Problem 37 - Fundamentals of Mathematics

Question

For the following problems, perform the additions. If you can, check each sum with a calculator. $$381+88$$

Step-by-Step Solution

Answer

The sum of 381 and 88 is 469.

Step 1: Write down the numbers

Start by writing the numbers one below the other, aligning them by their rightmost digits. This helps in performing the addition systematically.\[\begin{array}{c} 381 \+ 88 \\hline\end{array} \]

Step 2: Add the rightmost column

Add the digits in the rightmost column: 1 (in the units place) + 8 = 9. Write the 9 below the line under the units column.

Step 3: Add the next column

Move to the tens column. Add the digits: 8 + 8 = 16. Since 16 is more than 9, write 6 below the line in the tens column, and carry over the 1 to the next column (hundreds).

Step 4: Add the hundreds column

Finally, add the digits in the hundreds column, considering the carry from the previous step: 3 + 1 (carryover) = 4. Write 4 below the line in the hundreds column.

Step 5: Write the result

Combine the calculated digits from each column to find the final sum:\[\begin{array}{c} 381 \+ 88 \\hline 469 \end{array}\]Thus, the sum is 469.

Step 6: Verify with a calculator

To ensure accuracy, you can verify the result using a calculator. Input 381 + 88 and confirm the result equals 469.

Key Concepts

Carry Over Method

When adding numbers, especially larger ones, the carry over method is essential. This method involves moving a digit from one column to the next highest place value upon reaching a sum that exceeds 9. For example, when adding the digits in the tens column of 381 and 88, we calculated 8 + 8 to get 16. Since 16 is greater than 9, we write down the 6 in the tens place and "carry over" the 1 to the hundreds column.
This process ensures each column maintains a single-digit value and helps in accurately summing the total.

• Carry over helps manage sums over 9.
• This keeps calculations organized.
• The carried number is added to the next column.

Using this systematic approach allows us to handle addition of two or more numbers with ease, focusing on one column at a time. By mastering the carry over method, you'll be able to perform addition accurately without confusion.

Aligning Digits in Addition

Aligning digits in addition is crucial for performing calculations correctly. When you start an addition problem, it's important to write each number so that the ones place, tens place, hundreds place, and so on are directly aligned in columns. This visual alignment allows you to systematically add digits from right to left. For example, in our problem, we align 381 over 88 with each digit right-justified:
- Hundreds, tens, and units places are all properly aligned. - This alignment ensures that when numbers are added, each digit is summed with its counterpart from the other number.
Proper alignment helps prevent mistakes and ensures that carries are accurately applied to the correct next column. This method significantly aids in skills needed for addition, ensuring that no number is left out or misplaced.

Addition Verification with Calculator

After manually calculating a sum, verifying it with a calculator is a good practice. It reassures you that your manual calculations are accurate. In our exercise, typing out 381 + 88 on a calculator should correctly confirm your sum as 469.
This step serves two purposes:

• Confirms the accuracy of manual calculations.
• Acts as a learning tool to identify and correct mistakes.

Verifying with a calculator can help students gain confidence in their arithmetic skills and help identify areas where they might need more practice. Over time, as students become more proficient with mental and manual calculations, their dependence on calculators should decrease, although it's always a handy tool for quick confirmation.