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Chapter 1: Problem 14

Identify the factors and the product. $$4 \cdot 3 \cdot 8=96$$

Short Answer

Expert verified
Factors are 4, 3, and 8. The product is 96.

Step by step solution

01

Identify Given Factors

The factors in the given expression are the numbers that are being multiplied together. In this case, the factors are 4, 3, and 8.
02

Understand the Product

The product is the result of multiplying the factors together. Here, it is given that the product is 96.
03

Verify the Product

To ensure accuracy, multiply the factors together: \[4 \times 3 = 12\], then multiply the result by the next factor: \[12 \times 8 = 96\]. The product is verified as 96.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factors
In mathematics, a factor is a number that divides another number without leaving a remainder. When identifying factors in multiplication, you focus on the numbers being multiplied together. For instance, in the expression \(4 \cdot 3 \cdot 8 \), the numbers 4, 3, and 8 are considered factors. Each of these numbers can be multiplied step-by-step to find the product. Factors play a crucial role in multiplication, as they form the basic building blocks of the product. To identify factors in any multiplication problem, simply look for the numbers connected by the multiplication operator (\cdot).
For example:
  • In the expression \(5 \cdot 6 = 30\), the factors are 5 and 6.
  • In the expression \(2 \cdot 4 \cdot 3 = 24\), the factors are 2, 4, and 3.
Product
The product in mathematics is the result of multiplying two or more factors together. In the given expression \(4 \cdot 3 \cdot 8 = 96\), the product is 96.
Think of the product as the answer to a multiplication problem. To find the product, you can multiply the factors one by one. Using our example:
  • First, multiply 4 and 3: \(4 \times 3 = 12\).
  • Then, multiply the result by the next factor, 8: \(12 \times 8 = 96\).

Thus, the product of multiplying 4, 3, and 8 together is 96. The product represents how many items you have in total when combining groups of different sizes. It is essential to understand this concept because it is the foundation of multiplication and helps in solving various math problems.
Verification
Verification in mathematics refers to the process of confirming the accuracy of a given calculation or solution. When dealing with multiplication problems, verifying the product ensures that the multiplication was performed correctly. Let's verify the product for the given expression \(4 \cdot 3 \cdot 8 = 96\).
  • First, multiply the first two factors: \(4 \times 3 = 12\).
  • Next, multiply the result by the third factor: \(12 \times 8 = 96\).
This confirms that the original product, 96, is correct.

Verification is a useful technique to avoid errors and build confidence in your solutions. By rechecking your calculations, you can ensure that your answers are accurate. This practice is especially important in more complex problems where multiple steps are involved.

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