Problem 47 - Prealgebra

Question

Perform the indicated operations. \(8 \times 2.54\)

Step-by-Step Solution

Answer

The result of the operation is 20.32.

Step 1: Identify the Operation

The problem requires you to multiply two numbers: 8 and 2.54. This means we need to take the number 8 and multiply it by 2.54.

Step 2: Multiply the Whole Numbers

Begin by multiplying the whole number 8 by the whole part of 2.54, which is 2. Calculate the multiplication: \(8 \times 2 = 16\).

Step 3: Multiply by the Decimal Part

Next, multiply the whole number 8 by the decimal part of 2.54, which is 0.54. Calculate the multiplication: \(8 \times 0.54 = 4.32\).

Step 4: Add the Results

Combine the results of the two previous parts to get the final answer. Add 16 (from step 2) and 4.32 (from step 3): \(16 + 4.32 = 20.32\).

Step 5: Confirm the Calculation

Double-check the calculation to ensure accuracy. The multiplication and addition were performed correctly, leading to the final result.

Key Concepts

Decimal Multiplication

When dealing with decimal multiplication, remember that you are multiplying a whole number by both the whole and decimal parts. This involves splitting the decimal into two parts for easier calculations. First, consider the whole part of the decimal number and multiply it by the whole number. For example, in the problem \(8 \times 2.54\), we multiply the 8 by the whole part, which is 2, to get 16.

Next, multiply the whole number by the decimal part. In our example, this means multiplying 8 by 0.54, resulting in 4.32.

Finally, you add the results of these two products to get the final answer. By breaking the decimal into whole and fractional parts, the process of multiplication becomes much more manageable, allowing you to ensure you handle each section of the number correctly.

Step-by-Step Math Solutions

Breaking down problems into a series of simple steps can help you not only solve the problem but also understand the process better. Each problem can be understood in clearer terms when approached one step at a time.

In the exercise \(8 \times 2.54\), we started by identifying the need to multiply these two numbers. Then, multiplying step-by-step first the whole number by the integer portion, followed by the fractional portion of the decimal. Finally, the key step involves adding these two products together. Completing these steps methodically ensures the problem is both solved and understandable.

This strategy not only aids in solving the problem but also builds your confidence and ability to tackle more complex problems down the line.

Prealgebra Problems

Prealgebra lays the foundation for all future math courses by introducing fundamental concepts like multiplication, division, and working with decimals. Understanding these concepts is crucial for students, as they form the building blocks for more advanced mathematics.

Using simple examples like \(8 \times 2.54\), students learn to handle basic operations involving decimals. By practicing these operations, students gain confidence in managing numbers that aren't whole and understand how different parts of a decimal contribute to its overall value.

Through repeated practice and guidance, students develop the skills needed to transition smoothly into algebra, where these basic operations become even more critical. So, don't rush. Take your time to practice and appreciate these foundational skills.