Module 1 Flashcards
What is a Whole Number?
A number without fractions or decimals. Examples: 1, 355, 72.
Adding Whole Numbers
Example: 12 + 35 = 47; 237 + 78 = 315.
Subtracting Whole Numbers
Example: 15 - 8 = 7; 432 - 121 = 311.
Multiplying Whole Numbers
Example: 12 x 8 = 96; 31 x 46 = 1426.
Dividing Whole Numbers
Example: 12 ÷ 4 = 3; 186 ÷ 2 = 93.
What is a Fraction?
Definition: A number with a numerator (top) and denominator (bottom). Example: 2/4.
Types of Fractions
Proper: Top < Bottom (e.g., ¾)
Improper: Top > Bottom (e.g., 7/3)
Mixed: Whole + Proper (e.g., 4 ½)
Simplifying Fractions
Reduce to lowest terms. Example: 2/4 = 1/2.
Multiplying Fractions
Multiply numerators and denominators. Example: 2/3 x 3/4 = 6/12 = 1/2.
Dividing Fractions
Invert the second fraction and multiply. Example: 3/4 ÷ 1/3 = 9/4.
Adding Fractions
Find the Lowest Common Denominator (LCD). Example: 2/3 + 3/6 = 4/6 = 2/3.
Subtracting Fractions
Same as addition: find LCD and subtract. Example: 7/8 - 2/5.
What are Decimals?
Whole numbers with a fractional part. Examples: 0.003, 3.54.
Rounding Decimals
Rules for rounding: Up if ≥5, stay if ≤4. Example: 4.456 → 4.5.
Adding Decimals
Line up decimals. Example: 45.67 + 1.37.
Subtracting Decimals
Line up decimals. Example: 45.98 - 1.44.
Pharmacy Rounding Rules
Weight: 1 decimal; Money: 2 decimals; BSA: 2 decimals.
Multiplying Decimals
Line up right, count decimal places. Example: 32 x 4.25.
Dividing Decimals
Remove decimals by shifting right. Example: 12.8 ÷ 4 = 128 ÷ 40.
Definition of a Fraction:
Indicates a portion of a whole; expression of division (Numerator/Denominator).
Types of Fractions
Proper: Numerator < Denominator; value < 1.
Improper: Numerator > Denominator; value ≥ 1.
Mixed: Combination of whole number and proper fraction; value > 1.
Complex: Numerator/Denominator can be proper, improper, or mixed.
Comparing Fractions:
Same Numerator: Smaller Denominator = Larger Value.
Same Denominator: Smaller Numerator = Smaller Value.
Reducing to Lowest Terms:
Divide both by the largest non-zero number that divides evenly.
Enlarging Fractions:
Multiply both by the same non-zero number.
Adding/Subtracting:
- Convert mixed to improper.
- Find LCD.
- Add/Subtract numerators; place over LCD.
- Convert to mixed/reduce.
Multiplying:
- Convert mixed to improper.
- Cancel terms.
- Multiply 4.numerators/denominators.
5.Reduce.
Dividing:
- Convert mixed to improper.
- Invert second fraction.
- Multiply numerators/denominators.
- Reduce.
What is a decimal?
A decimal is a fraction where the denominator is a power of ten (10, 100, 1000, etc.), represented by a decimal point separating whole numbers from fractional parts.
How do you read a decimal?
Read a decimal by stating the whole number, saying “point,” and then stating the decimal fractions. For example, 1.1 is read as “one point one.”
Why is it important to place a zero before a decimal point?
Placing a zero (e.g., 0.1 instead of .1) prevents misinterpretation of dosages, which can lead to administering ten times the intended dose.
What are the steps for adding and subtracting decimals?
- Align decimal points vertically.
- Perform addition or subtraction from right to left.
- Keep the decimal point in the same position in the result.
Provide an example of adding decimals.
20.4 + 21.8 = 42.2
Provide an example of subtracting decimals.
52.4 - 15.2 = 37.2
What are the steps for multiplying decimals?
- Multiply as usual.
- Count total decimal places in both numbers.
- Place the decimal in the product according to the total decimal places.
Provide an example of multiplying decimals.
2.05 × 0.2 = 0.410 (3 decimal places)
What are the steps for dividing decimals?
