Problem 19 - Fundamentals of Mathematics

Question

Translate each phrase or sentence to a mathematical expression or equation. Negative nine added to a number.

Step-by-Step Solution

Answer

The expression is \( -9 + x \).

Step 1: Identify Variables

The problem refers to 'a number' that is unspecified. To translate this into a mathematical expression, let's use a variable to represent this number, typically we use the variable \( x \).

Step 2: Understand the Operation

The phrase 'added to' indicates addition. We'll represent the operation of adding something to our variable.

Step 3: Translate Each Part

The phrase 'Negative nine added to a number' translates mathematically to: negative nine, which is \( -9 \), added to the variable \( x \), written as \( -9 + x \).

Step 4: Write the Expression

Combine the understood components into a mathematical expression: \( -9 + x \).

Key Concepts

Variables in Mathematics

In mathematics, variables are used as placeholders to signify unknown values or numbers. They are symbolized by letters, such as \( x \), \( y \), or \( z \). Using variables allows us to write expressions and equations that can be solved or simplified. For example, if there's a phrase indicating 'an unknown number,' we can use a variable like \( x \). This abstract representation enables us to perform operations without specifically knowing the numeric value.

Variables provide the flexibility to solve a range of problems steadily.

They help generalize equations, making it possible to perform operations on them regardless of the specific numbers involved.

This way, variables in mathematics are essential for creating expressions that can express general rules or principles applicable to many situations.

Addition Operation

Addition is one of the basic operations in mathematics, signified by the plus sign \( + \). When a problem mentions 'added to,' it refers to the operation of addition, which combines two numbers or terms into a sum. Let's dive into how this applies practically.
If you have a phrase like 'negative nine added to a number,' the word 'added' tells us to perform addition.

• The 'negative nine' can be written as \( -9 \).
• The 'number' is represented by a variable, say \( x \).
• Hence, the expression is written as \( -9 + x \).

Through addition, you can combine both \( -9 \) and \( x \) into a complete expression, which reflects the relationship conveyed in the original phrase.

Mathematical Expressions

Mathematical expressions are combinations of numbers, variables, and operators that reflect a particular mathematical situation. They offer a way to translate real-world words or phrases into a mathematical format that can be managed and solved.

• Expressions like \( -9 + x \) are crafted by comprehending the words and mapping them to operations and variables.
• They must follow the correct order and structure, ensuring that each part—like numbers, variables, and operations—is represented accurately.

Creating mathematical expressions requires understanding the terms used in the phrase and then forming a coherent equation or expression. This translation process is fundamental in math as it sets the basis for solving problems and understanding relationships between different mathematical components.