Whats the difference between an algebraic expression and a verbal expression?

Here's the breakdown of the difference between algebraic and verbal expressions:

Algebraic Expressions

* Use symbols: They use letters (variables) and numbers to represent quantities.

* Operations: Incorporate mathematical operations like addition, subtraction, multiplication, division, exponents, etc.

* Examples:

* `3x + 5`

* `y^2 - 2`

* `(a + b)/c`

Verbal Expressions

* Use words: They describe mathematical concepts using everyday language.

* Represent relationships: They express how quantities are related to each other.

* Examples:

* "Three times a number plus five"

* "The square of a number minus two"

* "The sum of two numbers divided by a third number"

Connecting the Two

The key connection is that algebraic expressions represent verbal expressions. We translate words into symbols to create algebraic expressions. For instance:

* Verbal: "Three times a number plus five"

* Algebraic: `3x + 5` (where 'x' represents the unknown number)

In Summary

* Verbal expressions: Use words to describe mathematical ideas.

* Algebraic expressions: Use symbols and operations to represent those ideas in a compact and precise way.