Transcript Chapter 6 Notes

Math Basics
for the Health Care Professional
FOURTH EDITION
UNIT
6
Combined
Applications
Copyright © 2014, 2009 by Pearson Education, Inc.
All Rights Reserved
Student Learning Outcomes
1. Convert among fractions, decimal
numbers, ratios, and percents
2. Learn the relationships among
fractions, decimal numbers, ratios, and
percents
3. Use ratio to convert between units of
measure
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Overview
• Bringing together and converting
among:




Fractions
Decimals
Ratios
Percents
1
4
2.485 3:4 59%
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Conversion: Quick Review
• Basics of conversion







Fraction to decimal
Decimal to fraction
Proper fraction to ratio
Ratio to proper fraction
Mixed number to ratio
Ratio to mixed number
Decimal to percent
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Conversion: Quick Review
• Basics of conversion
 Percent to decimal
 Fraction to percent
 Decimal to ratio
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Quick Review
• Fraction to decimal
 Method: Divide denominator into
numerator.
 Example: ¾ = 3.0 ÷ 4 = 0.75
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Quick Review
• Decimal to fraction
 Method: Count the decimal places;
place the number over 1 (with enough
zeros to match the same number of
decimal places).
 Example: 0.02 (2 places) 
2/100 (add 2 zeros)  1/50
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Quick Review: Continued
• Proper fraction to ratio
 Method: Simply change the symbol.
 Example: 1/8  1 : 8
• Ratio to proper fraction
 Method: Change symbol; first number
is numerator; second number is
denominator; reduce.
 Example: 4 : 31  4/31
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Quick Review: Continued
• Mixed number to ratio
 Method: If fraction is mixed number,
mixed number must first be made into
an improper fraction before setting up
the ratio. Keep the original
denominator.
 Example:
3
7
1
4


 1 4 3 
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
4
 7:4
Quick Review: Continued
• Ratio to mixed number
 Method: Convert ratio to fraction. If it
becomes improper fraction, make it a
mixed number.
11
3
 Example:
11: 4 
4
 11  4  2
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
4
Quick Review: Continued
• Decimal to percent
 Method: Move decimal two places to
right. Add % sign.
 Example: 0.25  25.%  25%
 Example: 1.456  145.6%
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Quick Review: Continued
• Percent to decimal
 Method: Move decimal two places to left
(add zeros if needed).
 Example: 90%  90.%  0.9
 Example: 5%  5.%  0.05
 Example: 57½ %  57.½ % 
0.57½  0.575
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Quick Review: Continued
• Fraction to percent
 Method: Convert fraction to decimal,
and then to percent.
 Example: ¾  0.75  75/100 
75%
• Decimal to ratio
 Method: Convert decimal to fraction,
and then change percent sign to colon.
 Example: 0.75  75/100  75 :
100  3 : 4
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Converting Number Systems
Fraction
Decimal
Ratio
Percent
Ratio
Percent
0.05
Fraction
Decimal
0.05
5%
Fraction
Decimal
Ratio
Percent
5/100  1/20
0.05
Fraction
Decimal
Ratio
Percent
1/20
0.05
1 : 20
5%
5%
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Converting: Suggested Order
• Suggested order of operations
 Carefully select the order of
conversions.
 Minimize extra work!
IF STARTING WITH:
percent
ratio
MOVE FROM:
decimal → fraction → ratio
fraction → decimal → percent
fraction
ratio → decimal → percent
decimal
percent → fraction → ratio
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Some Handy Helpers
• One-half
1
 ½  0.5  50%
• One-quarter
 ¼  0.25  25%
• Three-quarters
 ¾  0.75  75%
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
1
4
2
3
4
Some Handy Helpers
• One-third
 1/3  0.33 1/3 
33 1/3 %
• Two-thirds
 2/3  0.66 2/3 
66 2/3 %
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
1
3
2
3
Converting: Another Example
Fraction
Decimal
Ratio
Percent
7 3/5
7 x 5 + 3 = 38 
38/5
7 3/5
38 : 5
7 3/5
7
3 ÷5 = 0.6
7 + 0.6 = 7.6
38 : 5
7.6
7.6  760. 
7 3/5
7.6
38 : 5
760%
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Systems of Measurement
• 3 systems of measurement
 Household (or standard) measurement
(e.g., tsp, cup, etc.)
 Metric measurement
 Apothecary measurement
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Systems of Measurement
To measure:
Units of Measure
Height
Feet, inches, meters, centimeters
Weight
Pounds, ounces, kilograms, grams
Liquid volume
Gallons, quarts, pints, cups, tablespoons, teaspoons
Medication
Tablespoons, teaspoons, tablets, ounces, milliliters,
dosages
milligrams
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Standard Abbreviations
ft
foot
t
yd
yard
qt
quart
oz
ounce
pt
pint
gtt
drop
T
or tbsp tablespoon
or tsp
teaspoon
lb
pound
gal
gallon
c
cup
in
inch
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Standard Units of Measure
Note: drams and grains are slowly being phased out; metric replacements are being used.
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister
Combined Applications
• Sometimes two conversions are
necessary.
 Problem: convert ounces to teaspoons
oz  mL  tsp


 Step 1: Convert oz to mL.
1 oz.
30 mL

8 oz.
? mL
 240mL
 Step 2: Convert mL to teaspoons.
1t
5 mL

? t
240 mL
 48 teaspoons
Math Basics for the Health Care Professional, Fourth Edition
Michele Benjamin Lesmeister