1. Chapter 1: Fractions and Decimals
Math and Dosage Calculations for Health Care Third Edition Booth & Whaley
Chapter 1: Fractions and Decimals
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2. Learning Outcomes
1.1 Compare the values of fractions in various formats.
1.2 Accurately add, subtract, multiply, and divide fractions.
1.3 Convert fractions to mixed numbers and decimals.
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3. Learning Outcomes (cont.)
1.4 Recognize the format of decimals and measure their relative value.
1.5 Accurately add, subtract, multiply, and divide decimals.
1.6 Round decimals to the nearest tenth, hundredth, or thousandth.
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4. Introduction
Basic math skills are building blocks for accurate dosage calculations.
Need confidence in math skills.
A minor mistake can mean major errors in the patient’s medication.
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5. Fractions and Mixed Numbers
Measure a portion or part of a whole amount
Written two ways:
Common fractions
Decimals
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6. Common Fractions Represent equal parts of a whole
Consist of two numbers and a fraction bar
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
is the whole
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7. Common Fractions (cont.)
Scored (marked) tablet for 2 parts
You administer 1 part of that tablet each day
You would show this as 1 part of wholes or ½
Read it as “one half”
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8. Check these equations by treating each fraction as a division problem.
Fraction Rule
Rule When the denominator is 1, the fraction equals the number in the numerator.
Examples
Check these equations by treating each fraction as a division problem.
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9. Mixed Numbers 2 (two and two-thirds)
Combine a whole number with a fraction.
2 (two and two-thirds)
Example
Fractions with a value greater than 1 are written as mixed numbers.
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10. Mixed Numbers (cont.) Rule 1-2
If the numerator of the fraction is less than the denominator, the fraction has a value of < 1.
If the numerator of the fraction is equal to the denominator, the fraction has a value =1.
If the numerator of the fraction is greater than the denominator, the fraction has a value > 1.
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11. Applied only if the numerator is greater than the denominator
Mixed Numbers (cont.)
Rule 1-3 To convert a fraction to a mixed number:
Divide the numerator by the denominator. The result will be a whole number plus a remainder.
Write the remainder as the number over the original denominator.
Combine the whole number and the fraction remainder. This mixed number equals the original fraction.
Applied only if the numerator is greater than the denominator
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12. Mixed Numbers (cont.) Convert to a mixed number: Example
Divide the numerator by the denominator
= 2 R3 (R3 means a remainder of 3)
The result is the whole number 2 with a remainder of 3
Write the remainder over the whole = ¾
Combine the whole number and the fraction = 2¾
Example
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13. Mixed Numbers (cont.)
Rule 1-4 To convert a mixed number ( ) to a fraction:
Multiply the whole number (5) by the denominator (3) of the fraction ( )
5x3 = 15
Add the product from Step 1 to the numerator of the fraction
15+1 = 16
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14. Mixed Numbers (cont.)
Rule 1-4 (cont.) To convert a mixed number to a fraction:
Write the sum from Step 2 over the original denominator
The result is a fraction equal to original mixed number. Thus
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15. Practice What is the numerator in ? What is the denominator in ?
Answer 17
What is the denominator in ?
Answer 100
Twelve patients are in the hospital ward. Four have type A blood.What fraction do not have type A blood?
Answer
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16. Equivalent Fractions same as same as
Two fractions written differently that have the same value
Rule 1-5
To find an equivalent fraction, multiply or divide both the numerator and denominator by the same number.
Example
same as
same as
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17. Equivalent Fractions (cont.)
Find equivalent fractions for
Example
Exception:
The numerator and denominator cannot be multiplied or divided by zero.
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18. Equivalent Fractions (cont.)
Rule 1-6 To find missing numerator in an equivalent fraction:
If the denominator of the equivalent fraction is larger than the original denominator:
Divide the larger denominator by the smaller one.
Multiply the original numerator by the quotient from Step a.
Click to go to Example
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19. Equivalent Fractions (cont.)
Rule 1-6 To find missing numerator in an equivalent fraction: (cont.)
If the denominator of the equivalent fraction is smaller than the original denominator:
Divide the larger denominator by the smaller one.
Divide the original numerator by the quotient from Step a.
Click to go to Example
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20. Equivalent Fractions (cont.)
Example 1
Example 2
Answer ? = 7
Answer ? = 8
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21. Practice Find 2 equivalent fractions for . Answers
Find the missing numerator
Answers
Answer
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22. Simplifying Fractions to Lowest Terms
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.
Note: When 1 is the only number that divides evenly into the numerator and denominator, the fraction is reduced to its lowest terms.
