Problem 104 - Prealgebra

Question

In the following exercises, add. $$28,925 + 817 + 4,593$

Step-by-Step Solution

Answer

34,335

Step 1: Align the numbers

Write the numbers vertically, aligning the digits by place value (units, tens, hundreds, thousands, ten thousands): 28925 + 817 + 4593

Step 2: Add the units place

Add the digits in the units place (rightmost column): 5 + 7 + 3 = 15. Write down 5 and carry over 1.

Step 3: Add the tens place

Add the digits in the tens place along with the carried over value: 2 + 1 + 9 + 1 (carry) = 13. Write down 3 and carry over 1.

Step 4: Add the hundreds place

Add the digits in the hundreds place along with the carried over value: 9 + 8 + 5 + 1 (carry) = 23. Write down 3 and carry over 2.

Step 5: Add the thousands place

Add the digits in the thousands place along with the carried over value: 8 + 4 + 2 (carry) = 14. Write down 4 and carry over 1.

Step 6: Add the ten thousands place

Add the digits in the ten thousands place along with the carried over value: 2 + 1 (carry) = 3. Write down 3.

Step 7: Write the final answer

Combine all the digits: The final sum is 34,335.

Key Concepts

step-by-step addition

Step-by-step addition is a methodical way to add numbers, where you break down the addition process into smaller steps. This technique is particularly useful when dealing with multi-digit numbers. By focusing on one place value at a time, you can reduce the complexity of the task. To do this:

• Start with the rightmost digits (units place).
• Move left to the tens, hundreds, thousands, and so on.
• Add the digits in each column systematically.
• Combine the results to get the final sum.

This structured approach minimizes errors and ensures that every digit is taken into account, making it easier to handle large numbers accurately.

carrying in addition

Carrying in addition is an essential skill required when the sum of a column exceeds 9. When this happens, you need to carry over the extra digit to the next column. Here's a closer look:

• Add the numbers in the current column.
• If the sum is 10 or more, write down the rightmost digit in the current column.
• Carry over the leftmost digit to the next higher place value column.

For instance, when adding 28,925 + 817 + 4,593, adding the units place digits (5 + 7 + 3) gives 15. Write down 5 and carry over 1.

This process ensures that each place value is correctly addressed, speeding up the overall addition procedure while ensuring precision.

place value alignment

Place value alignment is crucial in addition to ensure that digits are added correctly by their respective place values. Misalignment can lead to incorrect sums. Here's how to align numbers properly:

• Write each number in a vertical format.
• Align the digits by their place values: units, tens, hundreds, thousands, etc.
• Fill in any empty spaces with zeroes for easier calculation.

For example, to add 28,925, 817, and 4,593, align them like this:
28,925
+ 817
+ 4,593
This approach ensures that you are correctly adding the units with units, tens with tens, and so on, helping avoid common mistakes in arithmetic.

basic arithmetic

Basic arithmetic forms the foundation for virtually all other areas of mathematics. In addition, the principles and methods used are straightforward but require practice to master. Key concepts include:

• Basic addition facts and memorization.
• Understanding place value.
• Carrying over in addition (as explained previously).

Regular practice of basic arithmetic enhances your ability to handle more complex math problems. Focus on mastering the steps:

• Start with simple single-digit addition and progress to multi-digit numbers.
• Utilize step-by-step methods to break down complex problems.
• Consistently check your work for errors.

Mastery of basic arithmetic ensures a strong foundational skill set for tackling more advanced mathematical concepts.