Problem 20 - Fundamentals of Mathematics

Question

For the following problems, perform the additions. If you can, check each sum with a calculator. $$ \begin{array}{r} 916 \\ +\quad 62 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The sum is 978.

Step 1: Add Ones Place

Begin by adding the digits in the ones place. We have 6 (from 916) and 2 (from 62), which gives us:\[6 + 2 = 8\]

Step 2: Add Tens Place

Next, add the digits in the tens place. We have 1 (from 916) and 6 (from 62), which gives us:\[1 + 6 = 7\]

Step 3: Add Hundreds Place

Now, add the digits in the hundreds place. The only digit we have in this column is 9 from 916:\[9 + 0 = 9\]

Step 4: Combine the Results

Put all the separate sums together from each column. The ones place is 8, the tens place is 7, and the hundreds place is 9, forming the number 978.

Step 5: Verify with a Calculator

To ensure our addition is correct, use a calculator to verify: When 916 is added to 62, the result is 978.

Key Concepts

Understanding the Ones Place

In addition, the ones place is the rightmost digit of a number. It's essential because it sets the stage for understanding basic sums. When you're adding, always start with the ones place. This ensures that any overflow or carry is correctly managed as you move to the left.
In this exercise, we add the digits from the ones place of two numbers: 6 from 916 and 2 from 62.

• Calculation: \(6 + 2 = 8\)
• The result is simply 8 since there is no carry to the tens place.

After you've added the ones digits, place the result under the line, ready for the next step in your addition process.

Exploring the Tens Place

The tens place is the next column to the left of the ones place. It’s crucial for larger sums as it handles the 'tenfold' of quantities added.
In our step-by-step solution, we identified the tens digits: 1 from 916 and 6 from 62.

• Add these numbers: \(1 + 6 = 7\)

The sum does not exceed 10, so no carrying to the hundreds place is needed. Write 7 beneath the tens column to represent this intermediate result. This step shows how groups of ten build more significant numbers efficiently.

Decoding the Hundreds Place

While the hundreds place is the third column from the right, its role is even more substantial in maintaining numerical order in large additions.
In our example, the only number in the hundreds place is 9 from 916. The 62 lacks a hundreds digit, so it represents 0 at that level.

• Add: \(9 + 0 = 9\)

Since no carry or additional number impacts this column, you place the 9 directly below the line. Recognizing when there is or isn't a need to add extra digits helps ensure accurate multi-digit addition.

Verify the Sum Using a Calculator

Finally, it's always wise to double-check your work with a calculator, especially in exercises or homework tasks. This helps solidify your confidence in the manual process.
To verify:

• Input 916 on your calculator.
• Add 62 to it.
• Confirm the displayed result is 978.

This confirms that our step-by-step addition is correct. Using a calculator as a verification tool can catch mistakes before they become bigger issues, enhancing your problem-solving reliability.