Problem 97 - Fundamentals of Mathematics

Question

For the following problems, find the solutions. Subtract 1,127 from the sum of 2,161 and 387 .

Step-by-Step Solution

Answer

The result is 1,421.

Step 1: Calculate the Sum

First, we need to find the sum of the numbers 2,161 and 387. We add them together: \[2,161 + 387 = 2,548\]

Step 2: Subtract from the Sum

Next, we need to subtract 1,127 from the sum we calculated in Step 1, which is 2,548. Let's perform the subtraction:\[2,548 - 1,127 = 1,421\]

Step 3: Verify the Calculation

Let's verify each step to ensure accuracy. First, the addition: 2,161 plus 387 indeed equals 2,548. Then, check the subtraction: when 1,127 is subtracted from 2,548, it equals 1,421. The calculations are correct.

Key Concepts

Addition

Addition is the process we use when we combine numbers to find their total or sum. It's one of the basic arithmetic operations that allow us to solve problems where we need to figure out how much we have when different quantities are put together. Think of it as the mathematical way of increasing or growing the total you have. When you add two numbers, their places in terms of units, tens, hundreds, and so on are added separately. This is important for keeping the addition accurate.
For example, in the exercise given, we need to add 2,161 and 387. This problem can be solved by lining up the numbers vertically by their place values and adding each column starting from the rightmost digit. Here's a quick breakdown:

• Add the ones place: 1 + 7 = 8
• Add the tens place: 6 + 8 = 14 (put down 4 and carry over 1)
• Add the hundreds place: 1 + 3 + the carried over 1 = 5
• Add the thousands place: 2 + 0 = 2

Thus, 2,161 + 387 results in 2,548.

Subtraction

Subtraction occurs when we need to find the difference between two numbers. It is essentially the opposite of addition and is needed when one quantity is to be taken away from another. For many, subtraction can seem more challenging than addition, but with practice, it becomes straightforward. In subtraction, we take a number called the subtrahend away from another number called the minuend to find the remainder.
In our exercise, we're tasked with subtracting 1,127 from 2,548. Breaking it down step-by-step helps:

• Subtract the ones place: 8 - 7 = 1
• Subtract the tens place: 4 - 2 = 2
• Subtract the hundreds place: 5 - 1 = 4
• Subtract the thousands place: 2 - 1 = 1

Therefore, 2,548 minus 1,127 leaves us with 1,421. Double-checking your subtraction by adding the remainder back to the subtrahend can confirm your answer.

Verification of Calculations

Verification is crucial for ensuring the calculations you've done are correct. By verifying, you avoid mistakes and confirm your answers are reliable. This process can involve checking each step in your calculation to catch any errors you might have made. After performing an operation, especially in problems involving both addition and subtraction, it's good practice to review your work.
In our problem, we verified the answer as follows:

• First, check the addition: Confirm 2,161 + 387 = 2,548, reviewing each column to ensure each step was calculated right.


• Then, verify the subtraction by re-adding the subtrahend (1,127) to the result (1,421) to see if it gives back the original minuend (2,548). In calculation terms, if 1,421 + 1,127 equals 2,548, your result is verified.

This helps cement the understanding that each arithmetic step contributes to the final solution being accurate.