Chapter 2 Flashcards
Review of Basic Mathematical Skills
What is a whole number?
A whole number is a number without fractions or decimals, consisting of one or more digits (e.g., 0, 1, 2, 10, 100).
What are the four basic operations you can perform with whole numbers?
Addition, subtraction, multiplication, and division.
What is a fraction?
A fraction is a part of a whole, consisting of a numerator (top number) and a denominator (bottom number).
What is the difference between a proper fraction and an improper fraction?
A proper fraction has a numerator less than the denominator. An improper fraction has a numerator equal to or greater than the denominator.
What is a mixed number?
A mixed number contains both a whole number and a fraction (e.g., 2 1/3).
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder is placed over the original denominator.
What is a decimal?
A decimal is a fraction where the denominator is a power of 10, represented with a decimal point (e.g., 0.25).
How do you convert a fraction to a decimal?
Divide the numerator by the denominator.
How do you round decimals to the nearest tenth?
Look at the hundredths place. If it is 5 or greater, round up. If it is less than 5, leave the tenths place as is.
What is a percentage?
A percentage represents a part of 100 (e.g., 50% means 50 out of 100).
How do you convert a percentage to a decimal?
Divide the percentage by 100 (e.g., 25% becomes 0.25).
How do you convert a decimal to a percentage?
Multiply the decimal by 100 (e.g., 0.75 becomes 75%).
What is a ratio?
A ratio is a comparison between two numbers, often expressed as “a to b” or a
What is a proportion?
A proportion is an equation that shows two ratios are equal (e.g., 1/2 = 3/6).
How do you solve a proportion?
Cross-multiply and then divide to find the unknown value.
Why do you need a common denominator when adding or subtracting fractions?
To make the fractions comparable, their denominators must be the same.
How do you simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor (GCD).
How do you add or subtract decimals?
Align the decimal points and then perform the operation.
How do you multiply fractions?
Multiply the numerators together and the denominators together. Simplify if necessary.
How do you divide fractions?
Invert the second fraction (take the reciprocal) and multiply.
How do you multiply decimals?
Multiply the numbers as if they were whole numbers, then count and place the decimal in the product based on the total number of decimal places in both numbers.
How do you divide decimals?
Move the decimal point in the divisor to the right to make it a whole number. Move the decimal in
What are leading and trailing zeros?
A leading zero is placed before a decimal for numbers less than one (e.g., 0.5). Trailing zeros follow the decimal and are not needed unless they indicate precision (e.g., 1.50).
Why is estimation important in pharmacy math?
Estimation helps ensure that the calculated answer is reasonable, which is critical to avoid medication dosing errors.
How do you convert a percentage to a fraction?
Write the percentage as a fraction over 100 and simplify (e.g., 50% becomes 50/100 = 1/2).
How do you calculate a dose using ratio and proportion?
Set up a proportion with the known dose and amount and the unknown dose. Solve by cross-multiplying and dividing.
What is 154+376+1,063+25 154+376+1,063+25?
The sum is 1,618.
What is
256÷16?
The quotient is 16.
Add 1/3 + 2/3
The sum is 1
Simplify 25/100
1/4
Subtract 7/10 - 3/5. First find the common denominator.
1/10
Convert the improper fraction 43/8 to a mixed number
5 3/8
Convert 7/8 to a decimal
7/8 = 0.875
25.6 + 35.67
61.27
12.56 x 65.031
816.59
Round 75.0023 to the nearest hundredth
75.00
655.08 / 1.2
545.90
Convert 44% to a fraction
44/100, simplifies to 11/25
Convert 33% to a decimal
0.33
Solve proportion: 330/x = 15/5
x = 110
Express the ratio 5 mg to 25 ml and reduce
The reduced ratio is 1:5
What is 85% of 200?
85% x 200 = 170
Estimate 18.32 × 3.7 by rounding.
Round to 18 × 4 = 72 (estimate)
A patient is ordered 250 mg of a medication, and the bottle contains 125 mg per 5 mL. How many mL should the patient be given?
250÷125=2. So, the patient should take 5 × 2 = 10
Round 9.64 to the nearest whole number.
The rounded number is 10.
A pharmacy offers a 10% discount on a $25 prescription. How much will a senior save?
The discount is 10%×25=2.50 10%×25=2.50. The senior saves $2.50.
