P T Exam (#3-Chapter9) Basic Pharmacy Math

Rx: Doxycylcine Hyclate 100 mg/5mL _______mL Directions: 10 mL stat then 5 mL po bid x 20d How many milliliters are needed to fill this prescription

210 mL

Which concentration is less concentrated 10 mg / 100mL 50mg / 100mL

10 mg / 100 ml

1000 grams = ?

1000 grams = 1 kilogram = 1kg

There are 150 coins on the floor and you picked up 75 of them. What is the fraction of the total coins you now have in your possession.

75/150= Divide the top and bottom by the same number =75 into 75 =1 Now dividing the bottom (denominator) by 75 as well = 150/75 =2 The answer in a fraction is 1/2 The answer in decimal form = 0.50

If a syringe contains 20 mg of medication in each 10 mL of solution, how many milligrams are administered to the patient when 3 mL is injected? Here you are only going to inject 3mL of a total of 10 mL. i.e. 3 tenths, or 3/10. If you are injecting 3/10ths of the total of mL then the answer is 3 tenths x 20 mg = 3/10 x 20= 10 into 20 is 2 and 2 time 3 is 6

Answer is 6 mg

You have a bottle of prednisone 5mg/5mL. How may milliliters are needed to give this patient an exact 12 mg dose?

Each bottle of prednisone contains 5mg/5 mL which is equal to 1 mg/1 mL. If you want the patient to receive a 12 mg dose, then you need 12 mL of prednisone

Proper Fraction

Has a numerator smaller than the denominator

Arabic number: 10, 20, 30, 40, 50, 100, 500, 1000

Roman Numeral x,xx,xxx,xl,l,c,d,M

Ratio and Proportion Method Term 1 / Term 2 = Term 3 / Term 4 Term 1 x Term 4 = Term 2 x Term 3 Example: 50 g / 100 ml = x g / 10 ml

Term 1 = 50 g Term 4 = 10 ml Term 2 = x mg Term 3 = 100 ml xg (100 ml) = 50g x 10ml Xg = (50g)(10 ml) divided by 100 Xg = 500 / 100= 5grams

How many capsules need to be dispensed for the following prescription order: amoxicillin 250 mg, qty: XXVI

XX=20 VI= 6 Answer = 26

0.5 0.50 0.500 What is the fractional value of each?

0.5. = 5 tenths. =1/2 0.50 = 50 hundredths = 1/2 0.500. = 500 one thousandths =1/2 The numbers all have the same fractional value of 1/2

Decimals: half of a dollar= 50 cents 1 dollar cut into half = 1/2= 50 cents. State the decimal equivalent

0.50

Starting with the Arabic number 1 Create the equivalent number in Roman Numerals and continue through 9

1 -i 2-ii 3-iii 4-iv 5-v 6-vi 7-vii. 8-viii 9-ix

Convert the improper fraction to a mixed fraction 8/5= 8 divided by 5 5 into 8 = 1 plus a remainder of 3

1 and 3/8 1 3/8

Determine the lowest common denominator 1/2 2/4 4/8 5/10

1/2 1/2 1/2 1/2

1 mg / 100mL and 10 mg /100mL . Which one has a greater concentration

10 mg / 100mL

How much drug is needed to make a 1:100 120 mL solution?

12 g

Change 1 3/4 to an improper fraction

1= 4/4 3/4= 3/4 Adding the two = 7/4 If a pie is cut into 4 pieces and you have 4. Pieces then you have 1 full pie. If you have a second pie and it is also cut into 4 pieces but you only have 3 pieces you have 3/4 of the second pie. If you put all the pieces of both pies together you have: 4/4 + 3/4= 7/4 of the pies.

$1.00/ 5= ?

20 cents = 0.20

$1.00/4= ?

25 cents =0.25

Round 4.23891 to the nearest hundredth.

4.23891 is to the nearest 10 thousandth NOT hundredths 4.239 is to the nearest 1 thousandth NOT hundredths 4.24 is to the hundredths 4.23 is to the hundredths also, but 4.239 rounds to 4.24 as the third digit "9" is larger than 5 therefore the it increases the value of the next number to 4 NOT 3. Answer is 4.24

What is the lowest common denominator 4/8, 1/16 3/4

4/8=2(4/8)=8/16 1/16=1/16 3/4=4 (3/4)=12/16 16 is the lowest but happens to be the highest of the fractions shown because 1/16 cannot be broken down further.

A clinical study of a new drug showed that the drug was effective in 586 of he 803 patients enrolled in the study. What is the DECIMAL expression of the patients who benefited from the drug.

