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Chapter 1: Problem 13

Add. $$\begin{array}{r} 12 \\ 15 \\ +32 \\ \hline \end{array}$$

Short Answer

Expert verified
The sum is 59.

Step by step solution

01

Align the Numbers

Write the numbers vertically with the units' digits (rightmost digits) aligned for easy addition.
02

Add the Units Column

Add the digits in the units column (rightmost column): 2 + 5 + 2 = 9.
03

Add the Tens Column

Add the digits in the tens column (leftmost column): 1 + 1 + 3 = 5.
04

Combine the Results

Combine the sums of each column. The units column sum is 9 and the tens column sum is 5. Therefore, the result is 59.

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Key Concepts

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

Aligning Numbers
When solving an addition problem, it is crucial to align the numbers correctly. This ensures that each digit is in the correct column, making the addition process straightforward.
Start by writing the numbers vertically. Align the units (rightmost) digits directly above and below one another. For example, for the numbers 12, 15, and 32:

12
15
+32
------
Each number's units digit (2, 5, and 2, respectively) is directly aligned in one column, and the tens digits (1, 1, and 3, respectively) are aligned in the next column. This step helps avoid mistakes by keeping the place values consistent.
Units Column Addition
Once the numbers are aligned, we focus on adding the units column. The units column consists of the rightmost digits of the numbers.
In this example, the units digits are 2, 5, and 2. Add these digits together step by step:
  • First, add 2 and 5, which equals 7.
  • Next, add the result (7) to the last units digit, which is 2, giving us a final sum of 9.

This sum of the units column, 9, will be part of our final result.
Tens Column Addition
With the units column complete, we move on to the tens column. The tens column contains the leftmost digits of the numbers.
For the numbers 12, 15, and 32, the tens digits are 1, 1, and 3. Add these digits step by step:
  • First, add 1 and 1, which equals 2.
  • Next, add the result (2) to the final tens digit, which is 3, giving us a final sum of 5.

This sum of the tens column, 5, will be combined with the sum from the units column.

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