Problem 55 - Prealgebra

Question

Perform the indicated operations. \(2,000 \div 16.39\) (Round your answer to the nearest whole number.)

Step-by-Step Solution

Answer

The solution to the division is approximately 122, rounded to the nearest whole number.

Step 1: Understand the Problem

The task is to perform the division of 2,000 by 16.39 and then round the result to the nearest whole number.

Step 2: Set Up the Division

Write the division expression as a fraction: \( \frac{2000}{16.39} \). This sets up the problem for calculation.

Step 3: Perform the Division

Carry out the division of 2000 by 16.39 using a calculator or long division: \( \frac{2000}{16.39} = 122.029 \) (approximately).

Step 4: Round to the Nearest Whole Number

Since the decimal part of 122.029 is less than 0.5, round down to 122.

Key Concepts

Rounding Numbers

Rounding numbers is a fundamental skill in arithmetic that simplifies complex calculations and results. It's particularly useful when you need a quick estimation or when precise values aren't necessary. To round a number to the nearest whole number, you must look at the decimal part:

• If the decimal portion is 0.5 or greater, round up by adding 1 to the whole number portion.
• If the decimal portion is less than 0.5, round down, keeping the whole number part the same.

In the example of the division problem, the result was 122.029. Because the decimal part (0.029) is less than 0.5, we rounded the number down to 122. This rule ensures clarity and minimizes errors in everyday calculations, making it easier to communicate and understand numerical information.

Fractions

Fractions represent a part of a whole. They are key in expressing numbers that aren't whole numbers themselves. In division problems like the one provided, fractions can be a useful way to set up the calculation, setting the stage for an easier understanding of the operation.

A fraction consists of a numerator (the top number) and a denominator (the bottom number). In the given problem, dividing 2,000 by 16.39 can be expressed as the fraction \(\frac{2000}{16.39}\). This shows how many times 16.39 fits into 2,000.

• The numerator in this context is the number to be divided (2,000).
• The denominator is the number you are dividing by (16.39).

Using a fraction to represent this division gives a visual interpretation of the problem, making it clearer what operations are to be performed.

Prealgebra

Prealgebra lays the groundwork for understanding mathematical concepts that become crucial as students progress into higher levels of math, like algebra, calculus, and beyond. It encompasses basic arithmetic, like addition, subtraction, multiplication, and division, and helps students understand more about how numbers work together.

The division example highlights multiple components of prealgebra:

• It involves understanding how to manipulate numbers and apply division to real-world scenarios.
• Recognizing that operations like division can be expressed through fractions, enhancing comprehension.
• Students also practice decision-making when rounding numbers, integrating different mathematical skills.

Prealgebra serves as a powerful tool for developing problem-solving skills, enabling students to tackle more complex problems confidently. By engaging with exercises like dividing and rounding, learners receive a natural introduction to more complicated algebraic concepts.