586 / 803 is the fractional expression but is not the decimal 73% is an expression in percentage and not decimal 0.73 is the only expression in decimal form. Answer = 0.73

Drug X has a concentration of 200 mg/5mL 360 mL. What is the total amount of active drug in this bottle. Stated mathematically: 200 mg/ 5 mL = x mg / 360 mL 40 mg / 1mL = x mg / 360 (40 mg / 1 mL) x 360 mL = x mg 40 x 360 = 14,400 mg = x

Answer = 14,400 mg

Drug X has a concentration of 125 mg/5mL. How many milliliters are needed t give a 400 mg dose? xmL is to 400mg as 5 mL is to 125mg xmL / 400mg = 5mL / 125 mg x mL = (5 / 125) x 400 = 1/25 x 400 = 16Answer

Answer = 16 mL

If a potassium chloride solution contains 20 mEq in each 15 mL, which volume of solution provides 35 mEq for the patient? The answer is achieved by stating the proportion: 20 mEq is to 15 mL as 35 mEq is to x mL.or 20 / 15 = 35 / x Cross multiplying 20 x "x" = 35 x 15 20 x = 525 x = 525/20

Answer = 26.25

You have a bottle of Ceclor with the concentration of 125 mg/ 5mL. How many milliliters are needed to give this patient an exact 200mg dose. If 125 mg of concentration contains 5 mL, then each mg contains 125/5 = 25 or 25 mg/ 1mL. Then you want the patient to receive 200 mg dose...25 goes into 200 = 8 times

Answer = 8 mL

Which of the following ratio strength solutions is the most concentrated A. 1:200 , B. 1:1,000, C 1:5,000, D. 1:10,000

Answer = A, 1:200

Round 0.4912 to the nearest tenth

Answer is 0.5

Ferrous sulfate elixir contains 220 mg of ferrous sulfate per 5 mL. How much ferrous sulfate is in 473 mL of elixir? If there is 220 mg in each 5mL, then we need to know how many 5mL are in the total elixir. 473 / 5 = 94.6 Therefore we simply multiply 220 x 94.6

Answer is 20,812 mg

How much active drug is in the container? Rx; Azithromycin 500 mg/mL 200 mL Directions: 10mL stat then 5mL po bid x 20d

Answer: 20,000 mg

How many milliliters should you give for the following directions: 5 mL po tid x 10d?

Answer: 5 mL orally 3 times a day for 10 days 5 x 3 x 10 = 150 mL

Rx: Azithromycin 500 mg/5mL 200mL What does 200 mL mean in this problem:

Answer: volume of medication is on hand

Which of the following is an incorrect way to state a proportion

Answers to choose from are: A. a is to b as c is to d B. a:b = c:d C. a/b = c/d D. ab = cd Answer is D. That is NOT a correct way to state a proportion

Mixed fractions

Both whole numbers and fractions: 1 1/2 86 3/8 46 1/9.

What is the Arabic number for the following Roman numeral: CXXXIV

C= 100 XXX=30 IV=4 Therefore CXXXIV=134

Solvent

Component of a solution present in a greater amount. (What is dissolving something else)

Solute

Component of a solution present in the lesser amount. (What is being dissolved)

Concentration is the amount of a solute (active drug) in a solution per standard amount of solvent (solution)

Define Concentration

What is the lowest term of 21/51?

Divide the top and bottom by 3, as 3/3=1 therefore the division does not change the results. 21/2=7 51/3=17 Answer = 7/17

Convert 5/8 to a decimal.

Execute the function, which is 5 divided by 8. 8 into five is less than 1 therefore the first part of the answer is 0. the next digit is achieved by dividing 8 into 50 which results into a 6 with a remainder of 2. Next digit is achieved by dividing 8 into 20 which is "2" with a remainder of 4. The final digit of the answer is achieved by dividing 40 by 8 which is 5. Answer = 0.625

Which fraction is the largest: 1/12, 3/32, 12/72, 5/20

Find the common denominator: It isn't 12, it isn't 32, it isn't 72, and it isn't 20. Therefore a low common denominator has to be a whole number, so lets try a big number like 20 x 72, which the denominator of the last two fractions. Here you get 1440: Therefore; 1/12 = 20/1440 (1440/12 = 20) 3/32 = (3)45/1440= 135/1440 12/72= 240/1440 5/20 = 360/1440 Answer = 5/20 = 360/1440

If a concentration of drug is 400 mg/5ml, how many milligrams will a 12 ml dose give?

Have = Want (400 mg) / 5 mL = x g/ 12 mL Cross multiply Xg = (400 mg) x 12 mL = x mg (5 mL) Xg = (400 X 12 ) / 5 = 4800 / 5 XG = 960 mg

Expressing your age as 21 years can be stated as a fraction by the following: 21/1 = 21 You can also state your age as 42/2 as you have multiplied the top and bottom by 2/2 which is equivalent to one.

If someone stated their age as 63/3 years. How old are they in a whole number? Answer = 21 years

1 milligram = ?

