Problem 87 - Prealgebra

Question

The Labor Department’s Job Openings and Labor Turnover Survey claims that employers hired about 4.08 million people in January 2010 while 4.12 million people were fired or otherwise left their jobs. How many more people lost jobs than were hired? Convert your answer to a whole number. Associated Press- Times-Standard 03/10/10 Job openings up sharply in January to 2.7M.

Step-by-Step Solution

Answer

40,000 more people lost jobs than were hired.

Step 1: Understand the Problem

First, identify the numbers given in the problem. We know that employers hired about 4.08 million people, and 4.12 million people were fired or left their jobs.

Step 2: Set Up the Equation

To find out how many more people lost their jobs than were hired, we need to subtract the number of hired people from the number of people who lost their jobs.

Step 3: Perform the Subtraction

Subtract the number of people hired (4.08 million) from those who were laid off or left (4.12 million): \[ 4.12 - 4.08 = 0.04 \]

Step 4: Convert to Whole Number

The result from the subtraction is 0.04 million, which needs to be converted to a whole number. Multiply by 1,000,000 to convert from millions to individuals:\[ 0.04 \times 1,000,000 = 40,000 \]

Key Concepts

Whole Numbers

Understanding whole numbers is crucial for solving many real-life problems, including subtraction issues like the one involving job hires and losses. Whole numbers are simply numbers without fractions or decimals, such as 0, 1, 2, 3, and so on. They are the building blocks of mathematics and are essential when precise, round numbers are needed. When working with calculations, especially in contexts like population statistics or finances, rounding to whole numbers offers a clearer picture of the scenario.
In our exercise, after determining how many more people lost their jobs than were hired, it's important to express this difference using a whole number for clarity and comprehension. This ensures that when communicating results, especially in reports and statistics, the information remains straightforward and easy to understand by a broader audience.

Understanding Word Problems

Word problems can initially seem daunting, but breaking them down into manageable parts makes them easier to understand and solve. The first step is always to clearly identify what is being asked. In the given exercise, we need to find out how many more people lost jobs compared to those who were hired.
Next, identify the key numbers and information provided: 4.08 million people were hired, and 4.12 million people lost their jobs. These numbers are crucial because they determine how we approach solving the problem. Upon extracting the numbers, set up the mathematical operation required—in this case, we need to perform a subtraction. Understanding what subtraction entails in this context means figuring out the 'difference.'

• Recognize the details mentioned, like 'hired' and 'lost,' which indicate the need for subtraction.
• Know that subtraction helps quantify differences or reductions between numbers.

By effectively breaking down word problems, one can systematically arrive at a solution.

Conversion from Millions to Individuals

Converting numbers from millions to individual units is vital when detailing large quantities, ensuring detailed accuracy. This process involves simple multiplication because 'million' indicates a factor of one million. For instance, when given a value in millions, convert it to individuals by multiplying by 1,000,000. This conversion is crucial in fields where precision matters, such as in job statistics or when disseminating data for better public understanding.
In our job scenario, after calculating how many more people lost jobs than were hired, we arrived at 0.04 million individuals. To make this figure more accessible and comprehensible:

• Multiply 0.04 by 1,000,000, resulting in 40,000 individuals.
• This means, in tangible terms, 40,000 more people lost jobs compared to those who were hired.

Conversions like these are key in ensuring that statistical data retains its meaning and remains practically applicable to various audiences.