Chapter 3: Basic Math Review

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.

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

Whole Numbers Whole numbers are counting numbers.

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

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.

Fractions  

Proper Fraction  

Mixed Number  

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

Fractions with Like Denominators  

Fractions with Like Numerators  

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.

Adding Fractions  

Adding Fractions  

Adding Fractions  

Adding Fractions  

Subtracting Fractions  

Subtracting Fractions  

Subtracting Fractions  

Subtracting Fractions  

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

Multiplying Fractions  

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.”

Dividing Fractions  

Dividing Fractions  

Dividing Fractions  

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.

Decimals The number 63,207.5184 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

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

Adding Decimals Example: 4.3 2.16 + 3.289 9.749

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.

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.

Dividing Decimals Example: 1.34÷2.1

Dividing Decimals Example: 1.34÷2.1 1.34×100=134 2.1×100=210

Dividing Decimals Example: 1.34÷2.1 1.34×100=134 2.1×100=210 134÷210=0.638

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.

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