On the number line, numbers get larger as they go from left to right. This spatial relationship can be used to explain the inequality symbols $$<$$ and $$>$$. If $$a$$ is to the left of $$b$$ on the number line, then $$a < b$$. If $$a$$ is to the right of $$b$$, then $$a > b$$.

Number Line and Inequalities

When two quantities have the same value, they are equal, and we connect them with an equal sign. The symbol $$=$$ is called the equal sign. The expression $$a = b$$ is read '$$a$$ is equal to $$b$$'.

Claude

To write algebraically, we use operation symbols along with numbers and variables. The four basic arithmetic operations and their common notations are:
- Addition: $$a + b$$ represents the sum of $$a$$ and $$b$$.
- Subtraction: $$a - b$$ represents the difference of $$a$$ and $$b$$.
- Multiplication: $$a \cdot b$$, $$ab$$, $$(a)(b)$$, $$(a)b$$, or $$a(b)$$ represents the product of $$a$$ and $$b$$.
- Division: $$a \div b$$, $$a/b$$, or $$\frac{a}{b}$$ represents the quotient of $$a$$ and $$b$$.

Arithmetic Operation Symbols

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OpenStax Intermediate Algebra

Equality Symbol

In mathematics, a sum is the result of an addition operation. When two or more numbers or quantities are added together, the final value obtained is called the sum. For example, when adding $$a$$ and $$b$$, the result is the sum of $$a$$ and $$b$$.

Definition of Sum

A difference is the result obtained from a subtraction operation. It represents how much one number differs from another. For example, when subtracting $$b$$ from $$a$$, the resulting value is the difference of $$a$$ and $$b$$.

Definition of Difference

A product is the result of a multiplication operation. When two or more numbers or variables are multiplied, the final value is known as the product. For instance, in the operation of multiplying $$a$$ and $$b$$, the outcome is the product of $$a$$ and $$b$$.

Definition of Product

A quotient is the result of dividing one number by another. It represents the number of times the divisor is contained within the dividend. When dividing $$a$$ by $$b$$, the resulting value is the quotient of $$a$$ and $$b$$.

Definition of Quotient

Division can be written using various mathematical notations, such as the standard division symbol ($$a \div b = c$$), a fraction bar ($$\frac{a}{b} = c$$), or the traditional long division bracket. In all these formats, the vocabulary remains consistent: the number being divided ($$a$$) is the **dividend**, the number dividing into it ($$b$$) is the **divisor**, and the result ($$c$$) is the **quotient**. For example, in long division, the divisor is written outside the bracket, the dividend inside, and the quotient on top.

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