Problem 78 - Fundamentals of Mathematics

Question

In 1980 , there were 83,000 people arrested for prostitution and commercialized vice and 11,330,000 people arrested for driving while intoxicated. How many more people were arrested for drunk driving than for prostitution?

Step-by-Step Solution

Answer

11,247,000 more people were arrested for drunk driving.

Step 1: Understand the Numbers

First, identify how many people were arrested for each offense. The problem states that in 1980, there were 83,000 arrests for prostitution and 11,330,000 arrests for driving under the influence.

Step 2: Calculate the Difference

Subtract the number of people arrested for prostitution from the number of people arrested for driving under the influence to find how many more people were arrested for drunk driving. Perform the subtraction: 11,330,000 - 83,000.

Step 3: Subtraction Result

Calculate the result of the subtraction: 11,330,000 - 83,000 = 11,247,000.

Key Concepts

integer subtraction

Integer subtraction is a process of finding the difference between two whole numbers, known as integers. In the exercise, you start with two big numbers: 11,330,000 and 83,000. Subtraction shows how many units one number exceeds another. It's foundational in math, helping us understand the concept of taking away or counting backwards.

To subtract integers effectively, follow these steps:

• Align the numbers vertically by their place value, with larger numbers on top.
• Starting from the right, subtract each digit of the bottom number from the corresponding digit of the top number.
• If a digit in the top number is smaller than the corresponding digit in the bottom number, "borrow" from the next left digit of the top number.

In the given problem, you would subtract from right to left, borrowing if necessary, to find that 11,330,000 - 83,000 equals 11,247,000.

arithmetic problem-solving

Arithmetic problem-solving is the method of identifying the mathematical operations needed to solve real-world problems. It often involves interpreting the problem, choosing the right operations, and then calculating to find a solution.

In the exercise, we face a problem that requires the use of subtraction. To solve such problems:

• Identify and understand the context and numbers involved. For instance, you'll need to know the number of arrests in two different categories.
• Decide on the appropriate arithmetic operation. Here, since we're looking for how many "more" people were arrested for one offense compared to another, subtraction is the required operation.
• Execute the operation you have chosen. Carefully perform the subtraction to ensure accuracy in the final result.

These steps guide you through solving arithmetic problems efficiently, ensuring you arrive at the correct solution.

numerical comparison

Numerical comparison involves evaluating two numbers to determine their relationship. This can mean figuring out which number is greater, smaller, or by how much they differ. It's an important skill that allows us to understand data and make informed decisions.

Within this exercise, the task is to find out how many more people were arrested for one offense than another, which involves comparing the two numbers (arrest counts for drunk driving and prostitution). Here, you're specifically looking at the concept of finding the "difference" through subtraction.

To compare numbers effectively:

• Understand the context of the numbers—what each number represents.
• Use subtraction to find the exact difference when quantifying how much one number exceeds the other.
• Interpret and analyze the result to apply it to the given context.

The ability to compare numbers is crucial in many real-world scenarios, and arithmetic problems like this strengthen and test that ability.