Problem 35 - Prealgebra

Question

Divide. $$378.9 \div 21.05$$

Step-by-Step Solution

Answer

The answer is approximately 18.

Step 1: Convert Divisor to a Whole Number

To simplify the division, let's convert the divisor, 21.05, to a whole number by moving the decimal point two places to the right. This changes 21.05 to 2105. We also move the dividend's decimal two places to maintain equality, so 378.9 becomes 37890.

Step 2: Divide Whole Numbers

Now that both numbers are whole, perform the division: 37890 ÷ 2105. Since this division doesn't result in a whole number, we'll perform the division to find a decimal answer. The division results in approximately 18.

Step 3: Verify the Division

Multiply 18 (the quotient) by the divisor 2105 to check the result. Performing the multiplication: 18 × 2105 = 37890, which matches our adjusted dividend, verifying the correctness of the division.

Key Concepts

Whole Numbers

Whole numbers are numbers without any fractional or decimal part. They are the numbers 0, 1, 2, 3, and so on. These numbers are simple to work with in division because they don't have complex decimal places, which can make calculations easier and clearer.

In division, dealing with whole numbers is often preferable as it simplifies the arithmetic. When dividing 378.9 by 21.05, the process becomes more straightforward by converting these numbers into whole forms — making it easier to conduct the division.

To achieve this, we need to adjust for any decimal points in play. For instance, if you move a decimal point two places to the right, you effectively multiply by 100. In this problem, converting 21.05 to 2105, and 378.9 to 37890 helps us handle the task with whole numbers.

Division Verification

When you divide two numbers and find a quotient, it's always good to verify your result to ensure accuracy. Division verification is a methodical way to check your work through multiplication.

Imagine you get a quotient of 18 from dividing 37890 by 2105. To check, multiply 18 back by the divisor (2105).

• If the product matches the dividend you adjusted earlier — which is 37890 in this case — your division is correct.
• If it doesn't match, you may need to reassess your division.

Verifying is crucial especially when dealing with decimals, as small errors can lead to significant differences in results. Ensure you double-check, particularly in exams or homework, for impeccable answers.

Converting Decimals

When dividing decimals, a crucial step is converting them into whole numbers. This makes calculations easier and more straightforward. The main challenge here is ensuring your adjustment preserves the equality of the division operation.

Here's how converting works:

• Identify how many decimal places are in the divisor. For 21.05, there are two decimal places. To convert this into a whole number, move the decimal two places to the right turning it into 2105.
• Apply the same adjustment to the dividend. For 378.9, you also move its decimal point two places to the right, converting it to 37890.

This transformation is equivalent to multiplying both numbers by 100 (for two places), maintaining the proportionality of the equation. This step is paramount for accurate results, allowing you to perform operations that are easier and more reliable.