Problem 56 - Prealgebra

Question

Perform the indicated operations. \(2,200 \div 16.39\) (Round your answer to the nearest whole number.)

Step-by-Step Solution

Answer

The result of the division is 134 when rounded to the nearest whole number.

Step 1: Understand the Operation

The problem asks us to divide 2,200, which is our dividend, by 16.39, which is our divisor. The result will be rounded to the nearest whole number.

Step 2: Set Up the Division

Write the division as a fraction: \( \frac{2200}{16.39} \). This setup shows the division problem, with 2200 on top and 16.39 on the bottom.

Step 3: Perform the Division

Use a calculator to divide 2200 by 16.39. Upon calculation, you will find the result to be approximately 134.329.

Step 4: Round to the Nearest Whole Number

Since the division result is 134.329, we look at the digit in the tenths place, which is 3. Because it is less than 5, we round down, resulting in 134 as the nearest whole number.

Key Concepts

Understanding Decimal Division

Decimal division involves dividing a number, the dividend, by another number, the divisor, when one or both numbers are decimals. In the example provided, we're dividing 2200 by 16.39. When performing decimal division, it's important to set up the problem correctly to ensure accurate results.
Here's how you can approach decimal divisions:

• Write the division problem in fraction form, which helps visualize the relationship between the dividend and divisor.
• Use a calculator for more accurate results, especially when dealing with many decimal places.
• If the divisor is a decimal, you can also multiply both the dividend and divisor by 10 or 100 to convert the divisor to a whole number, simplifying the division process.

By mastering decimal division, you're equipped to handle more complex arithmetic tasks involving decimals.

The Process of Rounding

Rounding is a mathematical technique used to simplify numbers by eliminating less significant digits. When rounding, you determine which place value you're rounding to, then observe the following digit to decide whether to round up or down.
For instance, take 134.329 from our division problem:

• Look at the tenths place: it’s 3.
• Since 3 is less than 5, you round down, making the whole number 134.

This approach keeps numbers manageable without drastically altering their value, particularly useful when calculating estimates or performing quick mental math. Understanding rounding ensures precision in reporting and easy interpretation of results.

Executing Division Operations

Division operations are a fundamental part of arithmetic, helping us calculate how many times one number is contained within another. In our exercise, we divided the number 2200 by 16.39. Executing division operations involves the following:

• Identifying the divisor and the dividend.
• Setting up the division problem, either traditionally or with a calculator.
• Calculating the result, paying attention to decimals if involved.

After conducting the division, checking the answer is important, especially if further calculations rely on it. Being systematic and precise in division helps when confronting more advanced mathematical problems and improves overall arithmetic skills.