Subtracting 26894 From The Sum Of 45629 And 41235 A Step-by-Step Guide

by THE IDEN 71 views

In the realm of mathematics, we often encounter problems that require us to perform a series of operations. This article delves into one such problem: subtracting 26894 from the sum of 45629 and 41235. This seemingly simple arithmetic problem provides a great opportunity to explore the fundamental operations of addition and subtraction, and how they work together to arrive at a solution. Understanding the order of operations is crucial in solving mathematical problems accurately, and this particular problem perfectly illustrates the importance of following the correct sequence. In this comprehensive guide, we will break down the problem step-by-step, ensuring that every aspect of the solution is clearly explained and understood.

Understanding the Problem

At the heart of this mathematical challenge lies a straightforward question: What is the result when we subtract 26894 from the sum of 45629 and 41235? To tackle this, we must first decipher the order of operations. The problem explicitly states that we need to find the sum of 45629 and 41235 before subtracting 26894. This is a critical point, as changing the order would lead to a different, and incorrect, answer. The problem is designed to test our understanding of basic arithmetic and our ability to follow instructions precisely. Before we dive into the calculations, it's helpful to visualize the problem. We can think of it as having two separate piles of objects, represented by the numbers 45629 and 41235. We first combine these piles (addition), and then we remove a certain number of objects, represented by 26894 (subtraction). This visualization can make the abstract numbers feel more concrete and easier to grasp. Now, let's move on to the first step: finding the sum of 45629 and 41235. This involves adding the two numbers together, carefully aligning the digits according to their place value (ones, tens, hundreds, etc.) to ensure accuracy. Addition is a fundamental operation, but even seemingly simple additions can become complex with larger numbers, requiring careful attention to carrying over digits when the sum in a particular place value column exceeds 9. This problem serves as a great reminder of the importance of mastering these basic skills, as they form the foundation for more advanced mathematical concepts. With a clear understanding of the problem and the necessary steps, we are well-prepared to embark on the solution process.

Step 1: Adding 45629 and 41235

The initial step in solving this problem is to find the sum of 45629 and 41235. Addition is a fundamental mathematical operation that combines two or more numbers to find their total. In this case, we are adding two five-digit numbers, which requires a systematic approach to ensure accuracy. The most common method for adding large numbers is to align the digits according to their place value (ones, tens, hundreds, thousands, and ten-thousands) and then add the digits in each column, starting from the rightmost column (the ones place). If the sum in any column is greater than 9, we need to carry over the tens digit to the next column on the left. Let's break down the addition process step-by-step:

  1. Align the numbers:
  45629
+ 41235
-------

  1. Add the ones column (9 + 5 = 14):

    • Write down the 4 in the ones place of the result.
    • Carry over the 1 to the tens column.
  45629
+ 41235
-------
      4

  1. Add the tens column (2 + 3 + 1 (carried over) = 6):

    • Write down the 6 in the tens place of the result.
  45629
+ 41235
-------
     64

  1. Add the hundreds column (6 + 2 = 8):

    • Write down the 8 in the hundreds place of the result.
  45629
+ 41235
-------
    864

  1. Add the thousands column (5 + 1 = 6):

    • Write down the 6 in the thousands place of the result.
  45629
+ 41235
-------
   6864

  1. Add the ten-thousands column (4 + 4 = 8):

    • Write down the 8 in the ten-thousands place of the result.
  45629
+ 41235
-------
  86864

Therefore, the sum of 45629 and 41235 is 86864. This sum now becomes the starting point for the next step in our problem, which is to subtract 26894 from this result. Understanding the process of addition, including carrying over digits, is crucial for accurate calculations, especially when dealing with larger numbers. This step-by-step breakdown allows for a clear understanding of how the sum is derived, paving the way for the subtraction operation in the next section.

Step 2: Subtracting 26894 from 86864

Now that we have calculated the sum of 45629 and 41235, which is 86864, the next step is to subtract 26894 from this sum. Subtraction is another fundamental mathematical operation that finds the difference between two numbers. In this case, we are subtracting a five-digit number (26894) from another five-digit number (86864). Similar to addition, subtraction requires a systematic approach to ensure accuracy, especially when dealing with larger numbers. The process involves aligning the digits according to their place value and then subtracting the digits in each column, starting from the rightmost column (the ones place). If the digit being subtracted is larger than the digit it is being subtracted from, we need to borrow from the next column to the left. Let's break down the subtraction process step-by-step:

  1. Align the numbers:
  86864
- 26894
-------

  1. Subtract the ones column (4 - 4 = 0):

    • Write down the 0 in the ones place of the result.
  86864
- 26894
-------
      0

  1. Subtract the tens column (6 - 9):

    • Since 9 is greater than 6, we need to borrow 1 from the hundreds column.
    • The 8 in the hundreds column becomes 7, and the 6 in the tens column becomes 16.
    • Now, subtract (16 - 9 = 7). Write down the 7 in the tens place of the result.
  867(16)4
- 26894
-------
     70

  1. Subtract the hundreds column (7 - 8):

    • Since 8 is greater than 7, we need to borrow 1 from the thousands column.
    • The 6 in the thousands column becomes 5, and the 7 in the hundreds column becomes 17.
    • Now, subtract (17 - 8 = 9). Write down the 9 in the hundreds place of the result.
  8(5)(17)(16)4
- 26894
-------
    970

  1. Subtract the thousands column (5 - 6):

    • Since 6 is greater than 5, we need to borrow 1 from the ten-thousands column.
    • The 8 in the ten-thousands column becomes 7, and the 5 in the thousands column becomes 15.
    • Now, subtract (15 - 6 = 9). Write down the 9 in the thousands place of the result.
 (7)(15)(17)(16)4
- 26894
-------
   9970

  1. Subtract the ten-thousands column (7 - 2 = 5):

    • Write down the 5 in the ten-thousands place of the result.
 (7)(15)(17)(16)4
- 26894
-------
  59970

Therefore, the result of subtracting 26894 from 86864 is 59970. This completes the problem, providing us with the final answer. Understanding the process of subtraction, including borrowing, is crucial for accurate calculations, especially when dealing with larger numbers. This step-by-step breakdown allows for a clear understanding of how the difference is derived, solidifying our grasp of basic arithmetic operations.

Final Answer

After performing both the addition and subtraction operations, we arrive at the final answer. We first added 45629 and 41235 to get 86864. Then, we subtracted 26894 from 86864, which resulted in 59970. Therefore, the solution to the problem