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Pharmacy Calculations > Q&A - Chapter 2 > Flashcards

Q&A - Chapter 2 Flashcards

1
Q

Q: What are the key goals when working with numbers in pharmacy?

A

Add, subtract, multiply, and divide whole numbers.
Add, subtract, multiply, and divide fractions, reduce them to the lowest terms, and discuss mixed numbers.
Add, subtract, multiply, and divide decimals, and round them to specific place values.
Convert between fractions, decimals, and percentages.
Express numbers in ratios and proportions, and solve for unknowns.
Visual Example: A flowchart showing whole numbers → fractions → decimals → percentages with arrows between them.

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2
Q

Q: What does “complex fraction” mean?

A

A: It’s a fraction where either the numerator, the denominator, or both are fractional units themselves.
Visual Example: A fraction like (1/2) / (3/4) with labels showing how both parts are fractions.

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3
Q

Q: What does “convert” mean in math?

A

A: It means changing something from one form to another, like turning a fraction into a decimal or a percentage.
Visual Example: A number like 1/2 being transformed into 0.5 and then 50% with arrows connecting them.

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4
Q

Q: What’s a decimal?

A

A: It’s a fraction with a denominator that’s a power of 10, written with numbers to the right of a decimal point.
Visual Example: A number like 0.75 shown as 3/4 with the decimal point highlighted.

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5
Q

Q: What are decimal places?

A

A: They are the positions of numbers to the right of the decimal point, like tenths, hundredths, and thousandths.
Visual Example: A number like 3.141 with labels for the tenths, hundredths, and thousandths places.

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6
Q

Q: What’s the denominator in a fraction?

A

A: It’s the bottom part of the fraction that shows how many equal parts make up the whole.
Visual Example: A fraction like 3/4 with the “4” labeled as the denominator.

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7
Q

Q: What does “improper fraction” mean?

A

A: It’s a fraction where the numerator is equal to or greater than the denominator, like 5/3.
Visual Example: A fraction like 7/4 highlighted with the numerator larger than the denominator.

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8
Q

Q: Why do we find the least common denominator?

A

A: It’s the smallest number that all the denominators in a problem can divide evenly into, helping with adding and subtracting fractions.
Visual Example: Fractions like 1/4 and 1/6 being rewritten as 3/12 and 2/12 with a shared denominator.

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9
Q

Q: Why do we use a leading zero?

A

A: It’s a zero before the decimal point in numbers less than 1, like 0.5, to reduce mistakes in dosing.
Visual Example: A number like “.5” crossed out and replaced with “0.5” to emphasize safety.

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10
Q

Q: What’s a mixed number?

A

A: It’s a number that combines a whole number and a fraction, like 2 1/2.
Visual Example: A picture of 2 1/2 with the whole number and fraction labeled separately.

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11
Q

Q: What does “invert” mean in fractions?

A

A: It means flipping the numerator and denominator, like turning 2/3 into 3/2.
Visual Example: An arrow flipping a fraction like 4/5 into 5/4.

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12
Q

Q: What is the numerator?

A

A: It’s the top number in a fraction that shows how many parts you have.
Visual Example: A fraction like 3/4 with the “3” labeled as the numerator.

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13
Q

Q: What does “percent” represent?

A

A: It shows a portion out of 100 parts, like 50% means 50 out of 100.
Visual Example: A pie chart split into 100 parts, with 50 shaded to represent 50%.

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14
Q

Q: What does “product” mean in math?

A

A: It’s the result of multiplying two numbers together.
Visual Example: A simple multiplication problem: 3 × 4 = 12, where 12 is the product.

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15
Q

Q: What is a proper fraction?

A

A: It’s a fraction where the numerator (top number) is smaller than the denominator (bottom number), like 3/4.
Visual Example: A pizza with 3 out of 4 slices shaded, showing the fraction 3/4.

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16
Q

Q: What does “proportion” mean?

A

A: It shows the relationship between parts, often using ratios like 1:2.
Visual Example: A scale with two sides: one holding 1 apple and the other holding 2 apples, labeled as 1:2.

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17
Q

Q: What is the quotient in division?

A

A: It’s the answer to a division problem. For example, in 10 ÷ 2 = 5, the quotient is 5.
Visual Example: A division problem written out, with the quotient highlighted.

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18
Q

Q: What does “ratio” mean?

A

A: It’s a way of comparing two numbers, like 1:2 means for every 1 of something, there are 2 of something else.
Visual Example: Two jars, one with 1 marble and the other with 2 marbles, labeled as a 1:2 ratio.

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19
Q

Q: What is the remainder in division?

