply

Dividing Fractions (cont.)

Example Example

doses 121

121

16x

43

116

x43

1

4

1-55


Error Alert!

Write division problems carefully to avoid mistakes.

1. Convert whole numbers to fractions.

2. Be sure to use the reciprocal of the divisor when converting the problem from division to multiplication.

1-56


Practice

Find the following quotients:

Answer4528 Answer

92

75

94

43

61

1-57


Practice

A case has a total of 84 ounces of medication. Each vial in the case holds 1¾ ounce. How many vials are in the case?

43

184

Answer 48 vials

1-58


In Summary In this chapter you learned to:

produce fractions and mixed numbers in proper form;

produce and identify equivalent fractions and find a missing numerator;

determine the simplest form of a fraction.

1-59


In Summary (cont.)

In this chapter you learned to:

find the least common denominator;

compare the value of fractions;

add, subtract, multiply, and divide fractions.

1-60


Convert the following mixed numbers to fractions:

183

2 Answer 613

1839

Answer 109910

99

Apply Your Knowledge

1-61


Apply Your Knowledge Determine order from lowest to highest.

32

,22

,62

Answer:

22

,32

,62

1-62



Add the following:

Subtract the following:

52

32 Answer:

151

1

52

32 Answer:

154

1-63



Multiply:

Divide:

Answer: 52

31

x51

1

31

51

1 Answer: 53

3

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End of Chapter 1

He who is ashamed of

asking is ashamed of learning.

~ Danish Proverb

Health & Medicine

Chapter 1 PowerPoint Dosages and Calculations