## Basic Operations

The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.

**In basic mathematics there are many ways of saying the same thing:**

### LEARNING OBJECTIVES

Calculate the sum, difference, product, and quotient of positive whole numbers.

### KEY TAKEAWAYS

### 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.

### Key Terms

**associative**: Referring to a mathematical operation that yields the same result regardless of the grouping of the elements.**commutative**: Referring to a binary operation in which changing the order of the operands does not change the result (e.g., addition and multiplication).**product**: The result of multiplying two quantities.**quotient**: The result of dividing one quantity by another.**sum**: The result of adding two quantities**difference**: The result of subtracting one quantity from another.

#### 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:

1+1=2

### 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:

1-1=0

### 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.

### 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: