Question

Add \(17,432+627,381+62\) A. \(645,433\) B. \(645,343\) C. \(644,875\) D. \(644,785\)

Short answer

The correct answer is C. 644,875.

Step-by-step solution

Arrange the numbers

First, we write the numbers vertically to prepare for addition:\[\begin{array}{c} 17432 \ 627381 \+ 62\end{array}\]

Add the units column

Start with the rightmost column (units column). Add the digits 2 (from 17,432) + 1 (from 627,381) + 2 (from 62). This equals 5. Write 5 below the line in the units place.

Add the tens column

Move to the tens column. Add the digits 3 (from 17,432) + 8 (from 627,381) + 6 (from 62). This equals 17. Write 7 in the tens place below the line, and carry over 1 to the hundreds column.

Add the hundreds column

Add the digits from the hundreds column: 4 (from 17,432) + 3 (from 627,381) + the carry over 1. This equals 8. Write 8 below the line in the hundreds place.

Add the thousands column

Move to the thousands column. Add the digits 7 (from 17,432) + 7 (from 627,381). This equals 14. Write 4 below the line in the thousands place, and carry over 1 to the ten thousands column.

Add the ten thousands column

Now add the digits in the ten thousands column: 1 (from 17,432) + 2 (from 627,381) + the carry over 1. This equals 4. Write 4 below the line in the ten thousands place.

Add the hundred thousands column

Finally, add the digits in the hundred thousands column: 6 (from 627,381). Since there are no other numbers to add, write 6 below the line in the hundred thousands place.

Write the final sum

Combine all the results from each column: 644,875. Thus, the sum of the numbers is 644,875.

Key concepts

Step-by-Step Solution

A step-by-step solution is like a set of instructions that guides us through solving a problem one piece at a time. This method is especially useful in mathematics, where breaking down tasks into smaller, more manageable steps can lead to better understanding. In our exercise, we aim to add three numbers: 17,432, 627,381, and 62. This requires organizing and tackling each digit column by column, beginning with the smallest. Paying attention to details such as carrying over numbers and aligning digits correctly ensures accuracy in the final answer. The step-by-step approach helps build a strong foundation and boosts confidence in dealing with arithmetic operations.

Columnar Addition

Columnar addition involves organizing numbers in neat columns, making it easier to add them up. Each digit has its own column based on its place value, such as units, tens, hundreds, and so on. When we align numbers vertically, we ensure digits of the same place value are added together, reducing risks of error. For example, in our exercise:

• Arrange 17,432, 627,381, and 62 vertically.
• Make sure the digits line up correctly under their respective columns.

This method of aligning digits simplifies the process of adding large numbers and helps in managing carry overs.

Carry Over

Carry over, or regrouping, is a crucial part of addition, especially when dealing with large numbers or sums that reach ten or more. When a column's sum exceeds nine, carry the extra amount over to the next column on the left. In this exercise, we sometimes need to carry and add the excess to the next column:

• In the tens column: The sum is 17, so we write 7 and carry over the 1.
• In the thousands column: The sum is 14; write 4 and carry over 1.

Carrying over helps maintain the correct place value for each digit, leading to an accurate total.

Place Value

Understanding place value is fundamental to properly performing columnar addition and other arithmetic operations. Place value refers to the value of each digit in a number based on its position. From right to left, these positions are units, tens, hundreds, thousands, etc. Let's consider the number 627,381:

• The '6' is in the hundred thousands place.
• The '2' is in the ten thousands place.

Knowing each digit's place value allows us to add correctly, especially when carrying over becomes necessary. It's essential in organizing numbers for addition, ensuring each digit is in the right column.

Arithmetic Operations

Addition is one of the four primary arithmetic operations and is probably the most basic yet powerful tool in mathematics. It involves combining numbers to find their total value. Through tasks like our exercise, where we add 17,432 + 627,381 + 62, we apply the addition operation to derive a single sum. Arithmetic operations like addition, subtraction, multiplication, and division form the basis of more advanced mathematical concepts. Practicing these operations with a firm grasp of step-by-step methodologies, place value understanding, and carry-over techniques can greatly improve mathematical literacy and problem-solving skills.