Operations are essentially means of manipulating numbers in some specific way. There are plenty of operations across all of mathematics, but this section will introduce the basic Arithmetic Operations: add, subtract, multiply, and divide.
“Arithmetic” really just refers to these operations; arithmetic is addition, subtraction, multiplication, and division.
Operations are performed on terms. \color{cyan}{\textnormal{Terms}} are most commonly numbers, but as you’ll see in algebra, may be variable quantities (like x or y).
Operations are most commonly shown as a term, then an operation, then another term, such as:
2 + 2
This mathematical phrase is known as an \color{cyan}{\textnormal{expression}}, which is most simply a couple of terms with an operation performed on them.
Now, you may show equality between two expressions via an \color{cyan}{\textnormal{equal sign}}. An equal sign (that is, =) denotes that the two expressions represent the same exact quantity. So, when you see something like: 2 + 2 = 4, this states that the expression 2+2 is equal to 4. This mathematical sentence is known as an \color{cyan}{\textnormal{equation}}.
The Arithmetic Operations are addition, subtraction, multiplication, and division. These operations are the basis of a large portion of mathematics, and will be explored in the sections below.
Now, some extra details can be added to each of these operations.
Each term in an expression have a particular name to explicitly refer to them. In general, these terms are:
As an example, in 2 + 3, the operand describes the 2 and the 3, the operator describes the +, and the operation is addition!
Also, the result of the operation has special names depending on the operation. Plus, each operation refers to their operands differently.
This table summarizes the arithmetic operations.
| Operation | Operator | Operands | Result | Syntax | Inverse |
|---|---|---|---|---|---|
| Addition | + | Addend, summand | Sum | addend + addend = sum | Subtraction |
| Subtraction | - | Subtrahend then subtrahere | Difference | subtrahend - subtrahere = difference | Addition |
| Multiplication | *, \times, \cdot | Factor, multiplicand, multiplier | Product | factor \cdot factor = product | Division |
| Division | /, \div | Divisor then dividend. | Quotient | divisor / dividend = quotient | Multiplication |
Arithmetic is performed differently depending on the number.
In many cases with smaller numbers, you’ll have memorized the results so the amount of work shown will be minimal. Many situations are “taken for granted” in maths simply because they have been proven time-and-time-again, like 2+2=4 or 10+10=20. There’s no need to explicitly show the work because it will have been shown often.
For larger numbers, or if the result isn’t easily calculable, operations would need to be calculated by hand. To show your work on how to perform these operations by hand, you will use something called the “long-form” methods of computing the result of these operations. These will be introduced in their respective section (e.g., Long-Form Addition will be presented in Addition!) and will detail how to show the work properly.
| Previous | Next |
|---|---|
| ← 0.1.3: Characteristics of Numbers | 0.2.2: Addition → |