Problem 91 - Prealgebra

Question

In the following exercises, add. $$168 + 325$$

Step-by-Step Solution

Answer

493

Step 1 - Align the Numbers

Write the numbers 168 and 325 one below the other, aligning them by their right-hand digits (the ones place). This helps in adding each column correctly.

Step 2 - Add the Ones Place

Add the digits in the ones place: 8 + 5 = 13. Write down 3 in the ones place of the answer and carry over 1 to the tens place.

Step 3 - Add the Tens Place

Add the digits in the tens place along with the carry-over: 6 + 2 + 1 (carry) = 9. Write down 9 in the tens place.

Step 4 - Add the Hundreds Place

Add the digits in the hundreds place: 1 + 3 = 4. Write down 4 in the hundreds place.

Step 5 - Write the Final Answer

Combine the digits obtained from Steps 2, 3, and 4. The final sum is 493.

Key Concepts

Place Value

Place value is an important concept when dealing with numbers, especially in addition. Each digit in a number has a specific value depending on its position, or place, in the number. For example, in the number 168:

• The digit 1 is in the hundreds place, so its value is 100.
• The digit 6 is in the tens place, so its value is 60.
• The digit 8 is in the ones place, so its value is 8.

Understanding place value helps you add numbers correctly.Aligning the numbers by their place values ensures that you are adding digits in the correct columns and not mixing them up.

Carrying in Addition

Carrying in addition happens when the sum of digits in a column is more than 9. Here’s how it works:
When you add the digits in the ones place of 168 and 325, you get 13. Since 13 is more than 9, you place the 3 in the ones place of your answer and carry over the 1 to the tens column.

• This means you add the carry-over of 1 to the digits in the next column.
• It ensures that each column correctly reflects the values being added.

Without carrying over, the addition wouldn't be accurate and the final sum would be wrong.

Step-by-Step Addition

Step-by-step addition involves breaking down the addition process into smaller, manageable steps. Let’s use the example of adding 168 and 325:

Step 1: First, align the numbers by their place values.

• 168
• 325

Step 2: Next, add the digits in the ones place: 8 + 5 = 13. Write down 3 and carry over 1.

• Carry-over is written above the next column.

Step 3: Then, add the digits in the tens place along with the carry-over: 6 + 2 + 1 = 9. Write down 9.
Step 4: Finally, add the digits in the hundreds place: 1 + 3 = 4. Write down 4.

• Combine the digits from the columns for the final answer: 493.

By following these steps, you can easily solve addition problems without getting confused or making mistakes.