Prime numbers – whole numbers other than 1 that can be evenly divided only by themselves and 1
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23. Error Alert!
Reducing a fraction does not automatically mean it is simplified to lowest terms.
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24. Simplifying Fractions to Lowest Terms (cont.)
Example
Reduce
Both 10 and 15 are divisible by 5
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25. Practice Answer Answer Reduce the following fractions: then,
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26. Finding Common Denominators
Any number that is a common multiple of all the denominators in a group of fractions
Rule 1-8 To find the least common denominator (LCD):
List the multiples of each denominator.
Compare the list for common denominators.
The smallest number on all lists is the LCD.
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27. Finding Common Denominators (cont.)
Rule 1-9 To convert fractions with large denominators to equivalent fractions with a common denominator:
List the denominators of all the fractions.
Multiply the denominators. (The product is a common denominator.)
Convert each fraction to an equivalent with the common denominator.
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28. Practice Answer 21 Answer 48 Find the least common denominator for:
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29. Comparing Fractions Rule 1-10 To compare fractions:
Write all fractions as equivalent fractions with a common denominator.
Write the fraction in order by size of the numerator.
Restate the comparisons with the original fractions.
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30. Comparing Fractions Order from smallest to largest: Example
Write as equivalent fractions with a common denominator. LCD = 10.
Order fractions by size of numerator:
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31. Adding Fractions Rule 1-11 To add fractions:
Rewrite any mixed numbers as fractions.
Write equivalent fractions with common denominators. The LCD will be the denominator of your answer.
Add the numerators. The sum will be the numerator of your answer.
Click to go to Example
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32. Subtracting Fractions
Similar to adding fractions.
Rule To subtract fractions:
Rewrite any mixed numbers as fractions.
Write equivalent fractions with common denominators. The LCD will be the denominator of your answer.
Subtract the numerators. The difference will be the numerator of your answer.
Click to go to Example
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33. Adding and Subtracting Fractions
Example Addition
Add
LCD is 4
Example
Subtraction
LCD is 12
Subtract
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34. Multiplying Fractions
Rule 1-13 To multiply fractions:
Convert any mixed numbers or whole numbers to fractions.
Multiply the numerators and then the denominators.
Reduce the product to its lowest terms.
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35. Multiplying Fractions (cont.)
To multiply multiply the numerators and multiply the denominators
Example
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36. 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.
Cancel terms to solve 1 1 3 2
Answer will be
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37. Error Alert! Avoid canceling too many terms.
Each time you cancel a term, you must cancel it from one numerator AND one denominator.
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38. Practice Find the following products: Answer Answer Answer 234
A bottle of liquid medication contains 24 doses. The hospital has 9 ¾ bottles of medication. How many doses are available?
Answer
Answer
Answer 234
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39. Dividing Fractions Rule 1-15
Convert any mixed or whole number to fractions.
Invert (flip) the divisor to find its reciprocal.
Multiply the dividend by the reciprocal of the divisor and reduce.
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40. Dividing Fractions (cont.)
Example
You have bottle of liquid medication available and you must give of this to your patient. How many doses are available in this bottle?
by the reciprocal of
Multiply 1 4
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41. Error Alert! Write division problems carefully to avoid mistakes.
1. Convert whole numbers to fractions, especially if you use complex fractions.
2. Be sure to use the reciprocal of the divisor when converting the problem from division to multiplication.
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42. Practice Find the following quotients: divided by divided by Answer
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?
Answer 48 vials
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43. Decimals
Another way to represent whole numbers and their fractional parts
Used daily by health care practitioners
Metric system
Decimal based
Used in dosage calculations, calibrations, and charting
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44. Working with Decimals
Location of a digit relative to the decimal point determines its value
The decimal point separates the whole number from the decimal fraction
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45. Working with Decimals (cont.)
Table 1-3 Decimal Place Values
The number 1, can be represented as follows:
Whole Number
Decimal Point
Decimal Fraction
Table 1-3 Decimal Place Values
The number 1, can be represented as follows:
Whole Number
Decimal Point
Decimal Fraction
Thousands
Hundreds
Tens
Ones .
Tenths
Hundredths
Thousandths 1, 5 4 2 6 7
Thousands
Hundreds
Tens
Ones .
Tenths
Hundredths
Thousandths 1, 5 4 2 6 7
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46. Decimal Place Values The number 1,542.567 is read:
(1) - one thousand
(5) - five hundred
(42) - forty two and
(0.5) - five hundred
(0.067) – sixty-seven thousandths
One thousand five hundred forty two and five hundred sixty-seven thousandths
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47. Writing Decimals Rule 1-16 When writing a decimal number:
Write the whole number part to the left of the decimal point
Write the decimal fraction part to the right of the decimal point.