A

A: It’s the amount left over after dividing a number. For example, in 10 ÷ 3 = 3 R1, the remainder is 1.
Visual Example: A visual of 10 blocks divided into groups of 3, with 1 block left over.

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20
Q

Q: What does “round” mean in math?

A

A: It means adjusting a number to its nearest place value, like rounding 3.56 to 3.6.
Visual Example: A number line showing 3.56 rounded to 3.6.

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21
Q

Q: What is a scored tablet?

A

A: It’s a tablet with an indentation, making it easy to break into equal parts.
Visual Example: A picture of a round tablet with a clear line down the middle.

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22
Q

Q: What’s wrong with trailing zeros like “1.0”?

A

A: A trailing zero can be mistaken for a bigger number, like “10.” Writing 1 is safer.
Visual Example: A pill bottle labeled “1 mg” with “1.0 mg” crossed out.

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23
Q

Q: What is a whole number?

A

A: It’s a number with no fractions or decimals, like 1, 2, 3, and so on.
Visual Example: A group of apples labeled as 1, 2, 3, without any fractions.

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24
Q
  1. Adding Multiple Numbers: 154 + 1,063 + 25 + 376
    To add these numbers, start by lining them up vertically, aligning the digits by place value:
A

154
1,063
25
376
——
1,618

Step-by-step:

Add the digits in the ones place: 4 + 3 + 5 + 6 = 18 (write 8, carry 1).
Add the digits in the tens place: 5 + 6 + 2 + 7 = 20, plus the carried-over 1 = 21 (write 1, carry 2).
Add the digits in the hundreds place: 1 + 0 + 0 + 3 = 4, plus the carried-over 2 = 6.
Add the thousands place: 1 (from 1,063).
Final answer: 1,618

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25
Q
  1. Subtracting Two Numbers: 163 - 69
    When subtracting, align the digits and subtract column by column:
A

163
- 69
——
94

Step-by-step:

Start with the ones place: 3 - 9. Since 3 is smaller, borrow 1 from the tens place, making it 13 - 9 = 4.
Move to the tens place: After borrowing, it’s 5 - 6. Borrow again from the hundreds place to make it 15 - 6 = 9.
The hundreds place now has nothing left, so it’s 0.
Final answer: 94

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26
Q
  1. Multiplying Whole Numbers: 256 × 43
    To multiply these numbers, use long multiplication:
A

256
× 43
——
768 (256 × 3)
+ 10240 (256 × 40)
——
11008

Step-by-step:

Multiply 256 by 3 to get 768.
Multiply 256 by 40 (4 × 10) to get 10,240.
Add the results: 768 + 10,240 = 11,008.
Final answer: 11,008

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27
Q
  1. Dividing Whole Numbers: 256 ÷ 16
A

To divide, determine how many times 16 fits into 256:

Step-by-step:

Start with the first digit of 256 (2). Since 16 is larger than 2, consider the first two digits (25).
16 fits into 25 once, so write 1 above the line and subtract: 25 - 16 = 9.
Bring down the next digit (6), making it 96.
16 fits into 96 exactly 6 times: 96 ÷ 16 = 6.
Final answer: 16

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28
Q
  1. Adding Decimals: 25.6 + 456 + 35.67
    Align the decimal points before adding:
A

25.60
456.00
+ 35.67
———
517.27

Step-by-step:

Line up the decimal points and add zeros to fill in any blanks.
Add the numbers column by column, starting with the hundredths place: 0 + 0 + 7 = 7.
Move to the tenths place: 6 + 0 + 6 = 12 (write 2, carry 1).
Continue with the ones, tens, and hundreds places: Add each column as usual.
Final answer: 517.27

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29
Q
  1. Subtracting Decimals: 354.29 - 45.390
    Align the decimal points and subtract:
A

354.290
- 45.390
———
308.900

Step-by-step:

Align the decimals and add trailing zeros to ensure equal places.
Subtract each column, borrowing as necessary.
Keep the decimal point aligned in the answer.
Final answer: 308.90

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30
Q
  1. Multiplying Decimals: 12.56 × 65.031
    First, multiply as if the decimals are not there:
A

1256
× 65031
——–
1256 (1256 × 1)
37680 (1256 × 3)
628000 (1256 × 5)
8124000 (1256 × 6)
——–
81647936

Step-by-step:

Multiply the numbers as whole numbers to get 81647936.
Count the total decimal places in the original numbers (2 in 12.56 and 3 in 65.031, so 5 total).
Place the decimal point 5 places from the right: 816.47936
Final answer: 816.48 (rounded to the nearest hundredth).