Solve the complex fraction. (1/2) / (3/4)
Invert the second fraction and multiply. 1/2 x 4/3 = 4/6 = (2/3 as simplified)
Simplify the ratio
6:9.
The simplified ratio is
2:3.
Convert 0.4% to a decimal.
0.004.
Convert 0.75 to a percent.
75%.
If a prescription calls for 15 mL of water for a 20-mL vial, how many mL of water are needed for a 50-mL vial?
Set up a proportion: 15/20 = x/50, solve for x, x = 37.5 mL
A patient is prescribed 16 oz of medication and is instructed to take 1/16 of the bottle each night. How many ounces should the patient take per night?
The patient should take 1 oz per night.
What is a complex fraction?
A fraction where the numerator, denominator, or both are fractions themselves.
Solve (1/2) / (3/4)
Invert the denominator and multiply. 1/2 x 4/3 = 4/6 = 2/3
Simplify (5/8) / (2/3).
(5/8) x (3/2) = 15/16
A patient needs 250 mg of medication. The medication comes in a concentration of 125 mg per 5 mL. How many mL are required?
(125 mg)/5 ml = 250 mg / x ml, solve for x: x=10 ml
If a prescription costs $50, and a senior discount of 15% is applied, what is the total amount the senior will pay?
First, calculate the discount: 50 x 0.15 = 7.50. Then subtract the discount: 50 - 7.50 = 42.50. The senior will pay $42.50.
A medication label reads 2 mg per 10 mL. How much medication is needed for a dose of 6 mg?
Set up a proportion: 2 mg/ 10 ml = 6 mg / x ml. solve for x:x = 30 ml
What is 40% of 150 tablets?
40% x 150 = 60 tablets
Convert 3/8 to a percent.
3/8 = 0.375, so multiply by 100: 37.5%
A pharmacy tech can fill 6 prescriptions in 10 minutes. How many can they fill in 1 hour (60 minutes)?
Set up a proportion: 6 prescriptions / 10 minutes = x prescriptions / 60 minutes. Solve for x: x = 36 prescriptions in 1 hour
Solve [ (7 1/2)/3 ] / [ (5 1/4)/2 ]
Convert to improper fractions: (15/2)/3 = 15/6 = 2.5, and (21/4)/2 = 21/8. Then, invert and multiply: 2.5 x 8/21 = 20/21
A child is prescribed 50 mg of a liquid medication that has 25 mg per 5 mL. How many mL should the child take?
Set up a proportion: 25 mg / 5 ml = 50 mg / x ml, solve for x:x = 10 ml
Express the ratio 3 mg per 100 mL and reduce it.
3mg / 100 ml simplifies to 3/100.
75 is what percent of 300?
Set up a proportion: 75/300 = x/100, solve for x: x = 25%
A prescription calls for 3/4 teaspoon of medicine every 8 hours. How much medicine will a patient take in one day?
Multiply 3/4 x 3 (since the patient takes it 3 times a day): 9/4 = 2 1/4 teaspoons.
Round
5.6875 to the nearest hundredth.
5.69
Estimate
18.3×7.85.
18 x 8 = 144
Divide
84.56÷3.2.
845.6 / 32 = 26.425
A prescription cost increases from $40 to $48. What is the percent increase?
Percent increase = (48-40) / 40 x 100 = 20%
A bottle contains 500 mL, and the label states that 0.9% of the solution is sodium chloride. How many grams of sodium chloride are present?
Convert 0.9% to a decimal: 0.9% = 0.009 x 500 = 4.5 grams of sodium chloride.
A prescription calls for 120 mL of liquid, but you only have a bottle labeled 40 mL. How many bottles are needed to fulfill the prescription?
Set up a proportion: 120/x = 40/1. x = 3 bottles
A patient is prescribed 75 mg of medication. The pharmacy only has 25 mg tablets. How many tablets are required for the dose?
25 mg / 1 tablet = 75 mg / x tablets, solve for x = 3 tablets.
Multiply 0.75 x 3/4
Convert 0.75 to 3/4, then multiply: 3/4 x 3/4 = 9/16 or 0.5625
A medication order is for 365 mL, but you estimate the patient will only need 350 mL. What is the percent difference?
(365-350)/365 x 100 = 4.1%
