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⋅b,(a)(b),(a)b,a(b) a times b the product of a and b
Subtraction a−b a minus b the difference of a and b
Division a÷b,a/b,ab,b)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 lineAn image of a number line. The value a is placed on the left hand side of the number line, and the value b is placed in the center of the number line.
    • a>b is read a is greater than b
    • a is to the right of b on the number lineAn image of a number line. The value b is placed on the left hand side of the number line, and the value a is placed in the center of the number line.
Algebraic Notation Say
a=b a is equal to b
a≠b a is not equal to b
[latex]a a is less than b
a>b a is greater than b
a≤b a is less than or equal to b
a≥b a is greater than or equal to b
  • Exponential Notation
    • For any expression an is a factor multiplied by itself n times, if n is a positive integer.
    • an means multiply n factors of aAt the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as “base” and the letter n is labeled as “exponent”. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.
    • The expression of an is read a to the nth power.

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

  1. Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
  2. Exponents: Simplify all expressions with exponents.
  3. Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
  4. 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.