Chapter 01: General Mathematics
Tritak: Brown and Mulholland’s Drug Calculations: Ratio and Proportion Problems for Clinical Practice, 11th Edition

ESSAY

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, ?

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	8.	Which is smaller, 

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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.

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

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	24.	Change 1 to an improper fraction.

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	25.	Change  to a whole or mixed number.

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	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 mL 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 mL
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 NS to make 500 mL of a 10% solution.

Proof: 50 ´ 10 = 500
          1 ´ 500 = 500

Directions:
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 NS. 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 NS (solvent). This means one part hydrogen peroxide (solute) to three parts of NS (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
33.33 mL hydrogen peroxide
66.67 mL of NS

66.67 mL of NS 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 should be prepared.

b. 
Know          Want to Know
0.70 : 1 = x : 20 mL
x = 0.70 ´ 20 = 140
x = 14 mL of Betadine needed

Proof: 0.70 ´ 20 = 14.00
               1 ´ 14 = 14

c. 
20 mL needed
14 mL Betadine
6 mL NS 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 water will be needed?

ANS:	
a. 
Know        Want to Know
1 : 10 = x : 100
10x = 100
x = 10 mL of bleach need

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 4 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 per oxide 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 hydrogen peroxide
768 mL of water added a make a 20% 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 added a 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 in 12 oz.

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 of 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 in 10 oz

Proof: 30 ´ 10 = 300
          1 ´ 300 = 300

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

Proof: 3 ´ 300 = 900
          4 ´ 225 = 900

c. 
300 mL total needed
225 mL Sustacal
75 mL of water needed 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 in 12 oz

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 3 times daily.
a. How many total mL will be needed?
b. How many total mL of Sustacal will be needed for the three 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: 2 ´ 1200 = 3600
            4 ´ 900 = 3600

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

Directions: Change the following fractions to ratios in lowest terms.

	41.	

ANS:	
3 : 4

	42.	

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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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