Problem 13 - Prealgebra

Question

Write a numerical expression for each verbal phrase. the sum of eleven and sixteen

Step-by-Step Solution

Answer

The numerical expression is \(11 + 16\).

Step 1: Identify Key Elements

First, we need to identify the key mathematical operation and numbers from the verbal phrase. The phrase given is 'the sum of eleven and sixteen'. Here, 'sum' indicates addition, and the numbers involved are eleven (11) and sixteen (16).

Step 2: Translate into Mathematical Expression

Translate the verbal phrase into a mathematical expression based on the identified operation and numbers. Since 'sum' implies addition, the expression becomes: 11 + 16.

Step 3: Write the Numerical Expression

Write down the numerical expression obtained from the translation of the verbal phrase: \(11 + 16\).

Key Concepts

Addition

Addition is a fundamental mathematical operation that combines two or more numbers to get their total. It is one of the four basic operations in arithmetic, alongside subtraction, multiplication, and division. When you hear the term 'sum,' it refers specifically to the result of adding two or more numbers together. For example:

• 11 + 16 = 27
• 3 + 4 = 7
• 20 + 5 = 25

In our original exercise, 'the sum of eleven and sixteen' indicates the operation of addition. This means you would need to add 11 and 16 together to find the sum. Addition is a straightforward yet powerful tool that helps us solve numerous real-world problems, from balancing a checkbook to computing the total mileage of a trip. Understanding how and when to use it is crucial in math.

Verbal Phrases

Verbal phrases are expressions that describe mathematical operations using words rather than numbers or symbols. They are often used in word problems to convey mathematical terms and operations (such as addition, subtraction, etc.) clearly and contextually. In math, translating these verbal phrases into numerical expressions is essential to solving the problem they describe. For instance, when you encounter a verbal phrase like 'the sum of eleven and sixteen,' it describes using addition. Recognizing the keywords in verbal phrases, like 'sum' for addition or 'difference' for subtraction, helps you understand what mathematical operation to apply. Verbal phrases are not only found in math problems but also in our everyday language, providing a bridge between spoken language and mathematical notation. Getting comfortable with them allows you to translate real-world problems into mathematical language effectively.

Translating Expressions

Translating expressions involves converting verbal descriptions into a form that can be manipulated mathematically. This process is essential for solving word problems, where the first step is often shifting from words to numerical symbols. Let's break it down:

• Identify key terms, like 'sum,' 'product,' and 'difference.'
• Determine the mathematical operation these terms suggest—for example, 'sum' points to addition.
• Convert numbers and operations into a clear mathematical expression.

In the exercise provided, 'the sum of eleven and sixteen' translates simply to the mathematical expression 11 + 16. By mastering the skill of translating verbal phrases into numerical expressions, you improve your ability to tackle a variety of math problems efficiently. This practice often involves understanding both vocabulary and the specific context of the problem presented.