Decimal fractions are equivalent to fractions that have denominators of 10, 100, 1000, and so forth.
Use zero as a placeholder to the right of the decimal point.
Example: 0.201
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48. Writing Decimals (cont.)
Rule 1-17
Always write a zero to the left of the decimal point when the decimal number has no whole number part.
Makes the decimal point more noticeable
Helps to prevent errors caused by illegible handwriting
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49. Comparing Decimals
Rule 1-18 To compare values of a group of decimal numbers:
The decimal with the greatest whole number is the greatest decimal number.
If the whole numbers of two decimals are equal, compare the digits in the tenths place.
If the tenths place are equal, compare the hundredths place digits.
Continue moving to the right comparing digits until one is greater than the other.
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50. Comparing Decimals (cont.)
The more places a number is to the right of the decimal point the smaller the value.
Examples
0.3 is or three tenths
0.03 is or three hundredths
0.003 is or three thousandths
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51. Practice
Write the following in decimal form:
Answers
= 0.2
= 0.17
= 0.023
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52. Rounding Decimals Rule 1-19
Decimals are usually rounded to the nearest tenth or hundredth.
Rule 1-19
Underline the place value to which you want to round.
Look at the digit to the right of this target.
If 4 or less, do not change the digit
If 5 or more, round up one unit
Drop all digits to the right of the target place value.
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53. Practice Answer 14.3 Answer 9.3 Answer 8.80 Answer 10.54
Round to the nearest tenth:
14.34
9.293
Round to the nearest hundredth:
8.799
10.542
Answer
Answer 9.3
Answer
Answer
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54. Converting Fractions into Decimals
Rule 1-20
To convert a fraction to a decimal, divide the numerator by the denominator.
Example
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55. Converting Decimals into Fractions (cont.)
Rule 1-21
Write the number to the left of the decimal point as the whole number.
Write the number to the right of the decimal point as the numerator of the fraction.
Use the place value of the digit farthest to the right of the decimal point as the denominator.
Reduce the fraction part to its lowest term.
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56. Practice 100.4 1.2 Convert decimals to fractions or mixed number:
Answer or
1.2
100.4
Answer or
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57. Adding and Subtracting Decimals
Rule 1-22
Write the problem vertically. Align the decimal points.
Add or subtract starting from the right. Include the decimal point in your answer.
2.47
+ 0.39
2.86
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58. Adding and Subtracting Decimals (cont.)
Examples
Subtract
7.3 – 1.005
Answer
7.300
1.005
6.295
Add
Answer
13.561
13.660
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59. Practice Add or subtract the following pair of numbers: 48.669 + 0.081
Answer
– 1.625
Answer
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60. Multiplying Decimals Rule 1-23
First, multiply without considering the decimal points, as if the numbers were whole numbers.
Count the total number of places to the right of the decimal point in both factors.
To place the decimal point in the product, start at its right end and move the it to the left the same number of places.
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61. Multiplying Decimals (cont.)
Example
Multiply 3.42 x 2.5
3.42
X 2.5
1710
684
8550
There are three decimal places so place the decimal point between 8 and 5.
Answer
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62. Practice
A patient is given 7.5 milliliters of liquid medication 5 times a day. How many milliliters does she receive per day?
Answer x 5
7.5
X 5
37.5
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63. Dividing Decimals Rule 1-24 Write the problem as a fraction.
Move the decimal point to the right the same number of places in both the numerator and denominator until the denominator is a whole number. Insert zeros as needed.
Complete the division as you would with whole numbers. Align the decimal point of the quotient with the decimal point of the numerator, if needed.
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64. Dividing Decimals (cont.)
Example
Divide
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65. Practice Answer 32 divided by 0.4 Take 0.4 into 32
A bottle contains 32 ounces of medication. If the average dose is 0.4 ounces, how many doses does the bottle contain?
Answer 32 divided by 0.4
Take 0.4 into 32
Add a zero behind the 32 for each decimal place
320 divided by 4 = 80 or 80 doses
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66. Apply Your Knowledge Convert the following mixed numbers to fractions:
Answer
Answer
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67. Apply Your Knowledge Round to the nearest tenth: 7.091 Answer 7.1
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68. Apply Your Knowledge Add the following: 7.23 + 12.38
Answer
Multiply the following: x 1.005
Answer
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69. He who is ashamed of asking is ashamed of learning.
End of Chapter 1
He who is ashamed of asking is ashamed of learning.
~ Danish Proverb
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