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Chapter 1: Problem 31

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{l} 4,963 \\ 5,428 \\ \hline \end{array}$$

Short Answer

Expert verified
The sum is 10,391.

Step by step solution

01

Align the Numbers

Write the numbers one under the other, ensuring the digits are properly aligned by place value. This means all the thousands, hundreds, tens, and ones should line up vertically.
02

Add the Ones Column

Start with the rightmost column. Add the digits in the ones place: 3 + 8 = 11. Since 11 is two digits, write down 1 in the ones place and carry over 1 to the tens column.
03

Add the Tens Column

Move to the tens column, adding the carried-over 1. So, 6 + 2 + 1 = 9. Write down 9 in the tens place.
04

Add the Hundreds Column

In the hundreds column, add the digits: 9 + 4 = 13. Since 13 is two digits, write down 3 in the hundreds place and carry over 1 to the thousands column.
05

Add the Thousands Column

Finally, add the thousands digits along with any carried over: 4 + 5 + 1 = 10. Since this is the final column, write down the full result 10.
06

Write the Final Answer

Combine the results from all columns. Place the digits properly to get the final sum as 10,391.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value Alignment
When solving addition problems that require carrying, proper place value alignment is crucial. This concept ensures that each digit in a number is lined up correctly with the corresponding digit in the other number. By aligning numbers based on place value:
  • Place thousands under thousands.
  • Hundreds under hundreds.
  • Tens under tens.
  • Ones under ones.
When you align numbers properly, it prevents errors. Each aligned column represents a specific place value. Therefore, misalignment can lead to an incorrect sum.

For our example, aligning 4,963 and 5,428, you should have: - 4 and 5 in the thousands column, - 9 and 4 in the hundreds column, - 6 and 2 in the tens column, - 3 and 8 in the ones column.
Column Addition
Column addition is the process of adding numbers together, one column at a time, from right to left. It's a method that is especially useful for larger numbers as it keeps the addition organized and manageable.

Here's a step-by-step guide to carrying out column addition:
  • Start with the rightmost column, which is the ones place.
  • Add up the numbers in each column.
  • If a sum in a column is 10 or greater, leave the rightmost digit in that column and carry over the other digit to the next higher column.
In our initial problem, starting with the ones column, add 3 and 8 to get 11. Write down 1 and carry over 1 to the tens column. This process is repeated for the tens, hundreds, and thousands columns.
Step-by-Step Addition
Breaking down the addition process into steps can make solving such problems straightforward and less overwhelming. Each step focuses on a specific column, ensuring accuracy before moving on to the next.

Here's how the step-by-step addition was executed in the original exercise:
  • Step 1: Align the numbers by their place values.
  • Step 2: Add the ones column (3 + 8 = 11, write down 1, carry over 1).
  • Step 3: Add the tens column (6 + 2 + 1 = 9, write down 9).
  • Step 4: Add the hundreds column (9 + 4 = 13, write down 3, carry over 1).
  • Step 5: Add the thousands column (4 + 5 + 1 = 10, write down 10).
  • Step 6: Write the final answer as 10,391.
Following these steps carefully ensures that no part of the problem is overlooked, and carrying is handled correctly.

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