- If the denominator is not a whole number, move the decimal point to make it a whole number.
- Move the decimal in the numerator the same number of spaces.
- Perform long division.
Provide an example of dividing decimals.
15.9 ÷ 0.3 = 53 (after moving the decimal)
How do you round decimals to hundredths?
- Identify the hundredths place.
- Check the thousandths place to determine if rounding is needed.
- Round up if the thousandths place is ≥ 5; otherwise, keep the same.
Provide an example of rounding decimals.
0.123 rounds to 0.12 (thousandths place ≤ 4)
0.459 rounds to 0.46 (thousandths place ≥ 5)
What are the steps to convert a decimal to a fraction?
- Write the decimal as a whole number (numerator).
- Use a denominator of 1 followed by as many zeros as there are decimal places.
- Reduce to lowest terms.
Provide an example of converting a decimal to a fraction.
0.125 = 125/1000 = 1/8
What are the steps to convert a fraction to a decimal?
- Divide the numerator by the denominator.
- Place any whole number to the left of the decimal.
Provide an example of converting a fraction to a decimal.
¼ = 0.25
3 ½ = 3.5
What is the key takeaway regarding decimal operations in pharmacy?
Mastery of decimal operations is crucial for accurate medication dosing and safety in pharmacy practice. Always double-check calculations.
What is a percentage?
A method to express a part of a whole, always out of 100. For example, 85% signifies 85 out of 100.
How do you convert a decimal to a percentage?
Shift the decimal two places to the right and add a % sign. For example, 0.65 converts to 65%.
What is the process for converting a percentage to a decimal?
Move the decimal two places to the left. For example, 43% becomes 0.43.
How do you convert a fraction to a percentage?
Divide the fraction and shift the decimal two places to the right. For example, 3/5 translates to 60%.
How do you convert a percentage to a fraction?
Express it as a fraction over 100 and simplify. For example, 48% equals 48/100, which simplifies to 12/25.
What is a ratio?
A representation of the relationship between two numbers, formatted as a:b. For example, 3:5.
How do you express a percentage as a ratio?
Place the percentage over 100. For example, 76% becomes 76:100, which simplifies to 19:25.
What are proportions?
Illustrations of equality between two ratios, frequently used in pharmacy calculations.
How do you determine the percentage of a quantity?
Multiply the total by the decimal equivalent of the percentage. For example, 25% of 50 equals 12.5.
What is cross multiplying?
A technique for solving equations like “30 is 15% of what number?” by multiplying diagonally across the equal sign.
Why is understanding percentages vital in pharmacy?
It is essential for accurate dosage calculations.
Why are ratios and proportions key in pharmacy?
They are crucial for comparing quantities and ensuring precise measurements.
How do practical applications enhance comprehension?
Real-world examples help in understanding mathematical concepts better.
What is the significance of unit consistency in calculations?
Maintaining consistent units is crucial to prevent errors in calculations.
How can visual aids improve understanding of ratios and proportions?
Charts or diagrams can significantly enhance comprehension of these concepts.
Why are practice problems important?
Engaging with real-life scenarios can enhance calculation proficiency.
How can group study benefit learning?
Collaborating with peers can clarify complex mathematical concepts.
What role do digital tools play in learning?
Utilizing calculation apps can facilitate the learning process.
Why is continuous learning important?
Regularly revisiting these concepts strengthens knowledge retention.
What is a ratio?
A ratio is the comparison between two related quantities, expressed as one number compared to another, formatted as a:b.
How should ratios be stated?
Ratios should be stated in lowest terms. For example, 1:20 means one part of an active ingredient contained in 20 total parts.
What is the numerator in a ratio?
The numerator is the number to the left of the colon in a ratio.
What is the denominator in a ratio?
The denominator is the number to the right of the colon in a ratio.
How do you convert a proper fraction to a ratio?
Reduce the fraction to its lowest term, then write the numerator to the left of the colon and the denominator to the right.
How do you convert a decimal to a ratio?
Convert the decimal to a proper fraction, reduce to lowest terms, and then write the numerator and denominator in ratio format.
What is the process to convert a ratio to a fraction?
Write the number to the left of the colon as the numerator and the number to the right as the denominator, then reduce to lowest terms.
How do you convert a ratio to a decimal?
Convert the ratio to a fraction, then divide the numerator by the denominator.
