Basic Arithmetic

Addition
The result of adding two numbers together is called the sum of the two numbers.

Subtraction
The result of subtracting two numbers is called the difference of the two numbers.

Note: Subtracting a number is the same as adding the opposite of the number.

15 – (-6) = 15 + 6 = 21

Multiplication
The result of multiplying two numbers is called the product of the two numbers.

Division
The result of dividing two numbers is called the quotient of the two numbers.

Note: Dividing by a number is the same as multiplying by its reciprocal.

4 ÷ 12 = 4 x =

36 ÷ 5 = 36 x = or 7 or 7.2

There are times when improper fractions like are appropriate, and other times when mixed numbers like 7 are appropriate, and still other times when decimals like 7.2 are appropriate. Take great care, however, to note that is not equal to .33. We cannot replace by .33 unless rounding is required.

The following is a calculation of 853 / 3, using long division. The result can be written as 284 R1, where the R stands for remainder. However, at the university level, the preferred answer is 284 1/3.

Order of Operations

Mathematicians have agreed to perform the mathematical operations in the following order:

            1) Parentheses
            2) Exponents
            3) Multiplication and Division
            4) Addition and Subtraction.

This ordering is referred to as PEMDAS. One mnemonic device frequently used to remember the order of operations is: Please Excuse My Dear Aunt Sally.

Do calculations that occur inside parentheses and all other grouping symbols first (such as braces { } or brackets [ ]). When performing multiplication and division or addition and subtraction, work from left to right in the order written in the problem.

Examples

1) Simplify 2) Simplify

3) -3² = -9 while (-3)² = 9 This is a very important distinction and it is often done incorrectly!