Chapter 1
Arithmetic Needed for Dosage
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Adding Fractions:
Same Denominator
• Add two numerators and write the sum over the
denominator
• Example: 1/6 + 4/6 = 5/6
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Adding Fractions:
Different Denominators
• Convert each fraction, multiplying both numbers by
lowest common denominator
• Add two numerators together and reduce
• Example: 2/6 + ¼ =
– 2/6 (× 2/× 2)= 4/12
– ¼ (× 3/× 3) = 3/12
– 4/12 + 3/12 = 7/12
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Subtracting Fractions:
Same Denominator
• Subtract numerators and write the difference over
denominator
• Example: 14/24 – 9/24 = 5/24
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Subtracting Fractions:
Different Denominators
• Convert each fraction using lowest common denominator
• Subtract the numerators and reduce
• Example: 2/6 - ¼ =
– 2/6 (× 2/× 2)= 4/12
– ¼ (× 3/×3) = 3/12
– 4/12 - 3/12 = 1/12
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Multiplying Fractions
• Multiply numerators across
• Multiply denominators across
• Reduce lowest terms
• Example: 1/8 × 2/4 = 2/32 = 1/16
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Multiplying Fractions:
Mixed Numbers
• Change into improper fraction
– Multiply whole number by denominator and then add
total to the numerator
– Example: 2½ × 1/3 = 5/2 × 1/3 = 5/6
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Fraction to Decimal
• Divide numerator by the denominator
• Fraction numerator = dividend
• Fraction denominator = divisor
• Answer = quotient
• Example: 2/3 = 0.666
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Reading Decimals
• 0.2 is read as two tenths (2/10)
• 0.02 is read as two hundredths (2/100)
• 0.002 is read as two thousandths (2/1000)
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Rounding off Decimals
• Round off decimal, drop the final number
– Example: 4.624 becomes 4.62
• Exception: If final number is 5 or above, drop it and then
increase adjacent number by 1
– Example: 2.36 becomes 2.4
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Question
A neonate weighs 8¼ pounds. How would this weight be
reported as a decimal to the nearest hundredth?
A. 8.15
B. 8.21
C. 8.25
D. 8.32
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Answer
C. 8.25
• First change 8¼ into an improper fraction by
multiplying whole number by denominator and then
add total to the numerator. Answer: 8 x 4 = 32 + 1 =
33/4
• Divide numerator by the denominator. Answer: 33/4 =
8.25 pounds
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Adding Decimals
• Stack vertically, making sure all the decimal points line
up
• Add each vertical column of numbers
• Example:
1.45
+2.12
3.57
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Subtracting Decimals
• Stack vertically, making sure all the decimal points line
up
• Subtract each vertical column of numbers
• Example:
5.45
- 2.12
3.33
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Multiplying Decimals
• Line up numbers on the right and do not align decimal
points
• Multiple each top number by each bottom number
• Place the decimal point in the answer by starting at the
right and moving the point the same number of places
equal to the sum of the decimal points in the numbers
multiplied
• Example: 1.4 x 3.02 = 4.228
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Dividing Decimals
REMINDER
• Numerator = dividend
• Denominator = divisor
• Answer = quotient
• Write dividend and place a decimal point immediately
after it. Then place another decimal point above it on
quotient line.
• Example: 12/16 = 0.75
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Question
What is 6.326 to the nearest hundredths?
A. 6.3
B. 6.32
C. 6.33
D. 6.326
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Answer
C. 6.33
– 0.3 is to tenths
– 0.33 is to hundredths
– 0.326 is to thousandths place
• Round off decimal, drop the final number. Exception: If
final number is 5 or above, drop it and then increase
adjacent number by 1
– Example: 6.326 becomes 6.33
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Percentage
• Parts per hundred
• Fraction with variable numerator and a denominator
that’s always 100
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Fraction Converted to Percentage
• Denominator 100, write numerator as a percent
– Example: 15/100 = 15%
• Denominator not 100, convert fraction using 100 as
common denominator
– Example: 9/20 = 45/100 = 45%
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Ratios Converted to Percentage
• Second number in ratio is 100, write first number as
percent
– Example: 4:100 = 4%
• Second number in ratio not 100, convert ratio using 100
as common number
– Example: 2:20 = 10:100 = 20%
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Decimals Converted to Percent
• Move decimal point two places to right and write percent
sign
– Example: 0.06 = 6%
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Ratio and Proportion
• Fraction shows part (numerator) relates to whole
(denominator)
• Ratio relationship between two numbers
• Ratios written as two numbers separated by a colon
– Example 2:10
• Proportion relationship between two ratios or two
fractions
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Solving Ratio and Proportion
• Cross multiply
• Clear x
• Reduce
– Example:
7/70 = 11/x
7x = 70 x 11
70 × 11 / 7
x = 110
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Ratio and Proportion in Dosage
• Order: 1.5 mg of medication
• Supply: 0.75 mg per 4 mL
1.5/0.75 = x/4
6 = 0.75 x
x = 6/0.75
x=8
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Question
A client is to receive 150 mg of a medication. The
medication is supplied in 75 mg per 2 mL. Use ratio and
proportion formula to solve the problem. How many mL
should be administered?
A. 1½
B. 2
C. 3.5
D. 4
Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins
Answer
D. 4
• Order: 150 mg of medication
• Supply: 75 mg per 2 mL
150/75 = x/2
300 = 75x
x = 300/75
x=4
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