Problem 73 - Prealgebra

Question

Perform the indicated operations. $$3 \times 1,000 \times 100$$

Step-by-Step Solution

Answer

300,000

Step 1: Understanding the Problem

We need to perform a multiplication of the numbers 3, 1,000, and 100. The expression given is \(3 \times 1,000 \times 100\).

Step 2: Multiply the First Two Numbers

First, multiply 3 by 1,000 to simplify the expression. This calculation is \(3 \times 1,000 = 3,000\).

Step 3: Multiply the Result by the Third Number

Now that we have 3,000 from the previous calculation, multiply this by 100. This operation is \(3,000 \times 100 = 300,000\).

Key Concepts

Step-by-Step Multiplication

Step-by-step multiplication is an effective technique to solve complex multiplication problems by breaking them down into simpler, more manageable steps. Let's consider the multiplication problem provided: - Start with the first two numbers, which are 3 and 1,000. Multiply these to get an intermediate result. In this case, the calculation is \(3 \times 1,000 = 3,000\).- Next, take the intermediate result (3,000) and multiply it by the next number in the sequence, which is 100. So, the next calculation will be \(3,000 \times 100 = 300,000\).Using this step-by-step process not only makes large numbers easier to handle but also helps prevent common mistakes by allowing you to focus on each section of the problem. Step-by-step multiplication is particularly useful for prealgebra students who are just beginning to learn multiplication with larger numbers.

Problem-Solving in Mathematics

In mathematics, problem-solving involves understanding the problem, devising a plan, carrying out the plan, and evaluating the solution for accuracy. Let's apply this to our example:1. **Understanding the Problem:** Interpretation of what is being asked is critical. Here, the task is to multiply the numbers 3, 1,000, and 100.
2. **Devising a Plan:** Decide on the best way to tackle the problem. For multiplication, we choose to simplify the process by multiplying the numbers step-by-step.
3. **Carrying Out the Plan:** Perform the calculations as planned: first, multiply 3 by 1,000, then multiply the result by 100. Keep track of each result.
4. **Evaluating the Solution:** Always take a moment to double-check your work. We confirm that \(300,000\) makes sense, as multiplying by 100 appends two additional zeros to 3,000.This structured approach to problem-solving helps students develop their analytical thinking and boosts confidence in tackling various mathematical challenges.

Basic Arithmetic Operations

Basic arithmetic operations are the building blocks of mathematics, consisting of addition, subtraction, multiplication, and division. In our example, multiplication is the operation in focus. Here’s a quick guide to understanding it:- **Multiplication** is essentially repeated addition. For instance, \(3 \times 1,000\) means adding 1,000 three times.
- In the expression \(3 \times 1,000 \times 100\), the multiplication process uses associative and commutative properties to simplify calculations. Associative property allows you to regroup the numbers, while commutative property means the order you multiply numbers doesn’t affect the result.Understanding these properties not only helps simplify computations but also aids in performing arithmetic operations accurately. As you gain more proficiency with these foundational operations, tackling complex problems becomes easier and more intuitive.