Problem 95 - Prealgebra

Question

In the following exercises, add. $$832 + 199$$

Step-by-Step Solution

Answer

The sum of 832 and 199 is 1031.

Step 1: Align the Numbers

Write the numbers one below the other, ensuring that the digits are properly aligned by place value (units, tens, hundreds). \[ \begin{array}{r} 832 \ + 199 \ \hline \end{array} \]

Step 2: Add the Units Column

Add the digits in the units column (rightmost column). \[ 2 + 9 = 11 \] Write down 1 and carry over 1 to the tens column.

Step 3: Add the Tens Column

Add the digits in the tens column along with the carry. \[ 3 + 9 + 1 = 13 \] Write down 3 and carry over 1 to the hundreds column.

Step 4: Add the Hundreds Column

Add the digits in the hundreds column along with the carry. \[ 8 + 1 + 1 = 10 \] Write down 0 and carry over 1 to the thousands column.

Step 5: Write the Final Result

As there is no other digit in the thousands column except the carry, write it down as it is.\[ \begin{array}{r} 832 \ + 199 \ \hline 1031 \end{array} \]

Key Concepts

Understanding Step-by-Step Solutions

When solving math problems, especially in prealgebra, it's crucial to break down tasks step by step. This approach ensures clarity and minimizes errors. In our example, we are adding two numbers: 832 and 199.

• Breaking the problem into steps helps you see each small action. This makes it less overwhelming.
• Each step builds upon the previous one, ensuring a thorough understanding of the process.

Instead of rushing to the answer, taking it one step at a time lets you focus on each part of the problem. This method is particularly useful for addition involving larger numbers.
Start by aligning the numbers. Then, add column by column, handling any carries systematically. You'll find that complex problems become manageable when approached in this way.

Place Value Alignment

Place value alignment is essential in addition. It means ensuring that the digits in each column (units, tens, hundreds) are directly on top of one another.
For example, with 832 and 199:

• Write 832
• Write 199 directly below it, making sure the units, tens, and hundreds columns line up

This alignment makes addition more straightforward. Misalignment can lead to mistakes.
Proper place value alignment ensures that you're adding digits that represent the same values, such as only adding tens to tens and units to units.
Here's how it looks:
\[ \begin{array}{r} 832 \ +199 \ \ \hline\ \end{array} \]
By lining up the numbers correctly, we ensure accuracy in our calculations.

Carrying in Addition

Carrying in addition is a vital skill when sums exceed 9 in any given column. Here's how it is done:

• When the sum of two digits is 10 or more, write down the unit digit and carry over the tens digit to the next column.
• Continue this process for each column in the problem.

For instance, when adding 832 and 199:

• Start with the units column: 2 + 9 = 11. Write 1, carry over 1 to the tens column.
• Next, add the tens column: 3 + 9 + 1 = 13. Write 3, carry over 1 to the hundreds column.
• Finally, add the hundreds column: 8 + 1 + 1 = 10. Write 0, carry over 1 to the thousands column.

Here is the final setup:
\[ \begin{array}{r} 832 \ +199 \ \hline\ 1031 \end{array} \]
Carrying helps maintain the place value structure throughout the addition, ensuring accuracy and correct placement of each digit in the final sum.