What is the method to convert a percentage to a ratio?
Express the percentage as a fraction over 100, then reduce to lowest terms.
How do you convert a ratio to a percentage?
Convert the ratio to a fraction, divide the numerator by the denominator, multiply by 100, and add the percent sign.
What is the importance of reducing fractions and ratios?
Reducing to lowest terms ensures clarity and accuracy in representation.
What are the steps to convert a percentage to a fraction?
Express the percentage as a fraction over 100 and simplify.
How do you convert a percentage to a decimal?
Divide the percentage by 100.
What is the relationship between fractions, decimals, ratios, and percents?
They are all related equivalents, and understanding one helps in converting to the others.
What is the first step in converting a decimal to a ratio?
Convert the decimal to a proper fraction and reduce it to lowest terms.
How do you determine which of several values is the largest?
Convert all values to the same format (e.g., decimals or percentages) for comparison.
What is the significance of understanding ratios in pharmacy?
Ratios are crucial for comparing quantities and ensuring precise measurements in medication dosages.
What is a common example of a ratio in pharmacy?
A ratio of active ingredient to total solution, such as 1:20 for a medication.
How can you express the ratio 2:3 as a percentage?
Convert to a fraction (2/3), divide (0.6667), multiply by 100 to get approximately 66.67%.
What is the process for cross-multiplying in ratios?
To solve for an unknown in a proportion, multiply diagonally across the equal sign.
What does the term “percent” mean?
Percent means “by the hundred” and is represented by the symbol %.
How do you calculate a percentage of a whole quantity?
Use the formula:
Percentage (Part)
=
Percent
×
Whole Quantity
Percentage (Part)=Percent×Whole Quantity
How do you find 75% of 8 ounces?
Convert 75% to decimal (0.75) and multiply:
0.75
×
8
=
6
ounces
0.75×8=6 ounces
What are the steps to convert a percent to a fraction?
- Drop the % sign.
- Place the remaining number as the numerator over 100.
- Reduce to lowest terms.
Convert 75% to a fraction.
75%= 75/100 = 3/4
How do you convert a percent to a decimal?
Drop the % sign and divide by 100.
Convert 4% to a decimal.
4%= 4/100 =0.04
How do you convert a decimal to a percent?
Multiply the decimal by 100 and add the % sign.
Convert 0.5 to a percent.
0.5×100=50%
What is the importance of understanding percentages in healthcare?
It is essential for accurate dosing and patient care.
How do you find 20% of 150?
Multiply:
150
×
0.20
=
30
150×0.20=30
If a patient has an order for 500 mg of medication twice a day for 10 days, how many pills has he taken if he used 40% of 20 pills?
20×0.40=8 pills
How much sodium is in a box of salt weighing 80 ounces if it is 40% sodium?
80×0.40=32 ounces of sodium
What is the formula for finding a percentage (Part)?
Percentage (Part)=Percent×Whole Quantity
Why is mastering percentages, fractions, and decimals important?
It enhances critical thinking and analytical skills, essential for informed decision-making in various fields.
What is a proportion?
A proportion consists of two ratios that are equal to one another (e.g., 5:10 = 10:20).
What are the extremes in a proportion?
The extremes are the first and fourth terms of the proportion (e.g., in 5 : 10 = 10: 20, the extremes are 5 and 20).
What are the means in a proportion?
The means are the second and third terms of the proportion (e.g., in 5:10 = 10:20, the means are 10 and 10).
How do you set up a proportion?
You can set up a proportion using one of the following methods:
- mg = mg
- mg = tablets
- tablets = tablets
What is the cross multiplication rule in proportions?
The product of the means equals the product of the extremes (e.g., for (e.g. a/b = c/d, cross multiply to get a x d = b x c).
How do you solve for an unknown in a proportion?
Set up the proportion, cross multiply, and solve for the unknown variable.
Provide an example of setting up a proportion.
If three tablets contain 1950 mg of a substance, how many mg are in twelve tablets? Set up as:
1950 mg / 3 tablets = x mg / 12 tablets
What is the importance of proportions in real-world applications?
Proportions are used in various fields, such as healthcare for medication dosages and finance for budgeting.
How should answers be expressed when solving proportion problems?
Answers should be expressed as decimals rounded to two places.
