Problem 32 - Prealgebra

Question

Write a numerical expression for each verbal phrase. four less than eighteen

Step-by-Step Solution

Answer

The numerical expression is \(18 - 4 = 14\).

Step 1: Identify the Numbers Involved

In the phrase 'four less than eighteen,' the numbers involved are 18 and 4.

Step 2: Understand the Phrase 'Less Than'

The phrase 'less than' typically means that a subtraction operation is required. In this context, it means subtract the first number mentioned from the second number.

Step 3: Write the Numerical Expression

Using the understanding from the previous steps, 'four less than eighteen' translates to the expression: \(18 - 4\).

Step 4: Simplify the Expression

Now, perform the arithmetic operation. Subtract 4 from 18 to simplify the expression: \(18 - 4 = 14\).

Key Concepts

Understanding Verbal Phrases

Verbal phrases are descriptions or statements involving mathematical operations, articulated in words. In math problems, students often encounter phrases that describe arithmetic operations without directly naming them. This can be tricky, as understanding the language becomes crucial. Take the example: "four less than eighteen." Here, "less than" hints at subtraction. When reading such a phrase, identifying key words or signals is vital.

• "Sum" or "plus" often means addition.
• "Difference" or "less than" indicates subtraction.
• "Product" implies multiplication.
• "Quotient" suggests division.

Recognizing these cues helps translate verbal descriptions into numerical expressions, forming the foundation for effectively solving arithmetic problems.
With practice, students can seamlessly convert verbal phrases into math expressions.

The Art of Subtraction

Subtraction is one of the basic arithmetic operations that involves taking away or finding the difference between numbers. In a subtraction operation, two numbers are involved: the minuend and the subtrahend. The minuend is the starting number from which you subtract; the subtrahend is the amount you subtract from the minuend.

For example, in "four less than eighteen," 18 is the minuend, and 4 is the subtrahend, forming the operation: \[18 - 4\]The result of subtraction is often called the difference.

Key facts about Subtraction:

• It is not commutative, meaning the order of the numbers matters. \(a - b\) is not the same as \(b - a\).
• It is the inverse of addition. If \( a + b = c\), then \(c - b = a\).
• Subtraction results can also become negative if the subtrahend is larger than the minuend.

Mastery of subtraction is essential as it's frequently used in daily math operations.

Basics of Arithmetic Operations

Arithmetic operations are the foundational building blocks of mathematics. They include addition, subtraction, multiplication, and division. Mastery of these operations is crucial for solving both simple and complex math problems.

Let's dive into these operations:

• Addition: Combining two numbers to get a total. Example: \(3 + 5 = 8\).
• Subtraction: Taking one number away from another. Example: \(18 - 4 = 14\).
• Multiplication: Repeated addition of a number. Example: \(4 \times 3 = 12\).
• Division: Splitting a number into equal parts. Example: \(12 \div 3 = 4\).

Understanding these operations involves more than just memorizing facts. It's about recognizing patterns and logical relationships between numbers.

Practicing different arithmetic operations helps build problem-solving skills and boosts overall math confidence.