Problem 41 - Beginning and Intermediate Algebra

Question

41-54 Write each word phrase as an algebraic expression, using \(x\) as the variable. Twelve times a number

Step-by-Step Solution

Answer

12x

Step 1: Identify the keyword

The keyword in the phrase 'Twelve times a number' is 'times,' which indicates multiplication.

Step 2: Determine the number

The phrase refers to 'a number,' which will be represented by the variable \(x\).

Step 3: Formulate the expression

Combine the keyword 'times' with the determined number \(x\). Therefore, 'Twelve times a number' can be written as \(12 \cdot x\).

Step 4: Write the final algebraic expression

The final algebraic expression is \(12x\).

Key Concepts

Multiplication

Multiplication in algebra involves combining numbers and variables. When you see words like 'times,' it means you should multiply. For example, 'Twelve times a number,' means you multiply twelve by a number.

Example: If the number is represented by the variable \( x \), then twelve times this number is expressed as \( 12 \cdot x \) or simply \( 12x \). Multiplication helps to simplify and condense expressions, making them easier to work with.

Remember:

• The keyword 'times' signals multiplication.
• Multiplication can be shown with a dot (\( \cdot \)) or by placing numbers and variables next to each other (\( 12x \)).

Understanding this concept will make it easier to translate word phrases into algebraic expressions.

Variables

In algebra, variables are symbols that represent numbers. Typically, they are letters like \( x \) or \( y \). Variables allow us to write expressions and equations to solve various problems.

In Examples:

• 'A number' in the phrase 'Twelve times a number' is represented by a variable, let's say \( x \).

Important points about variables:

• Variables stand in for unknown quantities or values that can change.
• Using variables makes it easy to generalize and solve problems with different numbers.
• They help in forming expressions which can be manipulated to find solutions.

Becoming familiar with variables helps you easily formulate and manipulate algebraic expressions.

Writing Expressions

Writing algebraic expressions involves translating word phrases into mathematical language. You identify keywords and use variables to form expressions.

Let's break it down:

• First, identify the operation indicated by the keywords ('times' means multiplication).
• Next, identify what needs to be represented as a variable ('a number' becomes \( x \)).
• Finally, combine these elements to form the expression (\( 12 \cdot x \), or simply \( 12x \)).

Example:
'Twelve times a number' translates to \( 12x \).
Key Tips:

• The expression you write should clearly reflect the word phrase.
• Make sure the operations and the variables are correctly represented.
• Practice by breaking down each word phrase to ensure you form accurate expressions.

With practice, writing algebraic expressions becomes second nature.