Problem 27 - Prealgebra

Question

Write a numerical expression for each verbal phrase. seven increased by two

Step-by-Step Solution

Answer

The numerical expression is \(7 + 2\).

Step 1: Identify Numbers in the Phrase

The verbal phrase given is "seven increased by two." Here we identify the numbers mentioned: seven and two. These numbers will be part of our numerical expression.

Step 2: Determine Operation from the Phrase

The phrase "increased by" indicates an addition operation. When a number is increased by another number, we perform addition.

Step 3: Write the Numerical Expression

Using the numbers identified and the operation determined, we write the numerical expression. Since seven is increased by two, we write the expression as: \(7 + 2\).

Key Concepts

Verbal Phrases

Verbal phrases are ways of expressing mathematical operations using words. Understanding these phrases is crucial in translating word problems into numerical expressions. For this exercise, the verbal phrase "seven increased by two" is an example. Here, the couple of simple words encapsulates a mathematical operation.
A verbal phrase often contains keywords that signal specific math operations. These may include words like "increased by," "decreased by," "more than," "less than," and "times." Recognizing these keywords helps in determining which operation—such as addition, subtraction, multiplication, or division—is required.

• Increased by usually signals addition.
• Decreased by typically indicates subtraction.
• Times refers to multiplication.
• Divided by suggests division.

Learning to decode these verbal cues is a critical skill in problem-solving. It allows you to convert everyday language into the language of mathematics, making it easier to solve real-world problems.

Addition Operation

The addition operation is one of the four fundamental arithmetic operations in mathematics. When you hear phrases like "increased by" or "sum of," it tells you that addition is involved. In the given example, the phrase "seven increased by two" is directly associated with adding two numbers together.
Addition is straightforward: it involves combining two or more numbers to find their total. Numerically, this is represented with the "plus" sign "+". Thus, "seven increased by two" becomes the expression "7 + 2."
Understanding addition is essential because it forms the basis for more complex arithmetic operations. Here are a few additional points to consider:

• Addition is commutative, meaning the order of numbers doesn’t affect the sum: \(a + b = b + a\).
• The sum of any number and zero is the number itself: \(a + 0 = a\).

Mastery of addition not only aids in solving elementary problems but also builds a strong foundation for tackling more advanced mathematical challenges.

Writing Expressions From Verbal Cues

Writing expressions from verbal cues requires converting words into numbers and operations. To achieve this, follow a process of identifying numbers and operations as signaled by keywords in the verbal phrase. For instance, the phrase "seven increased by two" sets a clear task.
First, identify the numbers mentioned. Here, "seven" and "two" are the numbers to be used. Next, pinpoint the operation: "increased by" indicates addition. With this information, you can write the numerical expression: \(7 + 2\).
This transformation is akin to decoding a puzzle. Here’s how you can approach similar tasks:

• Spot Keywords: Look for keywords that indicate operations.
• Identify Numbers: Write down all numbers mentioned in the phrase.
• Create the Expression: Combine the identified numbers with the operation.

Practicing these steps will help you quickly and accurately convert verbal descriptions into numerical expressions, a skill useful in a wide range of math problems.