Mathematical Phrase:
* Like a phrase in English: A collection of numbers, variables, and operation symbols that *doesn't* express a complete thought.
* Examples:
* *x + 5* (The sum of x and 5)
* *3y - 2* (Three times y minus two)
* *√(16)* (The square root of 16)
* Can't be judged true or false: They don't make a statement about equality or inequality.
Mathematical Sentence:
* Like a sentence in English: A complete mathematical statement that expresses a complete thought.
* Includes a relation symbol: This symbol compares two expressions, like:
* = (equals)
* ≠ (not equals)
* < (less than)
* > (greater than)
* ≤ (less than or equal to)
* ≥ (greater than or equal to)
* Examples:
* *x + 5 = 10* (The sum of x and 5 is equal to 10)
* *3y - 2 < 8* (Three times y minus two is less than 8)
* *√(16) = 4* (The square root of 16 is equal to 4)
* Can be judged true or false: You can determine if the relationship between the expressions is accurate.
In short:
* A mathematical phrase is just a part of a sentence; it's incomplete.
* A mathematical sentence is a complete thought with a relation symbol that allows it to be true or false.