Problem 33 - Prealgebra

Question

Write a numerical expression for each verbal phrase. the cost of 3 notebooks at \(\$ 6\) each

Step-by-Step Solution

Answer

Expression: \(3 \times 6\) resulting in $18.

Step 1: Understand the Problem

We need to find the total cost when purchasing 3 notebooks, with each priced at $6.

Step 2: Identify the Mathematical Operation

To find the total cost, we should multiply the price of one notebook by the number of notebooks.

Step 3: Construct the Numerical Expression

Since each notebook costs $6 and there are 3 notebooks, the total cost can be expressed as: \(3 \times 6\).

Step 4: Simplify the Expression

Perform the multiplication: \(3 \times 6 = 18\). Thus, the total cost of the notebooks is $18.

Key Concepts

Understanding Multiplication in Context

Multiplication is one of the basic operations in mathematics that helps to quickly determine the total of equal groups. In the context of this problem, you can think of each notebook costing $6 as a single group, and since we have 3 notebooks, we have 3 groups in total.
To use multiplication effectively, you need to identify when it is the appropriate operation. Several scenarios call for multiplication, such as when you're calculating repeated addition or determining the area of a rectangular space. In the given exercise, multiplication helps us find out the total cost easily.
If the price of a single item is known, and the number of items is given, multiplication offers a quick way to calculate the overall cost or total quantity in such situations.

Approaching the Problem Solution

Problem solving in mathematics involves several steps, each requiring careful consideration. Let's break down this exercise into simple actions that lead us to the answer:

• Understanding the Problem: First, identify what you need to find. Here, it's the total cost for 3 notebooks.
• Selecting the Right Operation: Next, choose the mathematical operation needed to find the solution. Since the price per item and the number of items are known, multiplication will help us here.
• Constructing an Expression: Formulate a numerical expression using the numbers involved, which in this case means writing down 3 multiplied by 6.
• Solving the Expression: Finally, perform the multiplication to arrive at the solution.

This structured approach ensures accuracy and clarity, making problem solving manageable and straightforward.

Insight into Mathematical Operations

Understanding mathematical operations is crucial for solving various problems, including the one involving notebooks. These operations—addition, subtraction, multiplication, and division—are building blocks for more complex mathematical concepts.
Knowing when to use each mathematical operation is vital. For instance, multiplication is typically used when you want to add the same number multiple times. Division, on the other hand, is useful when you need to split a quantity into equal parts.
Using the correct operations is not just about memorizing rules, but also about understanding the problem context. In our example, knowing that each notebook costs $6 and you're buying 3 allows you to use multiplication because you are essentially adding $6 three times. By mastering these basic operations, you pave the way for understanding more complex mathematical concepts in future learning endeavors.