Problem 85 - Algebra 1: Concepts and Skills

Question

Divide. $$ 39.1 \div 0.01 $$

Step-by-Step Solution

Answer

3910

Step 1: Set Up the Problem

Set up the problem as a division of decimal places. Here, \(39.1 \div 0.01\).

Step 2: Move the Decimal Points

Since you are dividing by a decimal, move the decimal point in the divisor to the right until you have a whole number. Repeat this step for the dividend. This will ensure the correct placement of your decimals. Consequently, your adjusted calculation then looks like this: \(3910 \div 1\).

Step 3: Perform the Division

Now, simply perform the division as usual which results in: \( 3910 \div 1 = 3910\).

Key Concepts

Division with Decimals

When dealing with division involving decimals, the process can seem tricky at first. The key is to adjust the numbers so that normal division can be applied. To divide decimals, you move the decimal points to transform both the divisor and the dividend into whole numbers. For instance, in the original problem, we had to divide 39.1 by 0.01.

• First, identify where the decimal points are. In 39.1, it's after the first place, and in 0.01, it's after the second place.
• Next, move the decimal point in the divisor (0.01) two places to the right to turn it into a whole number (1).
• Equally shift the decimal point in the dividend (39.1) the same number of spaces to the right, making it 3910.

With this adjustment, you're left with a simpler division problem: 3910 divided by 1, which straightforwardly equals 3910. This method streamlines the process mainly by eliminating decimals from the equation.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. Division can be especially complex when decimals are involved.

• Division with decimals uniquely requires understanding how to manage decimal points.
• One must adjust decimals properly to simplify the division into a more manageable form.
• This involves moving the decimal points to the right, essentially converting decimals into whole numbers before performing the operation.

Mastering this adjustment strategy allows anyone to tackle decimal division with confidence. Practicing these steps in problems, like dividing 39.1 by 0.01, helps build a strong foundation in arithmetic.

Mathematics Education

Mathematics education highlights practical problem-solving skills, such as dividing decimals. This aspect of math builds logical reasoning and analytical skills. When students learn how to navigate decimal division, they sharpen their understanding of numbers and operations.

• Grasping decimal division involves real comprehension of place value.
• This type of exercise encourages students to recognize patterns and apply consistent methodologies for accuracy.
• By training with diverse problems, students develop versatility in mathematics, which is critical for advanced topics later on.

Educators aim to present these concepts in straightforward steps, enabling students to follow and apply them easily. As seen with dividing 39.1 by 0.01, the objective is to make abstract ideas clear and accessible.