Basic Operations
The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.
Learning Objective

Calculate the sum, difference, product, and quotient of positive whole numbers
Key Points
 The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.
 The basic arithmetic properties are the commutative, associative, and distributive properties.
Terms

difference
The result of subtracting one quantity from another.

sum
The result of adding two quantities.

quotient
The result of dividing one quantity by another.

product
The result of multiplying two quantities.

commutative
Referring to a binary operation in which changing the order of the operands does not change the result (e.g., addition and multiplication).

associative
Referring to a mathematical operation that yields the same result regardless of the grouping of the elements.
Full Text
The Four Arithmetic Operations
Addition
Addition is the most basic operation of arithmetic. In its simplest form, addition combines two quantities into a single quantity, or sum. For example, say you have a group of 2 boxes and another group of 3 boxes. If you combine both groups together, you now have one group of 5 boxes. To represent this idea in mathematical terms:
Subtraction
Subtraction is the opposite of addition. Instead of adding quantities together, we are removing one quantity from another to find the difference between the two. Continuing the previous example, say you start with a group of 5 boxes. If you then remove 3 boxes from that group, you are left with 2 boxes. In mathematical terms:
Multiplication
Multiplication also combines multiple quantities into a single quantity, called the product. In fact, multiplication can be thought of as a consolidation of many additions. Specifically, the product of
However, another way to count the boxes is to multiply the quantities:
Note that both methods give you the same result—8—but in many cases, particularly when you have large quantities or many groups, multiplying can be much faster.
Division
Division is the inverse of multiplication. Rather than multiplying quantities together to result in a larger value, you are splitting a quantity into a smaller value, called the quotient. Again, to return to the box example, splitting up a group of 8 boxes into 4 equal groups results in 4 groups of 2 boxes:
The Basic Arithmetic Properties
Commutative Property
The commutative property describes equations in which the order of the numbers involved does not affect the result. Addition and multiplication are commutative operations:

$2+3=3+2=5$ 
$5 \cdot 2=2 \cdot 5=10$
Subtraction and division, however, are not commutative.
Associative Property
The associative property describes equations in which the grouping of the numbers involved does not affect the result. As with the commutative property, addition and multiplication are associative operations:

$(2+3)+6=2+(3+6)=11$ 
$(4 \cdot 1) \cdot 2=4 \cdot (1 \cdot 2)=8$
Once again, subtraction and division are not associative.
Distributive Property
The distributive property can be used when the sum of two quantities is then multiplied by a third quantity.

$(2+4) \cdot 3 = 2 \cdot 3+4\cdot 3 = 18$
Key Term Reference
 Commutative Property
 Appears in this related concept: Adding and Subtracting Polynomials
 arithmetic
 Appears in these related concepts: Sums and Series, Sums, Differences, Products, and Quotients, and Arithmetic Sequences
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 real number
 Appears in these related concepts: Solving Problems with Inequalities, Introduction to Complex Numbers, and Zeroes of Polynomial Functions with Real Coefficients
 real numbers
 Appears in these related concepts: Piecewise Functions, Introduction to Domain and Range, and Linear Inequalities
Sources
Boundless vets and curates highquality, openly licensed content from around the Internet. This particular resource used the following sources: