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Chapter 1: Problem 26

Add. $$ \begin{array}{r} 989 \\ 566 \\ 834 \\ +\quad 703 \\ \hline \end{array} $$

Short Answer

Expert verified
3092

Step by step solution

01

Align the Numbers

Write down the given numbers in a column aligning the digits by their place values (units, tens, hundreds).
02

Add the Units Place

Add the digits in the units place: 9 + 6 + 4 + 3 = 22. Write down the 2 and carry over the 2 to the tens place.
03

Add the Tens Place

Add the digits in the tens place along with the carried-over value: 8 + 6 + 3 + 0 + 2 = 19. Write down the 9 and carry over the 1 to the hundreds place.
04

Add the Hundreds Place

Add the digits in the hundreds place along with the carried-over value: 9 + 5 + 8 + 7 + 1 = 30. Write down the 0 and carry over the 3 to the thousands place.
05

Write the Final Result

Since there is nothing left to add in the thousands place except the carried-over value, write down the 3. The final sum is 3092.

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Key Concepts

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

Place Value
Understanding place value is crucial in the addition of multi-digit numbers. Place value determines the value of each digit in a number based on its position. For instance, in the number 834, 8 is in the hundreds place, 3 is in the tens place, and 4 is in the units place. Imagine place value as different 'slots' where each slot has a unique value depending on its position.
When aligning numbers for addition, it is essential to line up the units, tens, hundreds, etc., correctly. This way, each digit in one number is added to the corresponding digit in another number.
Carrying Over
Carrying over is a fundamental concept in addition when the sum of the digits in a column exceeds 9. Each place value can only hold a single digit (0-9).
For example, in the units place, we add 9 + 6 + 4 + 3 = 22. Here, we write down the digit 2 in the units place and 'carry over' the digit 2 to the next column (the tens place).
Similarly, when adding the tens place, we include the carried-over value: 8 + 6 + 3 + 0 + 2 = 19. We write down the 9 and carry over 1 to the hundreds place. This process continues for each place value. The carried-over values ensure that the sum in each place value remains correct.
Column Alignment in Addition
Column alignment is vital for accurate addition. When given numbers like 989, 566, 834, and 703, start by writing each number in a column. Align the digits by their place values: units under units, tens under tens, and hundreds under hundreds.
  • Start with the rightmost digit (units place) and add down the column.
  • Move left to the tens place, including any carried-over value if needed.
  • Finally, move to the hundreds place and repeat the process.
Correct alignment ensures that each digit adds to the appropriate place value, keeping the calculation accurate and making it easier to handle carrying over.

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