1. Chapter 3: Basic Math Review

2. Chapter Objectives After reading this chapter, you will be able to:
Identify whole numbers.
Perform basic calculations using addition and subtraction.
Perform basic calculations using multiplication and division.
Set up and use fractions.
Compare fractions, express them as decimals, and find common denominators.
Perform basic mathematical calculations using fractions and decimals.
Understand and use percentages.
Perform basic mathematical calculations using percentages.

3. Numbers
A number is a quantity or amount that is made up of one or more numerals. There are several kinds of numbers:
whole numbers
fractions
decimal numbers

4. Whole Numbers
Whole numbers are counting numbers.

5. Addition and Subtraction
The sum is the amount obtained when adding numbers.
With subtraction, you take something away from a given number.
The difference is the amount obtained when subtracting numbers

6. Multiplication and Division
Multiplication and division are used constantly in performing pharmacy calculations.
The product is the amount obtained by multiplying numbers.
The quotient is the amount obtained by dividing one number by another number.

7. Fractions

8. Proper Fraction

9. Mixed Number

10. Comparing Fractions
Fractions can be compared using denominators that are the same or different, as well as numerators that are the same or different.

11. Fractions with Like Denominators

12. Fractions with Like Numerators

13. Adding and Subtracting Fractions
When you add and subtract fractions, it often helps to find the lowest common denominator. A common denominator is a number into which both denominators can divide evenly.

14. Adding Fractions

15. Adding Fractions

16. Adding Fractions

17. Adding Fractions

18. Subtracting Fractions

19. Subtracting Fractions

20. Subtracting Fractions

21. Subtracting Fractions

22. Multiplying Fractions
To multiply fractions, multiply the numerators of each fraction and the denominators of each fraction.

23. Multiplying Fractions

24. Dividing Fractions
To divide fractions, invert or reverse the numbers of the second fraction in the equation. Then multiply the numerators of each fraction and the denominators of each fraction, as you do when multiplying fractions. This is known as “invert and multiply.”

25. Dividing Fractions

26. Dividing Fractions

27. Dividing Fractions

28. Decimals
Decimal numbers are numbers that are written using place value. The decimal system includes 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Using these digits, you can express numbers of all sizes using a decimal point.

29. Decimals
The number 63, is used to illustrate decimal-system notation.
Value
Ten-thousands
Thousands
Hundreds
Tens
Ones
Decimal point
Tenths
Hundredths
Thousandths
Ten-thousandths
Sample Number 6 3 2 7 . 5 1 8 4

30. Adding and Subtracting Decimals
When adding and subtracting decimals, the numbers should be placed in columns so that the decimal points are all aligned.

31. Adding Decimals
Example:

32. Multiplying Decimals
When multiplying decimals, you multiply them as whole numbers, and then move the decimal the total number of places that were in the two numbers being multiplied. There is an implied decimal point for all whole numbers, which is placed at the end of the smallest or last digit in the number.

33. Dividing Decimals
When dividing decimals, first change each decimal to a whole number by multiplying each number by the same factor of 10. Then proceed with the division operation.

34. Dividing Decimals
Example: 1.34÷2.1

35. Dividing Decimals
Example: 1.34÷ ×100= ×100=210

36. Dividing Decimals
Example: 1.34÷ ×100= ×100= ÷210=0.638

37. Percentages
Pharmacy calculations often require the use of percentages. A percentage is represented by the % symbol and is used to express the number of parts of one hundred. It represents the same number as a fraction whose denominator is 100.

38. Percentages
Example: 0.9%=[0.9/100] 2%=[2/100] [5/100]=5%