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Chapter 1: Problem 37

Add the numbers. $$ \begin{array}{r} 554 \\ 184 \\ 883 \\ \hline \end{array} $$

Short Answer

Expert verified
The sum is 1621.

Step by step solution

01

Add the Units Column

Start by adding the digits in the units place. In this problem, the digits are 4 (from 554), 4 (from 184), and 3 (from 883). So, add: \(4 + 4 + 3 = 11\).Write down 1 and carry over 1 to the tens column.
02

Add the Tens Column

Next, add the digits in the tens place along with the carried over digit. The digits are 5 (from 554), 8 (from 184), and 8 (from 883), plus the carried over 1.So, add: \(5 + 8 + 8 + 1 = 22\).Write down 2 and carry over 2 to the hundreds column.
03

Add the Hundreds Column

Lastly, add the digits in the hundreds place along with the carried over digits. The digits are 5 (from 554), 1 (from 184), and 8 (from 883), plus the carried over 2.So, add: \(5 + 1 + 8 + 2 = 16\).Write down 16, as there are no more columns to add.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Column Addition
Column addition is a method used to add numbers in a structured way, aligning the numbers by their place values. This technique is particularly useful when adding large numbers. When performing column addition:
  • Ensure all numbers are aligned in vertical columns based on their place values: units, tens, hundreds, etc.
  • Start adding from the rightmost column (units column) to the leftmost column.
  • If the sum of a column exceeds 9, carry over the extra value to the next left column.
Column addition helps visualize the addition process and avoids mistakes by compartmentalizing the numbers into manageable segments.
Step by Step Solution
Following a step-by-step approach ensures that every part of the addition is executed correctly. It involves:
  • Adding the numbers in each column sequentially, starting from the units column.
  • Checking each column sum to determine if a carry over is needed.
  • Writing down the result or the excess value (from carry over) in its appropriate place.
Let's break down the given solution: First, you identify and add up all digits in the units column: 4, 4, and 3, resulting in 11. Write down 1 and carry over 1 to the tens column. Then add the tens column: 5, 8, and 8, plus the carried over 1, resulting in 22. Write down 2 and carry over 2 to the hundreds column. Finally, add the hundreds column: 5, 1, and 8, plus the carried over 2, resulting in 16. Since no further columns exist, jot down 16 as the final entry.
Carrying Over
Carrying over is an essential part of multi-digit addition. It involves transferring a digit to the next column when a column's sum exceeds 9. This ensures correct place value representation:
  • Add up the digits in any column, if the total is 10 or more, identify the carry over value.
  • The number in the units place of this sum is recorded in the current column.
  • The carry over, which is typically the tens digit of the sum, is moved to the next left column.
In the provided example, during the units step, the sum is 11, so 1 is carried over to the tens column. In the tens column, the sum is 22, leading to a carry over of 2 to the hundreds column. Practicing carrying over solidifies the understanding and execution of addition, keeping results accurate and well-organized.

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Most popular questions from this chapter

For the following problems, show that the pairs of quantities yield the same sum. $$(114+226)+108 \text { and } 114+(226+108)$$

Use the numbers 15 and 8 to illustrate the commutative property of addition.

Find the sums and differences. $$ \begin{array}{r} 1,642 \\ +\quad 899 \\ \hline \end{array} $$

Round 18,995 to the nearest ten.

Combine the numbers as indicated. $$19,040+813$$
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