Problem 50 - Prealgebra

Question

Perform the indicated operations. \(3 \times 5 \times 3.79\)

Step-by-Step Solution

Answer

The result of the operation is 56.85.

Step 1: Multiply the First Two Numbers

First, take the first two numbers and multiply them together: \( 3 \times 5 \). This gives you \( 15 \).

Step 2: Multiply the Result with the Third Number

Next, take the result from Step 1, which is \( 15 \), and multiply it by the third number: \( 15 \times 3.79 \). To do this, multiply as follows: \( 15 \times 3.79 = 56.85 \).

Key Concepts

Multiplication

Multiplication is one of the four fundamental arithmetic operations. It is the process of adding a number to itself a specified number of times. For instance, if you have the problem of multiplying 3 by 5, it means you are adding 3, five times: \( 3 + 3 + 3 + 3 + 3 = 15 \). Thus, \( 3 \times 5 = 15 \).
Multiplication simplifies the process of repeated addition into a more straightforward and quicker operation. This is particularly useful when dealing with large numbers or complex calculations.

• It is represented by the symbol \( \times \) or "times."
• The numbers being multiplied are called factors, and the result is the product.
• Multiplication is commutative: \( a \times b = b \times a \).

Understanding multiplication is crucial as it forms the basis for many other mathematical concepts.

Step-by-step solutions

A step-by-step solution is a clear and detailed breakdown of a problem-solving process. It helps students understand each phase of the calculation or operation, aiding them in grasping how the final answer is reached. In our example, the operation starts with \( 3 \times 5 \) first.
This approach not only ensures consistency and accuracy but also allows learners to track their own work against given steps.

• Identify and tackle parts of the problem sequentially.
• Verify each step before moving on to the next to avoid mistakes.
• Provides a logical flow, making complex problems easier.

By following step-by-step solutions, students can build a solid understanding of underlying concepts, improving their problem-solving skills in the process.

Arithmetic operations

Arithmetic operations are basic math processes that include addition, subtraction, multiplication, and division. These operations are the foundation of most calculations and essential for higher-level math.
In our exercise, the focus is on the multiplication operation, part of arithmetic. Here's a quick overview of all four:

• Addition: Combining two or more quantities. Example: \( 2 + 3 = 5 \).
• Subtraction: Determining the difference between two numbers. Example: \( 5 - 3 = 2 \).
• Multiplication: As discussed, repeated addition. Example: \( 4 \times 3 = 12 \).
• Division: Splitting a number into equal parts. Example: \( 12 \div 3 = 4 \).

Understanding how to perform and apply these operations is fundamental to both everyday mathematics and more complex mathematical challenges.