Brown: Drug Calculations, 9th Edition

Chapter 01: General Mathematics

Test Bank

SHORT ANSWER

Directions: Solve the following problems.

1.	Add and reduce to lowest terms: 

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2.	Add: 

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3.	Multiply and reduce to lowest terms: 

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4.	Multiply and reduce to lowest terms: 

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5.	Divide and reduce to lowest terms: 

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6.	Divide and reduce to lowest terms: 

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7.	Which is greater,  or ?

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8.	Which is smaller,  or ?

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9.	Change to a decimal: 

ANS:	
0.125

10.	Change to a fraction: 0.008

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11.	Which is smaller, 0.125 or 0.25?

ANS:	
0.125

12.	Which is greater, 0.25 or 0.05?

ANS:	
0.25

13.	Round to the nearest tenth: 3.124

ANS:	
3.1

14.	Round to the nearest hundredth: 0.42877

ANS:	
0.43

15.	Round to the nearest whole number: 5.742

ANS:	
6

16.	Round to the nearest ten thousandth: 0.576391

ANS:	
0.5764

17.	Divide 7.35 by 0.25.

ANS:	
29.4

18.	Multiply 4.25 by 0.2.

ANS:	
0.85

19.	Find 5% of 75.

ANS:	
0.05 ´ 75 = 3.75 (10% of 75 is 7.5; 5% would be one half of that)

20.	Find 55% of 120.

ANS:	
0.55 ´ 120 = 66 (a little more than one half of 120)

21.	Write  as a percentage and as a decimal.

ANS:	
10%, 0.1

22.	Write 0.05 as a fraction and as a percentage.

ANS:	
 (reduce to ), 5%

23.	Write 85% as a fraction and as a decimal.

ANS:	
 (reduce to ), 0.85

24.	Change 1 to an improper fraction.

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25.	Change  to a whole or mixed number.

ANS:	
6

26.	Which is larger, tens or tenths?

ANS:	
Tens

27.	Write three hundred seventy seven thousandths as a decimal.

ANS:	
0.377

28.	Make 150 of a 50% strength solution. How many mL of the solute will be needed?

ANS:	
75 mL

Know               Want to Know
1 mL : 2 mL :: x mL : 150 mL
2x = 1 ´ 150 = 150
x = 75 mL

Proof:  1 ´ 150 = 150
2 ´ 75 = 150

29.	You need to make a 75% Betadine solution for a total of 250 mL. How much Betadine will you need?

ANS:	
187.5 mL

Know                    Want to Know
75 mL : 100 mL :: x mL : 250 mL
3 : 4 :: x : 250
4x = 3 ´ 250 = 750
4x = 750
x = 187.5 mL of Betadine. Add 62.50 mL of solution for a total of 250 mL.

Proof:  3 ´ 250 = 750
4 ´ 187.5 = 750

30.	You need to make a 10% solution of hydrogen peroxide for a total of 500 mL. You are using normal saline (NS) as the solvent. How many mL of hydrogen peroxide will you need?

ANS:	
50 mL

Know                    Want to Know
10 mL : 100 mL :: x mL : 500 mL
1 : 10 :: x mL : 500 mL
10x = 1 ´ 500 = 500
x = 50 mL of hydrogen peroxide. Add 450 mL of normal saline to make 500 mL of a 10% solution.

Proof:  50 ´ 10 = 500
1 ´ 500 = 500

CALCULATING SOLUTIONS
Health care professionals need to know how to prepare solutions from stock solutions. A solution consists of a solute (concentrate) plus a solvent (liquid). A solute can be either liquid or a powder, and a solvent can be either water or normal saline. The resulting reconstituted solution will be a weaker strength than the original. The strength of the solution is represented by a ratio of solute to solvent. Many times health care workers have to prepare solutions for irrigations, tube feedings, infant formulas or perhaps cleaning solutions. This worksheet will give the student practice making up different types and strengths of solutions.

Prepare a 100 mL of a  strength solution of hydrogen peroxide (solute) using normal saline (solvent). This means one part hydrogen peroxide (solute) to three parts of normal saline (solvent).

