Problem 58 - Prealgebra

Question

Write the mathematical expressions that are equivalent to each of the following English phrases. The sum of a number and 5

Step-by-Step Solution

Answer

The expression is \( x + 5 \).

Step 1: Identify the Unknown Number

In the given problem, there is a reference to a quantity that is unknown. We will represent this unknown number using the variable \( x \).

Step 2: Understand the Phrase 'The Sum Of'

The phrase 'the sum of' indicates that we need to add two values together. Therefore, we will be performing an addition operation.

Step 3: Set Up the Expression

According to the phrase given, we are tasked with finding the sum of the unknown number \( x \) and the number 5.

Step 4: Write the Mathematical Expression

Combine your understanding from the previous steps to form the expression. The sum of a number \( x \) and 5 is written mathematically as \( x + 5 \).

Key Concepts

Variables

In algebra, a variable is a symbol used to represent an unknown value in mathematical expressions or equations. Typically, variables are denoted by letters such as \( x \), \( y \), \( z \), etc.
In our example, the variable is \( x \) and it represents a number that we want to find.
Variables are crucial because they allow us to work with general statements and equations.

• They help us solve problems where the exact number isn't given initially.
• They are placeholders that can take on different values, making them flexible and powerful for calculations and problem-solving.

Understanding variables gives you the ability to set up and manipulate various mathematical models. This skill is essential in solving algebraic equations.

Addition

Addition is one of the fundamental arithmetic operations, and it combines two or more numbers to give a total or sum.
The process of addition is indicated by the plus sign \(+\).

• It's a straightforward operation that involves starting with one number and counting up.
• It's the basis for many other operations and is essential for understanding more complex math topics.

In algebra, knowing how to perform addition with variables is important.
For example, in the exercise "the sum of a number and 5," we recognize that the operation we need to perform is adding the unknown variable \( x \) to the number 5. This is written as \( x + 5 \).
Mastery of addition allows you to create and simplify expressions and is foundational for grasping other mathematical operations.

Mathematical Phrases

Mathematical phrases are expressions that describe mathematical operations or relationships using words.
They are how we translate real-world problems into mathematical equations.

• Phrases such as "the sum of" indicate the operation needed. In this case, it directs you to perform addition.
• Understanding these phrases is critical for setting up equations that reflect the problem you are solving.

For the given exercise, understanding "the sum of a number and 5" helps us know that we're looking for an expression where a number (the unknown variable) is added to 5.
By associating words with operations, you can craft accurate mathematical expressions, facilitating problem-solving in algebra.
This ability translates verbal statements into mathematical logic, which is a vital skill in both academic settings and real-life applications.