Problem 9 - Prealgebra

Question

Perform each of the following divisions. [Examples \(1-5]\) $$28.8 \div 6$$

Step-by-Step Solution

Answer

The quotient of 28.8 divided by 6 is 4.8.

Step 1: Identify the Dividend and Divisor

First, we need to recognize the components of our division problem. We have the dividend, which is the number being divided, and the divisor, which is the number we are dividing by. In our problem, the dividend is 28.8, and the divisor is 6.

Step 2: Set Up the Division

We will set up the division as a long division problem or simply as a straightforward division of decimal numbers. For 28.8 divided by 6, we don't need to remove the decimal point as long as we ensure proper alignment of decimal points in the quotient.

Step 3: Perform the Division

We divide 28.8 by 6 as follows: First, divide 28 by 6, which results in 4 since 6 times 4 equals 24. Write 4 above the division line. Then, subtract 24 from 28, giving a remainder of 4. Bring down the 8 from the decimal part, making the number 48. Divide 48 by 6, which results in 8. Write 8 after the 4 in the quotient.

Step 4: Finalize the Quotient

The quotient we obtain from the division of 28.8 by 6 is 4.8. Ensure you place the decimal point directly above its position in the dividend, which happens between the 4 and the 8 in the quotient.

Key Concepts

Understanding Dividend and Divisor

In any division problem, identifying the dividend and divisor is the first crucial step. The dividend is the number you are splitting into equal parts. It's what you start with. Meanwhile, the divisor is the number that tells you how many equal parts to split the dividend into.
For example, if you are dealt with the division problem of 28.8 divided by 6, 28.8 acts as the dividend—the number you are breaking down, and 6 is the divisor—the number doing the dividing. These roles never swap, and recognizing them at the outset makes solving the problem clearer and more structured.
Once the dividend and divisor are clear, solving the division equation becomes much smoother. This clarity plays a significant role when you move to the next step of long division.

Long Division with Decimals Explained

While dealing with decimals might seem daunting at first, setting up long division with decimals is a straightforward process. Once you've identified the dividend (28.8) and the divisor (6), you can proceed with the setup. It's essential to maintain the alignment of decimal points to ensure accurate results.
Here's how you do it:

• Write down the division problem with the dividend inside the long division bracket and the divisor outside.
• Because the divisor is a whole number in this case, maintain the position of the decimal in the dividend above the line in the quotient.

The alignment of decimal places is crucial. It ensures the accuracy of your final answer and prevents common errors that occur due to misalignment.

Quotient Determination

Finding the quotient is the goal of your division problem. Once you have set up the long division correctly, determine the quotient by executing the division step-by-step. Let's break down how you get the quotient from our example: 28.8 divided by 6.
The steps are as follows:

• Start by dividing the whole number part of the dividend (28) by the divisor (6). 28 divided by 6 equals 4. However, 6 times 4 results in 24, leaving a remainder of 4.
• Bring down the next number from the decimals, the 8, making it 48.
• Divide 48 by 6, which gives you 8. Place 8 in the quotient right next to the 4.
• Since there are no more numbers to bring down, your division is complete, and your final quotient is 4.8.

This process showcases how each step, meticulously followed, leads to a precise answer. Observing the placement of the decimal in the quotient is key to obtaining the right solution.