EXAMPLE:
Know     Want to Know
1  :  3  ::  x  :  100
3x = 1 ´ 100 = 100 
3x = 33.33 mL of the solute hydrogen peroxide needed

Proof:  1 ´ 100 = 100
3 ´33.33 = 99.9

  100    mL solution wanted
–  33.3 mL hydrogen peroxide
    66.7 mL of normal saline

66.7 mL of normal saline added to the 33.33 mL of hydrogen peroxide yields 100 mL of a  strength hydrogen peroxide solution for irrigation.

31.	Prepare a 70% Betadine solution for traction pin care. Cleanse area twice daily with 10 mL of a 70% Betadine solution with NS.
a.	How many mL of total solution will you prepare?
b.	How many mL of Betadine will be needed?
c.	How many mL of NS will you add?

ANS:	
a. 10 ´ 2 times per day = 20 mL of 70% Betadine solution is needed.

b. 
Know        Want to Know
0.70 : 1 :: x : 20 mL
x = 0.70 ´ 20 = 14.00
x = 14 mL of 70% Betadine needed

Proof:  0.70 ´ 20 = 14.00
1 ´ 14 = 14

c. 
  20 mL needed
–14 mL Betadine
    6 mL normal saline added to make 20 mL of a 70% Betadine solution

32.	Prepare 100 mL of a 10% strength solution of bleach for cleaning.
a.	How many mL of bleach will be needed?
b.	How many mL of solution will be needed?

ANS:	
a. 
Know   Want to know
1 : 10 :: x : 100
10X = 100
x = 10 mL of bleach needed

Proof:  1 ´ 100 = 100
10 ´ 10 = 100

b. 
  100  mL total needed
–  10  mL bleach needed
     90 mL of water added to make 100 mL of bleach solution

33.	Make a  strength solution of hydrogen peroxide. Irrigate the wound with 100 mL of solution four times a day.
a.	How many total mL will be needed?
b.	How many mL of hydrogen peroxide will be needed?
c.	How many mL of sterile NS will be needed?

ANS:	
a. 100 mL ´ 4 times per day = 400 mL of solution needed

b. 
Know   Want to Know
1 : 4 :: x : 400
4x = 400
x = 100 mL of hydrogen peroxide needed

Proof: 1 ´ 400 = 400
          4 ´ 100 = 400

c. 
  400 mL total needed
–100 mL hydrogen peroxide
  300 mL of sterile NS added to make 400 mL of  strength solution

34.	Make 4 cups of a 20% vinegar solution for household cleaning.
a.	How many total mL will you prepare?
b.	How many mL of vinegar will be needed?
c.	How many mL of water will be needed?

ANS:	
a. 

Know                  Want to Know
1 cup : 240 mL :: 4 cups : x mL
x = 240 ´ 4 = 960
x = 960 mL total solution needed

Proof:  240 ´ 4 = 960
1 ´ 960 = 960

b. 
Know       Want to Know
20 : 100 :: x : 960
5x = 960
x = 192 mL of vinegar needed

Proof:  5 ´ 192 = 960
1 ´ 960 = 960

c. 
   960 mL total solution needed
 –192 mL vinegar needed
   768 mL of water added to make a 15% solution

35.	Make a 60% strength baking soda solution to clean your stainless steel sink. The directions read: 200 mL of a 60% solution will clean five stainless steel appliances.
a.	How many mL of baking soda will you need?
b.	How many mL of water will you need?

ANS:	
a. 
Know        Want to Know
0.60 : 1 :: x : 200
x = 0.60 ´ 200 = 120
x = 120 mL of baking soda needed

Proof:  0.60 ´ 200 = 120
120 ´ 1 = 120

b. 
  200 mL total solution needed
–120 mL baking soda
    80 mL of water needed to make a 60% solution

36.	Make a  strength drink of Ensure from a 12 oz. can.
a.	How many mL are in 12 oz?
b.	How many mL of Ensure will be needed?
c.	How many mL of water will be needed?

