Problem 24 - Fundamentals of Mathematics

Question

For the following problems, perform the additions. If you can, check each sum with a calculator. $$8,521+4,256$$

Step-by-Step Solution

Answer

8,521 plus 4,256 equals 12,777.

Step 1: Align the Numbers

Write the numbers 8,521 and 4,256 one on top of the other, aligning the digits according to their place values. \[\begin{array}{c} 8521 \+ 4256 \\hline\end{array}\]

Step 2: Add Unit Place

Add the digits in the unit place (rightmost digits). \[1 + 6 = 7\]

Step 3: Add Tens Place

Add the digits in the tens place. \[2 + 5 = 7\]

Step 4: Add Hundreds Place

Add the digits in the hundreds place. \[5 + 2 = 7\]

Step 5: Add Thousands Place

Add the digits in the thousands place. \[8 + 4 = 12\]

Step 6: Combine the Results

Combine the results while accounting for any carrying we've done, which in this case is none. Write the sum of each column below: \[\begin{array}{c} 8521 \+ 4256 \\hline 12777\end{array}\]

Step 7: Verification with Calculator

Use a calculator to confirm the sum is correct. Enter 8,521, then add 4,256, and check that the result is 12,777.

Key Concepts

Placing Values

Placing values is the foundation of successfully solving addition problems. It's all about understanding the roles of each digit in a number, which are determined by their position or "place value". In our example with 8,521 and 4,256, we place each number in a column format:

• The far right represents the "ones" place.
• Next to the left is the "tens" place.
• Continuing left, you have the "hundreds" place.
• The farthest left in this problem is the "thousands" place.

It is crucial to align numbers by matching their place values vertically. This makes sure that when you add, you’re combining equivalent units, leading to accurate results. Each position can only hold a single numeral from 0 to 9. If a sum exceeds 9, it affects the next column to the left.

Math Problems

Solving math problems often follows a systematic process. In addition, it includes aligning numbers, adding digit-by-digit, and possibly carrying over extra values to the next column. Our example, 8,521 + 4,256, showcases this.

You begin by adding the digits from right to left:

• "Ones" place: 1 + 6 = 7
• "Tens" place: 2 + 5 = 7
• "Hundreds" place: 5 + 2 = 7
• "Thousands" place: 8 + 4 = 12

Here, 12 in the "thousands" place means we write down the 2 and move (carry) the 1 over, if needed, to the left if there were more digits. This particular problem finishes here, with a final answer of 12,777.

Addition problems not only help practice mental arithmetic but also encourage carefulness and precision.

Calculation Verification

Verification is the final, essential step in any math problem. It confirms the accuracy of your solution. For addition like 8,521 + 4,256, reviewing steps mentally is one way. Another reliable method is using a calculator.

Here’s how to verify:

• Enter the first number: 8,521
• Add the second number: 4,256
• Check that the calculator displays: 12,777

This simple step ensures no errors occurred in manual calculations. With more complicated math, verification can prevent easily overshadowed mistakes. Both manual checking and using calculators are key tools in accurate math problem solving. They instill confidence, helping you trust the results you’ve worked hard to achieve.