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Chapter 1: Problem 13

Identify the factors and the product. $$3 \cdot 5 \cdot 2=30$$

Short Answer

Expert verified
The factors are 3, 5, and 2. The product is 30.

Step by step solution

01

Identify the Factors

The factors in the given multiplication problem are the numbers that are being multiplied together. In this case, the factors are 3, 5, and 2.
02

Multiply the Factors

To find the product, multiply the factors together. First, multiply 3 and 5 to get 15. Then, multiply 15 by 2. Mathematically, it looks like this: \[ 3 \times 5 = 15 \] \[ 15 \times 2 = 30 \]
03

Write the Final Product

The product of the factors 3, 5, and 2 is 30. Therefore, the product is 30.

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Key Concepts

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

Factors
In multiplication, 'factors' are the numbers you multiply together. They are the building blocks that combine to form another number, called the product.
For example, in the multiplication sentence \(3 \times 5 \times 2=30\), the numbers 3, 5, and 2 are the factors.
Understanding factors is crucial because they help you break down and simplify complex multiplication problems.
To identify factors:
  • Look at the numbers that are being multiplied.
  • In the problem given, the factors are 3, 5, and 2.
Product
The 'product' is the result you get after multiplying factors together.
If you multiply the factors 3, 5, and 2, the product is 30. Here's a step-by-step process:
First, multiply the first two factors:
  • \(3 \times 5 = 15\)
Then, multiply the result by the next factor:
  • \(15 \times 2 = 30\)
So, the product of multiplying 3, 5, and 2 is 30.
The product can also be understood as the total quantity you get when factors are combined together.
This is an essential concept in math since it shows how basic numbers can create larger ones through multiplication.
Step-by-Step Solution
Breaking down a multiplication problem step-by-step makes it easier to understand. Let's go through the given example again.

Step 1: Identify the Factors
The factors are the numbers that are being multiplied together. Here, the factors are 3, 5, and 2.
Step 2: Multiply the Factors
Multiply the first two factors:
  • \(3 \times 5 = 15\)
Then, multiply the result by the remaining factor:
  • \(15 \times 2 = 30\)
Step 3: Write the Final Product
The product is the result of multiplying all the factors. For this problem, the product is 30.
This methodical approach helps you understand each portion of the problem, leading to an accurate solution.

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