ANS:	
a. 
Know               Want to Know
1 oz : 30 mL :: 12 oz : x mL
x = 30 ´ 12 = 360 mL total needed

Proof:  30 ´ 12 = 360
1 ´ 360 = 360

b. 
Know   Want to Know
1 : 3 :: x : 360
3x = 360
x = 120 mL of Ensure needed

Proof:  1 ´ 360 = 360
3 ´ 120 = 360

c. 
  360 mL total needed
–120 mL Ensure
  240 mL water needed to make a  strength drink 

37.	Make a  strength drink of Sustacal from a 10 oz can.
a.	How many mL are in 10 oz?
b.	How many mL of Sustacal will be needed?
c.	How many mL of water will be needed?

ANS:	
a. 
Know                 Want to Know
10 oz : 30 mL :: 10 oz : x mL
x = 30 ´ 10 = 300
x = 300 mL total needed

Proof:  30 ´ 10 = 300
1 ´ 300 = 300

b. 
Know   Want to Know
3 : 4 :: x : 300
4x = 3 ´ 300 = 900
x = 225 mL

Proof:  3 ´ 300 = 900
4 ´ 225 = 900

c. 
  300 mL total needed
–225 mL Sustacal
    75 mL water added to make a  strength drink

38.	Make a  strength drink of 360 mL of Isomil.
a.	How many mL of Isomil will be needed?
b.	How many mL of water will be added?

ANS:	
a. 
Know   Want to Know
1 : 2 :: x : 360
2x = 360
x = 180 mL of Isomil needed

Proof:  1 ´ 360 = 360
2 ´ 180 = 360

b. 
  360 mL total needed
–180 mL of Isomil
180 mL of water added to Isomil to make a  strength drink

39.	Make a  strength drink from a 12 oz. can of Ensure.
a.	How many total mL of ensure is 12 oz?
b.	How many mL of Ensure will be needed?
c.	How many mL of water will be added?

ANS:	
a. 
Know                Want to Know
1 oz : 30 mL :: 12 oz : x mL
x = 30 ´ 12 = 360 mL
x = 360 mL of Ensure

Proof:  30 ´ 12 = 360
1 ´ 360 = 360

b. 
Know   Want to Know
2 : 3 :: x : 360 
3x = 2 ´ 360 = 720
x = 240 mL of Ensure needed

Proof:  2 ´ 360 = 720
3 ´ 240 = 720

c. 
  360 mL total needed
–240 mL of Ensure
  120 mL of water added to make a  strength drink

40.	Prepare 400 mL of a  strength drink of Sustacal for each nasogastric feeding three times daily.
a.	How many total mL will be needed?
b.	How many total mL of Sustacal will be needed for the 3 feedings?
c.	How many mL of water will be needed?

ANS:	
a. 400 mL ´ 3 times daily = 1200 mL

b. 
Know   Want to Know
3 : 4 :: x : 1200
4x = 3 ´ 1200 = 3600
x = 900 mL of Sustacal needed

Proof:  3 ´ 1200 = 3600
4 ´ 900 = 3600

c. 
  1200 mL total need for 3 feedings
–  900 mL of Sustacal needed
    300 mL of water added to make a  strength drink

Directions: Change the following fractions to ratios.

41.	

ANS:	
3:4

42.	

ANS:	
1:2

43.	

ANS:	
2:3

44.	

ANS:	
1:4

45.	

ANS:	
1:2

Directions: Change the following ratios to fractions and reduce to the lowest terms.

46.	5:25

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47.	5:100

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48.	3:9

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49.	4:12

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50.	50:200

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Directions: Change the following percentages to fractions and reduce to the lowest terms.

51.	5%

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		52.	10%

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		53.	4.5%

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		54.	7.6%

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		55.	20%

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Directions: Change the following percentages to ratios and reduce to lowest terms.

56.	8%

ANS:	
8:100 = 2:25

57.	10%

ANS:	
10:100 = 1:10

58.	0.9%

ANS:	
9:1000

59.	0.45%

ANS:	
45:10,000 = 9:2000

60.	50%

ANS:	
50:100 = 1:2

Directions: Change the following ratios to lowest term fractions and cross multiply.

61.	1 : 4 :: 16 : x

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62.	1 : 3 :: 80 : x

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63.	1 : 3 :: 60: x

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64.	25 : 75 :: 10 : x

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65.	80 : 20 :: 120 : x

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