Problem 22 - Algebra 1

Question

Find the sum. $$17+35$$

Step-by-Step Solution

Answer

The sum of 17 and 35 is 52.

Step 1: Identify the Numbers to Add

We need to find the sum of the given expression: \(17+35\).

Step 2: Perform the Addition

We add the numbers together, aligning place values and carrying over as needed.

Step 3: State the Result

The sum of 17 and 35 is 52.

Key Concepts

Place Value

Understanding place value is essential in performing basic addition. It's the foundation of the decimal number system. Each digit in a number has a place value, determined by its position. For example, in the number 345, the '5' is in the ones place (or units), '4' is in the tens place, and '3' is in the hundreds place. When we read '345', it's actually shorthand for '3 hundreds, 4 tens, and 5 ones'.

In the context of the given exercise, the number '17' consists of '7' in the ones place and '1' in the tens place, similarly, the number '35' has '5' in the ones place and '3' in the tens place. When we add these numbers, we must align them by their place values to ensure we are adding the same types of units together: ones with ones, and tens with tens.

Carrying Over

Carrying over is a technique used in addition when the sum of a column exceeds the highest value for a single digit (9). If we're adding single digits and the total is 10 or more, we 'carry over' the excess to the next column to the left, which represents the higher place value.

For instance, when adding the ones place values in our exercise, we get 7 (from the number 17) plus 5 (from the number 35). This adds up to 12. Since 12 is more than 9, we write down the 2 and carry over the 1 to the tens place. Carrying over ensures that our digits in each place remain within the range of 0-9, which is a fundamental aspect of the decimal system.

Addition of Whole Numbers

The addition of whole numbers follows a systematic process of lining up numbers by their place values and then adding each column starting from the rightmost digit, which is the ones place. Once you add the ones place values, move to the tens and so on, carrying over whenever necessary.

In our exercise, after carrying over the 1 from the ones place, we next add the tens place digits — 1 (from 17), 3 (from 35), and the carried over 1, resulting in 5. There's nothing left to carry over, so we complete the addition. We can observe that through careful alignment and an understanding of place values and carrying over, the sum of the whole numbers 17 and 35 is straightforwardly calculated to be 52.