Problem 57 - Prealgebra

Question

Write the mathematical expressions that are equivalent to each of the following English phrases. The sum of a number and 2

Step-by-Step Solution

Answer

The expression is \( x + 2 \).

Step 1: Identify the Unknown Variable

Since we are referring to an unknown number, let's assign a variable to it. Typically, we use the letter \( x \) to represent an unknown. So, let's let \( x \) be the number.

Step 2: Understand the Operation

The phrase 'the sum of' indicates an addition operation. We are adding something to the number. The phrase 'and 2' means we are adding 2 to the unknown number \( x \).

Step 3: Formulate the Expression

To express 'the sum of a number and 2' mathematically, we write \( x + 2 \). This equation shows that we take the unknown number \( x \) and add 2 to it.

Key Concepts

Understanding Unknown Variables

In prealgebra, the concept of an unknown variable is fundamental. Variables serve as placeholders for numbers that are not specified. They allow us to write expressions and equations that can represent a wide range of values. Typically, letters such as \( x \), \( y \), or \( z \) are used as these symbols. In the context of the exercise, we referred to the phrase "a number," which signifies something we don't specifically know yet. Thus, we use \( x \) as our unknown variable.

• Why Use Variables? They help us generalize mathematical operations, letting us apply the same rule to any number instead of solving for a specific value.
• Common Variable Symbols: Letters like \( x \), \( y \), or \( z \) are standard representations, but any symbol could function as a variable.

Grasping the idea of an unknown variable is crucial because it enables you to tackle algebraic expressions effectively. You'll soon learn that these variables can take different values depending on the equation's context.

The Role of Addition Operation

The addition operation is one of the basic arithmetic functions you will frequently encounter in math. In our exercise, when the term "the sum of" appears, it indicates that you need to perform an addition. Addition involves combining two numbers to get a total. For example, when we say "the sum of a number and 2," it indicates that we add 2 to our unknown number.

• How Addition Works: It merges or combines the values of numbers, resulting in a larger number, the sum.
• Symbol for Addition: The addition operation is represented by a "+" sign.

So, translating the phrase "the sum of a number and 2" into a math expression results in \( x + 2 \). This denotes you start with whatever value \( x \) holds and then add 2 to it. Simple addition operations like this are foundational for more complex mathematical ideas.

Translating Mathematical Phrases

Taking English descriptions and converting them into mathematical expressions is an essential skill in math, known as translation of mathematical phrases. It involves pinpointing the mathematical operations described by words such as "sum," "difference," "product," or "quotient." In our case, the phrase "the sum of a number and 2" clearly needs to be turned into a mathematical expression.

• Identifying Phrases: Identify keywords that indicate operations, like "sum" for addition.
• Converting to Math: Rewrite the phrase using numbers and symbols instead of words.

For example, 'the sum of a number and 2' becomes \( x + 2 \), where \( x \) is your unknown number. Mastering this skill helps you seamlessly switch between verbal and numerical representation, which is vital for tackling problem-solving scenarios in math efficiently.