Gray Morris

Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.

Unit One: Chapter 2

Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.

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After reviewing this chapter, you should be able to:

1. Compare the size of fractions2. Add fractions3. Subtract fractions4. Divide fractions5. Multiply fractions6. Reduce fractions

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Seen in • medical record, client record, charting,

and medical/nursing literature

Used in calculation types• Apothecary• Household

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A fraction is part of a whole number◦ ½ is a whole divided into two parts

Have a numerator & a denominator

Figure 2-2 Diagram representing fractions of a whole. Five parts shaded out of the six parts represent:Figure 2-2 Diagram representing fractions of a whole. Five parts shaded out of the six parts represent:

5 Numerator

6 Denominator

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Fractions may be used on drug labels in addition to metric equivalent to help clarify

and prevent errorsCohen, M. (2007). Medication

Errors, 2 ed. 2.5 mg (2½ mg) Coumadin on same label

how many parts of the Numerator whole you are taking

means Denominator how many equal parts into

which the whole is divided

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Proper• Numerator is less than denominator; the

fraction has a value of less than 1 • Examples:

Improper• Numerator is larger than, or equal, to

denominator; the fraction has a value of 1 or greater than 1

• Examples: 3 72 5

and

1 32 4

and

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An improper fraction can be changed to a mixed number or whole number by dividing the numerator by the denominator

6 1

6 5 15 5

10 2 1

10 8 1 and 18 8 4

reduced

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Mixed• A whole number and a fraction; the value

is greater than 1• Example:

Complex• Numerator, denominator, or both, are

fractions; the value may be less than, greater than, or equal to 1

• Example:

13

2

13

22

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Whole numbers• Have an expressed denominator of one

(1)• Examples:

1 3 100

1 3= 100=1 1 1

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1. If the numerators are the same, the fraction with the smaller denominator has the larger value

Example:

2. If the denominators are the same, the fraction with the larger numerator has the larger value

Example:

1 1 is larger than

150 300

3 1 is larger than

4 4

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A mixed number can be changed to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and placing the sum over the denominatorExample:

1 (5x8) 1 415

8 8 8

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1. The value of a number is unchanged when the numerator and denominator are multiplied or divided by same number

Example:

2. Change a fraction to lowest terms by dividing numerator and denominator by the largest whole number that will divide into both evenly

Example:

1 1x(2) 2 1 2

where and are equal value2 2x(2) 4 2 4

128 128 32 4288 288 32 9

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3. LCD (lowest common denominator) is the smallest whole number that can be divided evenly by all the denominators in the problem

Example:1 5

and 3 12

(12 is evenly divisible by 3, therefore12 is the LCD)

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Should always be reduced to lowest terms Numerator and denominator are each divided

by the largest number by which they are both evenly divisible

Example:

6 6 2 3

= (the lowest term)20 20 2 10

reduced

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With same denominator, add the numerators, then reduce to lowest termsExample:

With different denominators, change fraction to equivalent denominators by using the LCD, then add numerators as described aboveExample:

1 3 4 86 6 6 6

1 1 1 3 1 4 7=

4 3 4 12 3 12 12or or

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The rules for subtraction are the same as those for addition• If denominators are the same, perform

subtraction with the numerators, obtain the value, place it over the denominator, and reduce to lowest terms

• If denominators are different, find the lowest common denominator (LCD), change to equivalent fractions, subtract the numerators, and place that value over the common denominator. Reduce if necessary.

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Multiply numerators together Multiply denominators together Reduce if necessary

Note: Fractions can be reduced to lowest terms before multiplicationExpress whole numbers as fractions with a denominator of 1 to visually aid in multiplication

3 2 6 3

x4 5 20 10

reduced

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Invert the second number (turn it upside down) and then multiply. Reduce if necessary.

Note: Change mixed numbers to improper fractions before performing division steps

3 2 3 3 2

4 3 4 2 33x3 9 1

14 x2 8 8

was before inversion

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When dividing mixed fractions, change the problem visually so that division steps are easily seen

11 14

1 4 22

1 2 2 1then invert and multiply x

4 1 4 2

is same as