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Variables and Expressions

Expressions with Variables

If the length of one side of a square is , the perimeter of the square can be represented as . By using variables, we can express quantities and the relationships between them in simple mathematical expressions.

Omitting Multiplication and Division Symbols


The volume of a rectangular prism is calculated as
(length) (width) (height),
which can be expressed as . Using exponents, this becomes . This expression can further omit the multiplication symbol, resulting in .

In general, the following rules are applied when omitting the multiplication symbol in expressions involving variables:

Rules for Omitting the Multiplication Symbol

  1. In products involving numbers and variables or variables alone, the multiplication symbol is omitted.
  2. When multiplying numbers and variables, the number is written before the variable. In cases involving or , the is omitted.
  3. When multiplying variables, the variables are typically written in alphabetical order. If the same variable is multiplied, it is expressed using exponents.

Omitting the Division Symbol

The expression can be simplified by omitting the division symbol and written as .

In general, when omitting the division symbol in expressions involving variables, the following rule is applied:

Rule for Omitting the Division Symbol

The division operation is expressed in fractional form:
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