Problem 72 - Prealgebra

Question

Perform the indicated operations. $$5 \times 2,000$$

Step-by-Step Solution

Answer

The result of the operation is 10,000.

Step 1: Understand the Operation

The problem asks us to perform multiplication. We need to multiply the number 5 by 2,000.

Step 2: Set Up the Multiplication

Write the multiplication as an equation: 5 multiplied by 2,000, or \(5 \times 2000\).

Step 3: Perform the Multiplication

Multiply 5 by 2,000. One way to do this is to first multiply 5 by 2 and then add three zeros to the result (since 2,000 is 2 followed by three zeros).

Step 4: Calculate Multiplication of Smaller Numbers

Compute \(5 \times 2 = 10\).

Step 5: Add Zeros

Since the original problem was \(5 \times 2000\), we take the result from Step 4, which is 10, and add the three zeros from 2,000 to get 10,000.

Key Concepts

Understanding Mathematics

Mathematics is a universal language used to understand and express the patterns and relationships in our world. It forms the basis of many scientific and technical fields, offering a toolkit for solving problems through logic and numbers. One key area of mathematics is arithmetic, which includes basic operations like addition, subtraction, multiplication, and division. These operations are fundamental as they serve as the building blocks for more complex mathematical concepts. Multiplication, in particular, allows us to quickly calculate the total of grouped numbers by scaling one number by another. For example, multiplying 5 by 2,000 quickly finds the total number of items when combining several identical groups.

Exploring Arithmetic Operations

Arithmetic operations are at the core of mathematics, enabling us to perform calculations that solve everyday problems. These operations include:

• Addition: Combining two or more numbers to get a sum.
• Subtraction: Determining the difference between numbers.
• Multiplication: Finding the product by combining multiple groups of the same size.
• Division: Splitting a number into equal parts.

In this exercise, we focused on multiplication. To do this, we set up the problem with two numbers: 5 and 2,000. When multiplying, you're essentially scaling a number to see how many times one number contains another. Here, we faced the task of multiplying 5 groups of 2,000 items, achieving a product that combines all groups into a single total.

Learning from Step-by-Step Solutions

Step-by-step solutions break down complex problems into more manageable parts, making mathematical problems less intimidating and much easier to handle. By following a sequential approach, students can see every element of the calculation process clearly. Let's see how it works in this multiplication exercise:

• Set Up the Equation: Begin by writing the problem as an equation, such as \(5 \times 2000\).
• Break Down the Numbers: Simplify the multiplication by splitting it into smaller parts. Here, we multiply 5 by 2, followed by adding zeros.
• Compute and Combine: Calculate smaller numbers first: \(5 \times 2 = 10\). Add the zeros to scale up the result, yielding the final product.

This method not only helps ensure accuracy but also builds mathematical confidence by demystifying the operations involved. Every step acts like a building block, paving the way to mastery of more intricate calculations.