Summary: Using the Language of Algebra

Key Concepts

Operation Notation Say: The result is…
Addition [latex]a+b[/latex] [latex]a[/latex] plus [latex]b[/latex] the sum of [latex]a[/latex] and [latex]b[/latex]
Multiplication [latex]a\cdot b,\left(a\right)\left(b\right),\left(a\right)b,a\left(b\right)[/latex] [latex]a[/latex] times [latex]b[/latex] the product of [latex]a[/latex] and [latex]b[/latex]
Subtraction [latex]a-b[/latex] [latex]a[/latex] minus [latex]b[/latex] the difference of [latex]a[/latex] and [latex]b[/latex]
Division [latex]a\div b,a/b,\frac{a}{b},b\overline{)a}[/latex] [latex]a[/latex] divided by [latex]b[/latex] the quotient of [latex]a[/latex] and [latex]b[/latex]
  • Equality Symbol
    • [latex]a=b[/latex] is read as [latex]a[/latex] is equal to [latex]b[/latex]
    • The symbol [latex]=[/latex] is called the equal sign.
  • Inequality
    • [latex]a<b[/latex] is read [latex]a[/latex] is less than [latex]b[/latex]
    • [latex]a[/latex] is to the left of [latex]b[/latex] on the number line..
    • [latex]a>b[/latex] is read [latex]a[/latex] is greater than [latex]b[/latex]
    • [latex]a[/latex] is to the right of [latex]b[/latex] on the number line..
Algebraic Notation Say
[latex]a=b[/latex] [latex]a[/latex] is equal to [latex]b[/latex]
[latex]a\ne b[/latex] [latex]a[/latex] is not equal to [latex]b[/latex]
[latex]a<b[/latex] [latex]a[/latex] is less than [latex]b[/latex]
[latex]a>b[/latex] [latex]a[/latex] is greater than [latex]b[/latex]
[latex]a\le b[/latex] [latex]a[/latex] is less than or equal to [latex]b[/latex]
[latex]a\ge b[/latex] [latex]a[/latex] is greater than or equal to [latex]b[/latex]
  • Exponential Notation
    • For any expression [latex]{a}^{n}[/latex] is a factor multiplied by itself [latex]n[/latex] times, if [latex]n[/latex] is a positive integer.
    • [latex]{a}^{n}[/latex] means multiply [latex]n[/latex] factors of [latex]a[/latex]..
    • The expression of [latex]{a}^{n}[/latex] is read [latex]a[/latex] to the [latex]n\text{th}[/latex] 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.

Glossary

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.