Problem 70 - Fundamentals of Mathematics

Question

The number of persons on food stamps in \(1975,1979,\) and 1980 was \(19,179,000,19,309,000,\) and 22,023,000 , respectively. What was the total number of people on food stamps for the years 1975 , \(1979,\) and \(1980 ?\)

Step-by-Step Solution

Answer

The total number of people on food stamps was 60,511,000.

Step 1: Identify the numbers

List down the number of persons on food stamps for each year: - 1975: 19,179,000 - 1979: 19,309,000 - 1980: 22,023,000

Step 2: Set up the addition

To find the total number of persons on food stamps across these three years, we need to add the numbers together:\( 19,179,000 + 19,309,000 + 22,023,000 \)

Step 3: Perform the addition

Add the numbers to find the total:- Start by adding 19,179,000 and 19,309,000 to get 38,488,000.- Then add this result to 22,023,000:\[38,488,000 + 22,023,000 = 60,511,000\]

Step 4: Verify the result

Double-check each addition step to ensure there are no mistakes. - Verify: 19,179,000 + 19,309,000 = 38,488,000 - Verify: 38,488,000 + 22,023,000 = 60,511,000

Key Concepts

Step by Step Solution

Let's break down the process of adding these large numbers, step by step. Start with the list of numbers representing the years and their corresponding values:

• 1975: 19,179,000
• 1979: 19,309,000
• 1980: 22,023,000

Each step in the addition needs careful execution to ensure accuracy. First, add 19,179,000 and 19,309,000. This requires aligning the numbers properly and adding each corresponding digit: - Start adding from the rightmost digit (ones place) and move leftwards. - Handle any carries from each column's addition as you proceed. - After finding the intermediate total of 38,488,000, add 22,023,000 to it. Continue with the addition process, again starting from the rightmost digit. This ensures a clear, structured progression, reducing possible errors.

Double-Checking

After performing these additions, it's crucial to double-check your work. Errors can occur in any step, particularly with large numbers. Here’s a practical way to ensure correctness: - Re-verify each part of the operation, starting once again with the original pair of numbers, 19,179,000 and 19,309,000. - Confirm the sum derived matches the initial total of 38,488,000. If not, reassess each column’s process for carries and mistakes. Next, review the addition of 38,488,000 and 22,023,000. Break it into manageable sections: - Check individual digit sums, and reconcile any carries. - Ensure the cumulative total of 60,511,000 remains accurate. This double-check layer builds confidence, reducing errors and validating the accuracy of calculations.

Addition Verification

The final stage involves addition verification, a practice to confirm total correctness. This step gives added assurance beyond simple re-checking. To verify the total, employ these strategies:

• Reverse Operations: If time permits, try subtraction to see if starting sums return to their initial values. Deduct each number used in the addition from the total; results should be your original entries.
• Unit Analysis: Create interim comparisons and ensure consistency. For example, values must harmonize in size and progression relative to the context (years) given in the problem. The computed total should logically match expected growth from similar data comparisons.

Verification not only strengthens understanding but also cultivates good mathematical habits, crucial for tackling more complex problems in the future.