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31
Q
  1. Dividing Decimals: 655.08 ÷ 1.2
    Move the decimal point in both numbers to make the divisor a whole number, then divide:
A

6550.8 ÷ 12

Step-by-step:

Move the decimal one place to the right in both numbers: 655.08 becomes 6550.8, and 1.2 becomes 12.
Divide as usual: 6550.8 ÷ 12 = 545.9
Final answer: 545.90

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32
Q
  1. Adding Fractions: 1/2 + 3/4 + 7/8
    First, find a common denominator:
A

1/2 = 4/8
3/4 = 6/8
7/8 = 7/8

Step-by-step:

Convert all fractions to have a denominator of 8.
Add the numerators: 4 + 6 + 7 = 17.
The result is 17/8, which simplifies to 2 1/8.
Final answer: 2 1/8

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33
Q

Card 1: What is a whole number?

A

Answer:
A whole number is a complete value with no fractional or decimal part, such as 1, 2, or 3.

Visual Example: A stack of three complete apples.

34
Q

Card 2: What is a fraction?

A

Answer:
A fraction represents a part of a whole. It consists of a numerator (top) and a denominator (bottom). For example, (1/2)
means one part out of two.

Visual Example: A pizza cut into 2 equal slices, with one slice highlighted.

35
Q

Card 3: What is a decimal?

A

Answer:
A decimal is another way to show parts of a whole, using a point to separate the whole number from the fractional part. For example, (1/2)
​
is 0.5 in decimal form.

Visual Example: The number line showing 0, 0.5, and 1.

36
Q

Card 4: How do you align decimals when adding or subtracting?

A

Answer:
Line up the decimal points in both numbers before performing addition or subtraction to maintain accuracy.

Visual Example: Numbers like 3.45 + 1.2 with decimal points aligned vertically.

37
Q

Card 5: What are the numerator and denominator in a fraction?

A

Answer:
The numerator (top number) shows how many parts are being considered. The denominator (bottom number) shows how many equal parts the whole is divided into.

Visual Example: Fraction
(3/8) with 3 shaded slices out of 8 on a pie chart.

38
Q

Card 6: What is an improper fraction?

A

Answer:
An improper fraction has a numerator larger than or equal to the denominator, indicating more than one whole. For example, (9/8)
​can also be expressed as
1 (1/8).

Visual Example: A pie with 9 slices, where 1 full pie and 1 extra slice are shown.

39
Q

Card 7: What is a complex fraction?

A

Answer:
A complex fraction has a fraction in the numerator and/or denominator, such as
(1/2) / (3/4). To simplify, invert the denominator and multiply.

Visual Example: Fraction structure with both
(1/2)
and
(3/4)
​
and a flip to multiply.

40
Q

Card 8: What is a ratio?

A

Answer:
A ratio compares two values, such as 2:3, meaning for every 2 units of one item, there are 3 of another.

Visual Example: 2 apples compared to 3 bananas.

41
Q

Card 9: What is a proportion?

A

Answer:
A proportion connects two ratios and allows you to solve for unknowns. For example, if 2 apples correspond to 3 bananas, how many bananas match 4 apples?

Visual Example: Ratio table showing 2:3 and solving for the missing value with 4 apples.

42
Q

Card 10: What is a leading zero?

A

Answer:
A leading zero appears before the decimal point in numbers less than one, such as 0.5. It prevents errors, ensuring the number is not misread as 5.

Visual Example: “0.5” emphasized, with “5” crossed out to highlight the importance of the leading zero.

43
Q

Card 11: What is the least common denominator (LCD)?

A

Answer:
The LCD is the smallest number that both denominators share. For example, the LCD for
(1/2)
​
and
(3/4)
​
is 4.

Visual Example: Fractions
(1/2)
​
and
(3/4)
​
both converted to have a denominator of 4.

44
Q

Card 12: How do you divide fractions?

A

Answer:
To divide fractions, invert (flip) the second fraction and multiply. For example,
(1/2) / (1/3)
​
becomes

(1/2) x (3/1)
​
.

Visual Example: Diagram showing the fraction

(1/2) / (1/3)
​
flipping to multiplication.

45
Q

Card 13: Why are these concepts important?

A

These concepts ensure accuracy in fields like healthcare, where precise calculations can prevent serious errors, especially in medication dosing.

Visual Example: A medical dosage calculation, highlighting correct values and safety warnings for errors.

46
Q

Card 1: What are whole numbers?

A

Answer:
Oh! Whole numbers are numbers that are complete—like 1, 2, and 3! There’s nothing missing or broken. No parts of anything, just whole, perfect numbers! Cool, right?

