Problem 3 - Fundamentals of Mathematics

Question

Translate each phrase or sentence into a mathematical expression or equation. An unknown quantity less fourteen.

Step-by-Step Solution

Answer

The expression is x - 14.

Step 1: Identify the Unknown Quantity

Let the unknown quantity be represented by a variable. Commonly, the variable 'x' is used. So, we start by letting the unknown quantity be x.

Step 2: Expression of Less Than

The phrase 'less fourteen' indicates that we should subtract fourteen from the variable (unknown quantity). This is a common way of translating phrases into mathematical expressions where 'less' means subtraction.

Step 3: Combine to Form a Mathematical Expression

Combine the steps from above to form the mathematical expression: The unknown quantity x less fourteen, which translates to x - 14.

Key Concepts

Unknown Quantities

In math, terms like "unknown quantity" often pop up. They refer to values we're trying to find but don't know yet. When you see an exercise saying "an unknown quantity less fourteen," it doesn’t give a number to work with off the bat. This is where variables come to the rescue. They act as placeholders that stand in for these mysterious numbers.
To solve problems in math, acknowledging unknown quantities is crucial. It allows us to shape questions into forms that can be analyzed and solved. This way, rather than guessing numbers, we use logical steps to uncover them.

Mathematical Expressions

A mathematical expression is a combination of numbers, variables, and operators like plus or minus signs. It's like a sentence in math language representing a relationship or a rule.
When we take the phrase "an unknown quantity less fourteen," it needs to be converted into a mathematical expression. The word "less" signifies subtraction, so the expression should show this relationship. You start with the unknown quantity, which is our variable, and use "less" to indicate a subtraction of fourteen.
Thus, the expression becomes the unknown quantity minus 14, or in algebraic form, it’s represented as \(x - 14\). This expression summarizes the given verbal phrase in mathematical terms.

Variables in Algebra

Variables are symbols that denote unknown numbers or quantities in algebra. They usually take the form of letters like \(x\), \(y\), or \(z\). In the context of "an unknown quantity less fourteen," \(x\) is often used as the variable.
These variables are not just stand-ins; they allow us to perform calculations and solve equations. With them, abstract problems transform into manageable expressions and equations that can be worked through systematically.
By letting \(x\) represent the unknown quantity, we then adjust this with basic arithmetic operations, like subtraction, to mirror the problem's statement. This use of variables is fundamental in simplifying and solving algebraic problems. They help us bridge gaps from unknown to known through solution processes.