Summary: Using the Language of Algebra

Key Concepts

Operation	Notation	Say:	The result is…
Addition	$a+b$	$a$ plus $b$	the sum of $a$ and $b$
Multiplication	$a\cdot b,\left(a\right)\left(b\right),\left(a\right)b,a\left(b\right)$	$a$ times $b$	the product of $a$ and $b$
Subtraction	$a-b$	$a$ minus $b$	the difference of $a$ and $b$
Division	$a\div b,a/b,\frac{a}{b},b\overline{)a}$	$a$ divided by $b$	the quotient of $a$ and $b$

Equality Symbol
- $a=b$ is read as $a$ is equal to $b$
- The symbol $=$ is called the equal sign.
Inequality
- [latex]a
- $a$ is to the left of $b$ on the number line
- $a>b$ is read $a$ is greater than $b$
- $a$ is to the right of $b$ on the number line

Exponential Notation
- For any expression ${a}^{n}$ is a factor multiplied by itself $n$ times, if $n$ is a positive integer.
- ${a}^{n}$ means multiply $n$ factors of $a$
- The expression of ${a}^{n}$ is read $a$ to the $n$ th power.

Order of Operations When simplifying mathematical expressions perform the operations in the following order:

Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
Exponents: Simplify all expressions with exponents.
Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.

expressions: An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

equation: An equation is made up of two expressions connected by an equal sign.