Is 1 thousandth of a gram = 0.001 =1 mg

1 micro gram

Is one millionth of a gram

Reduce 36/27 to lowest terms

It is apparent that the top (numerator) and the denominator can easily be divided by 3. Therefore: 36/27 = 12/9. The result is still the same but it is more apparent that it is larger than 1. Dividing 12/9 is 1 with a remainder of 3. The answer is 1 3/9 = 1 1/3

What is the Arabic number for the following Roman numeral LXI

L= 50 X=10 I= 1 Answer is 61

Improper fraction

Numerator is equal to or larger than the denominator: (I.e. It has a value equal to or greater than 1)

Ferrous sulfate (FESO4) is an iron supplement which comes in a liquid suspension with a concentration of 220 mg/5mL. You are asked to give a dose of 100mg. How many mL are needed to give this exact dose?

Set up the proportion 220 mg/ 5mL = 100mg/xmL Cross Multiply (220 mg)(xmL)= (100mg)(5mL) divide each side of the equation by 220 mg (220 mg)(xmL)/220 mg = (100mg)(5mL)/220 mg the 220mg from the left side of the equation in the numerator cancels the 220 mg in the denominator leaving xmL= (100mg)(5mL)/220 mg = 100 (5mL)/220 xmL = 500 mL/220 = 500/220 mL = 227 mL x = 227

Erythromycin ethylsuccinate (EES) comes in a liquid suspension with a concertration of 333mg/5mL. If you are asked to give an exact dose of 200 mg, how many milliliters are needed?

Set up the proportion: 333mg/5mL = 200mg/xmL Cross multiply (333 mg)(xmL) = (200mg)(5mL) xmL = (200mg)(5mL)/333mg = 1000 mL/333 The mg from the numerator cancel the mg in the denominator and you are left with mL. 1000 mL/333 = 3 mL

A mixture consisting of a solute and a solvent

Solution

An oral antibiotic suspension makes 150 mL after reconstitution. Each dose is 5mL. Each dose makes up what fractional part of the total?

The answer is 5mL/150mL or reduced is found by dividing the top and bottom by 5. Result is 1 mL/30 mL = 1/30

If a cough syrup contains 4 mg of chlorpheniramine in each 5 mL, how much chlorpheniramine (in milligrams ) is contained in 240 mL of syrup?

The answer is achieved by first dividing 240 mL by 5 to see how many times you will need to multiply it by 4. 240 / 5 = 48 times 48 x 4 = 192

Convert 0.16 into a fraction

The answer is achieved by stating the number as a fraction: here it is 16 / 100 ths. Then simply reducing that to the lowest fraction. divide the top a bottom by 4 and the answer is 4 / 25 ths Answer = 4/25 ths

Denominator

The bottom number of a stated fraction

Which fraction is SMALLEST: 1/16, 1/8, 2/16, 3/32

The common denominator is 32. 1/16 = 2/32 1/8 = 4/32 2/16 = 4/32 3/32 = 3/32 Answer = 1/16 = 2/32 if YOU cut a pie into 32 pieces the person getting 2 pieces gets the least pie. If you have a pie

A pharmacist had 4 oz of dextromethorphan HCl syrup in stock. She used 12/4 oz. to fill a prescription order. How much of the origin syrup did she have left.

The key is "LEFT". She started with 4 oz. She used 12/4 oz, which is 3 oz as 12/4 is equivalent to 3 oz. If she started with 4 and used 3, she has 1 oz remaining Answer; 1 oz

How many tabs will be used for one dose of a medication with the following directions: Directions: iv tabs po bid x 10d

The key to this question is "ONE DOSE" = 4

Numerator

The top number of a stated fraction

Write 3/20 as a decimal

To convert a fraction into decimal form you simply execute the division implied: 3 divided by 20= 0.15

3/8=x/40

To make both sides of the equation equal you must convert 3/8 into a fraction with 40 as the denominator, that requires multipling 3/8 x 5/5. You can multiply by 5/5 because 5/5 equals 1 therefore you have not changed the value. You are simply making both denominators equal and what ever you do to the denominator you must do to the numerator 3 x 5 = 15 8 x 5 =40 3/8 = 15/40 X= 15.

Express 25 thousandths in decimal form

You have 25 parts of a 1000 so the number is less than 1. 0.25 = 25 one hundredths 0.025= 25 one thousandths 0.0025= 25 10 thousandths 0.00025=25 100 thousandths Answer = is 0.025

Example: amoxicillin 250 mg/5mL Directions: 100 mg po qid x 10 d What is the total volume you would give that will last for ten days?

see page 144 in text for the explanation 250mg/5mL = 100mg/xmL xmL = (100 mg)(5mL/250mg = 2 mL Directions call for 100mg by mouth four times a day for ten days.. Understand that 100 mg is the same as 2mL Directions: (2mL)(4)(10) = 80 mL Answer is 80 mL

If 1/2 = x/28 What is x?

to solve for x both sides of the equation have to be equal. therefore what the question is asking is what is 1/2 of 28: that answer is 14. Therefore: 1/2= 14/28