Definition
Symbolic representation
A symbolic representation shows a mathematical idea with agreed symbols and structure.
What it means
Symbols pack a mathematical idea into a compact form. A picture of four groups with three objects in each can be written as 4 × 3 = 12. The symbols are useful only when you know what each mark means and how the marks are arranged.
Remember it
Symbols are math’s compact code; structure tells you how to read it.
Example
The words “a number is 5 more than 12” can be represented symbolically as n = 12 + 5.
Watch for
A string of signs is not a useful symbolic representation just because it looks mathematical; it must follow agreed meanings and structure.
Common mix-up
A symbol is one mark. A symbolic representation is the whole expression, equation, or statement built from symbols.
Exact meaning
A symbolic representation uses agreed mathematical symbols—such as numerals, operation signs, relation signs, variables, and brackets—to represent quantities, operations, or relationships.