Problem 64 - Algebra for College Students

Question

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. The sum of a number and 4

Step-by-Step Solution

Answer

The algebraic expression is \(n + 4\).

Step 1: Identify Key Information

The problem asks us to translate an English phrase into an algebraic expression. We need to find the algebraic expression that represents 'the sum of a number and 4.' We will use the variable \(n\) to represent the unknown number.

Step 2: Understand the Word 'Sum'

In mathematics, the word 'sum' refers to the result of adding two or more quantities. In this case, we are adding a number, which we represent with \(n\), and the number 4.

Step 3: Translate the Phrase

To translate the phrase 'sum of a number and 4' into an algebraic expression, we write it as an addition expression: \(n + 4\). Here, \(n\) represents the unknown number and the operation is addition.

Key Concepts

Translating Phrases to Algebra

Translating English phrases into algebraic expressions is an essential skill in mathematics. Imagine coming across a phrase like 'the sum of a number and 4', and turning it into a formula you can work with. This process starts by identifying keywords in the phrase. Here, 'sum' is the keyword to focus on, indicating addition.

When translating phrases:

• Recognize key terms and their corresponding mathematical operations.
• Identify what represents unknown values, often using variables like \( n \).
• Arrange words into a logical mathematical expression.

It's like learning a new language, where you convert an entire sentence into a concise mathematical form. In this case, translating 'the sum of a number and 4' becomes simply \( n + 4 \). This helps in making complex problems simpler.

Mathematical Operations

Understanding mathematical operations is crucial when expressing phrases in algebra. Operations are the actions we perform, such as addition, subtraction, multiplication, and division. Each operation has key words associated with it.

For instance:

• 'Sum' indicates addition.
• 'Difference' points to subtraction.
• 'Product' refers to multiplication.
• 'Quotient' suggests division.

Knowing these keywords allows you to translate between everyday language and the precise language of mathematics efficiently. In our example, the term 'sum' clearly signals that we're dealing with addition. Therefore, the expression becomes \( n + 4 \). Understanding which operation to use is fundamental in building accurate algebraic expressions.

Unknown Variables

In algebra, we often use variables to represent unknown quantities. Variables are symbols, usually letters, that stand in place of numbers we don't know yet. Here, we use \( n \) as an unknown variable to signify a number.

• Variables make it possible to generalize problems.
• They allow us to work with expressions where the numbers can change.

Think of variables as placeholders. When we say 'a number', \( n \) can be any number we are trying to work out or solve for. In the phrase 'the sum of a number and 4', \( n \) represents that 'number'.This approach allows flexibility and precision in problem-solving. By learning how to manipulate these variables through various operations, you gain the ability to tackle a wide array of mathematical challenges.