Problem 11 - Prealgebra

Question

Write a numerical expression for each verbal phrase. the product of six and eight

Step-by-Step Solution

Answer

The numerical expression is \(6 \times 8\).

Step 1: Understanding the Verbal Phrase

The verbal phrase given is "the product of six and eight." In mathematics, the word "product" refers to the result of multiplying two numbers together.

Step 2: Identifying the Numbers

In the given phrase, the two numbers that we need to multiply are six and eight. These are the operands in our multiplication operation.

Step 3: Writing the Numerical Expression

To express the product of six and eight as a numerical expression, we write it in mathematical form as follows: \(6 \times 8\). This expression uses the multiplication operator \(\times\) to indicate the product of the numbers.

Step 4: Evaluating the Expression (Optional)

If we need to calculate the product, we perform the multiplication: \(6 \times 8 = 48\). However, since the exercise only asks for a numerical expression, this step is optional.

Key Concepts

Verbal Phrases

Verbal phrases are a way to express mathematical ideas using words. When you're given a verbal phrase in a problem, it's your job to translate those words into a mathematical expression. This is an essential skill in math, as it bridges language and numbers. For example, the verbal phrase "the sum of five and three" can be turned into a numerical expression as simply as writing 5 + 3. Some common clues in these phrases indicate specific operations:

• "Sum" typically signifies addition.
• "Difference" usually means subtraction.
• "Product" indicates multiplication.
• "Quotient" pertains to division.

Understanding these keywords allows you to quickly identify which mathematical operation to use, simplifying the process of solving any problem involving verbal phrases.

Mathematical Operations

Mathematical operations are the building blocks of numerical expressions. They are the processes by which numbers are combined or manipulated to calculate a result. The primary operations include addition, subtraction, multiplication, and division. Here's how each operation functions in the context of numerical expressions:

• Addition (+): Combines numbers to find a total, known as the sum.
• Subtraction (-): Determines the difference between numbers by removing one quantity from another.
• Multiplication (×): Involves finding the product by adding a number to itself a specified number of times. This is helpful in scenarios involving repeated addition.
• Division (÷): Splits a number into equal parts, expressing how many times one number is contained within another.

Gaining a solid grasp of these operations is crucial for succeeding in mathematics, as they form the basis for more complex problem-solving.

Multiplication Concepts

The concept of multiplication extends beyond just repeated addition. In mathematics, it refers to the process of scaling one number by another. This can involve real-world applications, like calculating areas or considering rates. Here's how multiplication becomes more than mere repetition:

• Scaling: When you multiply two numbers, the first number is increased by the number of times indicated by the second number.
• Geometric Interpretation: In geometry, multiplying length and width yields area, showcasing how multiplication calculates two-dimensional space.
• Comparison: Multiplication allows for expressing quantities in relation to others, demonstrating proportional relationships.

These concepts connect multiplication to various practical and theoretical scenarios, making it an indispensable tool in both everyday calculations and advanced mathematics. Understanding these broader perspectives allows students to see multiplication not just as a rote operation, but a versatile and meaningful mathematical concept.