Example: Imagine you have three whole apples. No half-eaten pieces here!

47
Q

Card 2: What’s a fraction?

A

Answer:
A fraction is when I only have a part of something. It’s split into two parts—the numerator and denominator. The numerator is the number of parts I have, and the denominator is how many parts make up the whole.

Example: I have half a pizza! That’s
(1/2)
​
—one part out of two. Yum!

48
Q

Card 3: What’s a decimal?

A

Answer:
Decimals are so neat! They’re another way to show parts of a whole. Instead of using a line like in fractions, decimals use a point! So, half a pizza is 0.5. Pretty handy, huh?

Example: Imagine a number line with 0, 0.5 (halfway), and 1. That point shows exactly where you are!

49
Q

Card 4: How do I add or subtract decimals?

A

Answer:
Oh, it’s easy if you line up the decimal points just right! It’s like keeping everything in neat columns so you don’t mix up the digits. Math is all about being organized!

Example: Adding 3.45 and 1.2 works perfectly when their decimal points are in the same column.

50
Q

Card 5: What are numerators and denominators?

A

Answer:
The numerator is the top part of a fraction—what I have. The denominator is on the bottom—it tells how many parts the whole has. Fractions are like puzzles!

Example: In
(3/8)
​
, I have 3 pieces of a pie, and the whole pie has 8 slices.

51
Q

Card 6: What’s an improper fraction?

A

Answer:
Oh, this one’s fun! An improper fraction means I have more than one whole. Imagine eating 9 slices of pizza, but each pizza only has 8 slices. That’s
(9/8)
​
! I can also say 1 and 1/8 pizza—one whole plus an extra slice.

Example: A whole pizza plus a bonus slice! Pizza math is my favorite!

52
Q

Card 7: What’s a complex fraction?

A

Answer:
This one sounds fancy but isn’t too scary! A complex fraction has a fraction inside another fraction—like a math sandwich! You solve it by flipping the bottom one and multiplying.

Example: It’s like flipping a card in a matching game to find the right solution!

53
Q

Card 8: What’s a ratio?

A

Answer:
A ratio compares two things. Like, for every 2 apples, there are 3 bananas. That’s a 2:3 ratio! Ratios help balance things perfectly!

Example: Picture two apples sitting beside three bananas. Perfect harmony!

54
Q

Card 9: What’s a proportion?

A

Answer:
A proportion is like magic! It connects two ratios and helps me figure out missing numbers. If I know 2 apples go with 3 bananas, I can figure out how many bananas I need for 4 apples.

Example: It’s like solving a mystery with numbers—my detective math skills in action!

55
Q

Card 10: What’s a leading zero?

A

Answer:
A leading zero is the little zero before a decimal point, like in 0.5. It’s super important because it keeps people from making mistakes. Without that zero, someone might think it’s 5 instead of 0.5!

Example: Imagine seeing .5 and thinking it’s 5. Yikes! That zero saves the day!

56
Q

Card 11: What’s the least common denominator (LCD)?

A

Answer:
The LCD is the smallest number that both denominators can share. It’s like finding a common language between fractions so they can work together!

Example: For
(1/2)
​
and
(3/4)
​
, the LCD is 4. Now both fractions can talk to each other!

57
Q

Card 12: How do I divide fractions?

A

Answer:
Here’s a fun trick—flip the second fraction and multiply! It’s like turning the problem upside down to make it easier.

Example: If I need to divide
(1/2) / (1/3)
​
, I flip the
(1/3)
​
to
(3/1)
​
and multiply. Problem solved!

58
Q

Card 13: Why are these concepts important?

A

Answer:
Because math isn’t just for homework! In real life, especially in healthcare, math keeps people safe. Imagine giving the wrong dose of medicine—math helps prevent that and saves lives.

Example: Picture a doctor calculating a perfect dose for a patient. Math is like a superhero here!

59
Q

Q: What is a percent, and how is it used?

A

A: A percent represents a part of a whole out of 100. For example, 25% means 25 out of 100. Percentages are useful for making comparisons, tracking discounts, and analyzing data.

Visual Example:
A pie chart showing 25% shaded to illustrate how a percent represents a portion of a whole.

60
Q

Q: What is a product in mathematics?

A

A: The product is the result of multiplying two or more numbers. For example, multiplying 4 by 5 gives a product of 20.

Visual Example:
Two sets of objects: 4 groups of 5 apples each, showing a total of 20 apples to represent the product.

61
Q

Q: What is a proper fraction?

A

A: A proper fraction has a numerator smaller than the denominator, representing a value less than one. For example, ¾ means three parts out of four.

