Problem 21 - Fundamentals of Mathematics

Question

For the following problems, perform the additions. If you can, check each sum with a calculator. $$ \begin{array}{r} 104 \\ +561 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The sum is 665.

Step 1: Line up the Numbers

Write the numbers 104 and 561 one below the other, aligning their digits by place value: \[\begin{array}{c}\phantom{+}104 \+561 \\hline\end{array}\]

Step 2: Add the Ones Column

Add the digits in the ones place: 4 + 1 = 5. Write 5 in the ones place of the answer:\[\begin{array}{c}\phantom{+}104 \+561 \\hline\phantom{0}5\end{array}\]

Step 3: Add the Tens Column

Add the digits in the tens place: 0 + 6 = 6. Write 6 in the tens place of the answer:\[\begin{array}{c}\phantom{+}104 \+561 \\hline65\end{array}\]

Step 4: Add the Hundreds Column

Add the digits in the hundreds place: 1 + 5 = 6. Write 6 in the hundreds place of the answer:\[\begin{array}{c}\phantom{+}104 \+561 \\hline665\end{array}\]

Step 5: Verify with a Calculator

Use a calculator to verify the sum. Enter 104 + 561 and confirm the result is 665.

Key Concepts

Understanding Place Value

In the world of mathematics, place value is a crucial concept that helps us understand the significance of each digit in a number. Each digit in a number has a specific place, with each place representing a different power of ten. This is what we mean by the term "place value."
For example, in the number 104:

• The digit 4 is in the ones place, meaning it represents 4 units.
• The digit 0 is in the tens place, meaning it represents 0 groups of ten.
• The digit 1 is in the hundreds place, representing 100 or 1 group of a hundred.

When adding numbers like 104 and 561, lining up the numbers by their place values is essential. This ensures that you are properly combining units, tens, and hundreds.
By doing this, you minimize errors and can easily track which numbers have been combined.

Breaking Down Each Step

Solving an addition problem step by step helps to simplify the process and make it more manageable. Following a systematic approach allows us to ensure that each component of the problem is addressed correctly.

• Step 1: Line Up the Numbers
  Align each digit according to its place value. This makes it easier to add the digits from right to left, beginning with the ones column.
• Step 2: Add the Ones Column
  Start by adding the digits in the ones place. For our exercise, 4 + 1 equals 5. Write this in the answer's ones place.
• Step 3: Add the Tens Column
  Next, add the digits in the tens place, 0 + 6 will result in 6. Write 6 in the tens place under the number line.
• Step 4: Add the Hundreds Column
  Finally, move to the hundreds place. Add 1 and 5 to get 6. Place this result in the hundreds column of your answer.

Using a Calculator for Verification

Calculators are valuable tools that not only help during trouble but also give us a means to verify our work.
After solving a problem like 104 + 561 by hand, using a calculator can confirm the accuracy of your manual calculation. Here's how:

• Enter the numbers clearly into the calculator.
• Press the addition button, followed by the equals button.
• Check if the calculator displays 665, matching your manual result.

This use of technology offers reassurance, especially when learning. Calculators help us see if our understanding of the process holds up and if our calculations are correct. It's always good practice to verify results to build confidence.