Chapter 1 PowerPoint Dosages and Calculations

Chapter 1 Fractions
© 2012 The McGraw-Hill Companies, Inc. All rights reserved.
PowerPoint® Presentation to accompany:
Math and Dosage Calculations
for Healthcare Professionals
Fourth 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
1
the whole 5

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
100
 
100
Fraction Rule
Rule 1-1 When the denominator is 1, the
fraction equals the number in the numerator.
Examples
4
4
1
1
Check these equations by treating each
fraction as a division problem.

1-11
2
2 (two and two-thirds) 3
Mixed Numbers
 Mixed numbers combine a whole number
with a fraction.
Example
 Fractions with a value greater than 1 are
written as mixed numbers.

1-12
Mixed Numbers (cont.)
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.
1
4
4


1-13
Rule 1-2 (cont.)
3. If the numerator of the fraction is greater than
the denominator, the fraction has a value > 1.
1
5

4

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:
Example 4
1. Divide the numerator by the denominator.
2.
The result is the whole number 2 with a
remainder of 3.
11
11  4  2R3

1-17
Example
3. Write the remainder over the whole = ¾
4. Combine the whole number and the fraction
= 2¾

1-18
1
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
3
5

1-19
Rule 1-4 (cont.)
3. Write the sum from Step 2 over the original
denominator.
16
4. The result is a fraction equal to original mixed
number. Thus:
3
16
3
1
5 
3

1-20
Practice
17
What is the numerator in ?
Answer = 17
Answer = 100
100
4
What is the denominator in ? 100

1-21
Practice
Twelve patients are in the hospital unit.
Four have type A blood. What fraction
does not have type A blood?
Answer =
8
12

1-22
same as same as 2
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.
3
6
Example
4
8
4

1-23
1
Equivalent Fractions (con’t)
Example Find equivalent fractions for
2
6
2
2
1
3
X 
3
Exception:
The numerator and denominator cannot be
multiplied or divided by zero.

1-24
Equivalent Fractions (cont.)
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.

1-25
Equivalent Fractions (cont.)
2 x

12 3
Example 1
2 x 12 = 24 24  3 = 8
Answer : x = 8

1-26
1
Practice
1. Find 2 equivalent fractions for
4
2
2. Find the missing numerator:
Answer: 128
10
16
8
x

Answers:
40
,
20

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
Simplifying Fractions (cont.)
10
Reduce
Both 10 and 15 are divisible by 5:
Example
15
2
3
5
5
10
15
 

1-31
1
3
3

Practice
Reduce the following fractions:
8
Answer 10
4
5
2
2
8
10



3
9
9
9
27
81



27
81
Answer
3
3
9


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
Finding Common
Rule 1-9 (cont.)
3. Convert each fraction to an equivalent
with the common denominator.

1-35
19
Finding Common
1
1
Convert and to equivalent
fractions with a common
denominator.
Example 7
1.
7x19  133
19
1x19
2. and
19
7
133
1x7
19x7

133
7x19

7
3. Equivalent fractions are and
133
133

1-36
Practice
Find the least common denominator for:
1
7
1
and
3
Answer = 21
7
12
5
48
and
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.

1-38
Comparing of Fractions (cont.)
Example Order from smallest to largest:
4
5
1
3
1. Write as equivalent fractions with a common
8
2
4

denominator. LCD = 10.
2
10
2
2
1
5
?
10
1
5



 
10
2
5
?
10
4
5


 
3
10
3
10

5
10

1-39
Comparing the Value of
Fractions
Example (cont.)
2. Order fractions by size of numerator:
8
10
3
10
2
10
 

1-40
7
,
Answer: they are in the
correct order 8
2
1
3
3
1  1

Practice
 Order from smallest to largest.
3
,
4
2
3
 Order from largest to smallest.
2
1 , , Answer:
3
1
4
5
3
1
5
5
5
4

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
5
3
5
23
Adding Fractions
2
1
2
1
Add: 3 
1
13
3   
4
1
2
2
4
4
4
10
4
10
13
4
  
Example
Addition 4
2
4
13
LCD is 4.   
4
5
2
13
4

1-44
Subtracting Fractions
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.

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
3
12
2

6
Example
Subtraction
Subtract:
LCD is 12.
1
12
2
3
   
12
4
12
3
12
6

1-47
Multiplying Fractions
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.

1-48
Multiplying Fractions (cont.)
7
8
To multiply multiply the
numerators and multiply the denominators:
56
16
x
21
8 x 7
1
6
56
336

336
21 x 16
7
16
x
8
21
 
Example

1-49
Multiplying Fractions (cont.)
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.
1 1
7
Cancel terms to solve:
16
x
8
21
3 2
1
6
Answer =

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
3
Practice
Find the following products:
4
x
8
9
3
Answer
1
6
4
5
5
1
x 7
6
Answer
10
14

1-52
24 x 9 Answer 234
Practice
A bottle of liquid medication contains 24
doses. The hospital has 9 ¾ bottles of
medication. How many doses are
available?
3
4

1-53
Dividing Fractions
Rule 1-15
1. 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.

1-54
Dividing Fractions (cont.)
3
You have bottle of liquid medication
1
available, and you must give of this to your patient.
How many doses are available in this bottle?
1
4
16
1
16
3
4
3
 4
16
Multiply by the reciprocal of
Example
12 doses
12
1
16
x
4
1
3
16
x
4
1
3
  
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
3
1
28 Answer
2
Practice
Find the following quotients:
5

4
Answer
45
9
7
9
4

6

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?
3
4
84  1
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
Apply Your Knowledge
Convert the following mixed numbers to
13
10 99
fractions:
3
2 Answer
18
6
39
18

Answer 10
9
9

1-61
 Determine order from lowest to highest.
2
,
2
3
2
2
,
6
Answer:
2
,
3
2
2
2
,
6

1-62
Add the following:
2
 Answer:
5
2
3
Subtract the following:
1
15
1
2
5
2
3
 Answer:
4
15

1-63
Multiply:
1
x
5
Divide:
Answer:
2
5
3
1
1
1
1
1  Answer:
3
5
3
3
5

1-64
End of Chapter 1
He who is
ashamed of
asking is
ashamed of
learning.
~ Danish Proverb

Chapter 1 PowerPoint Dosages and Calculations

More Related Content

Similar to Chapter 1 PowerPoint Dosages and Calculations (20)

More from kevinyocum4 (20)

Recently uploaded (20)

Chapter 1 PowerPoint Dosages and Calculations