Visual Example:
A pizza divided into 4 slices with 3 slices shaded, showing the fraction ¾.

62
Q

Q: What is a proportion, and why is it useful?

A

A: A proportion compares two equal ratios and helps maintain balance. For instance, if a 2:3 sugar-to-flour ratio is doubled, it becomes 4 parts sugar to 6 parts flour.

Visual Example:
Two bar graphs: One showing a 2:3 ratio and another with a doubled proportion of 4:6.

63
Q

Q: What is a quotient?

A

A: The quotient is the result of a division operation. For example, dividing 12 by 4 gives a quotient of 3.

Visual Example:
12 apples divided evenly among 4 baskets, with 3 apples per basket.

64
Q

Q: What is a ratio, and where is it used?

A

A: A ratio compares two quantities. For example, a 2:3 sugar-to-flour ratio means 2 parts sugar for every 3 parts flour. Ratios are used in recipes, budgeting, and project planning.

Visual Example:
A recipe card showing 2 cups of sugar and 3 cups of flour.

65
Q

Q: What is a remainder in division?

A

A: A remainder is the value left over when a number isn’t evenly divisible. For example, dividing 10 by 3 gives a quotient of 3 with a remainder of 1.

Visual Example:
10 marbles divided among 3 boxes, with 1 marble left over.

66
Q

Q: What does it mean to round a number?

A

A: Rounding adjusts a number to a simpler, approximate value. For example, rounding 48 to the nearest ten gives 50.

Visual Example:
A number line showing 48 rounded to 50.

67
Q

Q: What is a scored tablet?

A

A: A scored tablet is a pill with a line to allow splitting into equal doses, providing flexibility for medication adjustments.

Visual Example:
An image of a tablet with a line in the middle, indicating where it can be split.

68
Q

Q: What is a trailing zero, and why can it cause errors?

A

A: A trailing zero appears after a decimal point (e.g., 10.0). In healthcare, it can lead to misinterpretation, such as reading 10.0 as 100, so it’s avoided in documentation.

Visual Example:
A comparison of “10.0” vs. “10” with a caution symbol to highlight the risk of misreading.

69
Q

Q: What is a whole number?

A

A: A whole number is a non-negative integer without fractions or decimals, such as 0, 1, and 2. They are essential for counting and basic calculations.

Visual Example:
A row of whole number counters (e.g., 0, 1, 2, 3) shown without any fractions or decimals.

70
Q

Q: Why are these mathematical concepts important?

A

A: These concepts help solve real-world problems. Percentages and ratios improve data clarity, while multiplication, division, and rounding ensure precision in calculations like budgeting and healthcare dosing.

Visual Example:
A collage of scenarios, including a budget, recipe, and medication chart, showing how these concepts apply to everyday life.

71
Q
  1. How much water is needed to reconstitute a 50-mL vial if 15 mL of water is needed for a 20-mL vial?
A

(15ml) / (20 ml) = (x ml) / (50 ml)

x = (15 x 50) / 20

= 37.5 ml

72
Q
  1. How many prescriptions can be filled in 1 hour if 6 prescriptions are filled in 10 minutes?
A

Answer: 36 prescriptions
Explanation: In 10 minutes, 6 prescriptions are filled. Since 1 hour has 60 minutes, (60/10) = 6 intervals. Therefore 6 x 6 = 35 prescriptions.

73
Q
  1. How much will a senior save with a 10% discount on a $25 prescription?
A

Answer: $2.50
Explanation: Calculate 10% of $25:
0.10 × 25 = 2.50

74
Q
  1. 85 is what percent of 200?
A

Answer: 42.5 %

Explanation:

Percent = (85 / 100) x 100

= 42.5 %

75
Q
  1. How much medication is needed if a prescription calls for ¼ of a 480-mL supply?
A

Answer: 120 ml

(1/4) x 480 = 120 ml

76
Q
  1. What is half of a $45 prescription?
A

Answer: $22.50
Explanation: Half of $45 is
45 ÷ 2 = 22.50

77
Q
  1. How much change is given from a $20 bill for merchandise costing $2.98, $5.36, $1.69, and $3.45?
A

Answer: $6.52

Add it all up

Subtract from total.

78
Q
  1. How many milligrams is three 75-mg tablets?
A

Answer: 225 mg
Explanation: Multiply the dose per tablet by 3:

75×3=225mg.

79
Q
  1. How many ounces should be taken if a patient is prescribed 16 oz of medication with instructions to use 1/16 of the bottle each night?
A

The patient is to take (1/16) of the 16-oz bottle, which is 16 / 16 = 1 oz.

80
Q
A

Pharmacy Calculations (6 decks)

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