Problem 71 - Prealgebra

Question

Perform the indicated operations. $$3 \times 2,000$$

Step-by-Step Solution

Answer

The product of \( 3 \times 2,000 \) is 6,000.

Step 1: Understand the operation

The problem requires us to multiply two numbers: 3 and 2,000. This operation is a basic multiplication task.

Step 2: Write the multiplication

Start by writing the multiplication expression: \( 3 \times 2,000 \).

Step 3: Perform the multiplication

Multiply 3 by 2,000. You can think of this as multiplying 3 by 2 and then adding three zeros to the result: \( 3 \times 2 = 6 \), then add the three zeros to get \( 6,000 \).

Step 4: Verify the calculation

Re-check your steps to ensure that the multiplication was performed correctly: \( 3 \times 2,000 = 6,000 \).

Key Concepts

Step-by-step Solution

The first concept, the step-by-step solution, is like following a recipe. It's a way to break down the task of multiplication into manageable steps so that you can easily follow along.

Let's look at it closely:

• Understanding the Operation: You begin by clearly identifying the numbers involved—3 and 2,000 in this task. Recognizing what you're working with is crucial because it sets the stage for the entire process.


• Writing the Multiplication Expression: Next, you set up the problem as a multiplication expression: \( 3 \times 2,000 \). This is simply a way to organize the numbers so you can calculate them easily.


• Performing the Multiplication: The heart of the task is the multiplication itself. By recognizing that 2,000 can be broken down to \( 2 \times 1,000 \), you simplify the calculation. Multiply 3 by 2, which gives you 6, then append the three zeros from 1,000. The result is 6,000.

Verification of Calculation

Verifying a calculation is a very important part of mathematical operations. It helps ensure accuracy, just like double-checking your answers in a test.

To verify your calculation in this problem, all you need to do is re-evaluate your steps:

• First, check the multiplication of the significant numbers: 3 and 2. Is it correct that \( 3 \times 2 = 6 \)? Yes, it is!


• Next, confirm the placement of the zeros from 2,000. By recognizing 2,000 as \( 2 \times 1,000 \), you correctly add three zeros to the product of 6. Therefore, 6 becomes 6,000.

Verification helps you catch any errors before you complete a problem, which enhances your confidence in your math skills!

Understanding Operations

Understanding the basic multiplication operation is foundational to mastering higher-level math. Multiplication itself is just a quicker way of doing repetitive addition.

In the world of numbers:

• What is Multiplication? Think of multiplication as grouping or repeating addition. The expression \( 3 \times 2,000 \) implies adding 2,000 three times.


• The Role of Place Value: In large numbers like 2,000, place value is crucial. It helps you navigate the additional zeros, making the multiplication more manageable.


• Visualizing Multiplication: You can picture it as putting together blocks. Three groups of blocks, each containing 2,000 units, give you 6,000 units when combined.

Understanding these aspects makes the process of multiplication less daunting and more intuitive.