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Add multi-digit whole numbers

Addition of multi-digit whole numbers, including numbers through 1,000,000, is understood as combining quantities by aligning like place values and composing ten units of one place into one unit of the next. Place-value charts, expanded form, partial sums, and the standard algorithm show why regrouping works; estimation and inverse reasoning help judge whether a result is reasonable and prevent treating digits independently. This scope excludes decimals, negative numbers, and more abstract or unrestricted number systems.

Detailed Explanation: Add multi-digit whole numbers

To add multi-digit whole numbers:

  1. Line up the numbers by place value. Ones go under ones, tens under tens, and so on.
  2. Add from right to left, starting with the ones.
  3. If a sum is 1010 or more, regroup: write the ones digit and carry the tens digit to the next place.

Example:

458,763+276,589\begin{array}{r} 458{,}763\\ +276{,}589\\ \hline \end{array}

Add each place:

  • Ones: 3+9=123+9=12. Write 22 in the ones place and carry 11 ten.
  • Tens: 6+8+1=156+8+1=15. Write 55 and carry 11.
  • Hundreds: 7+5+1=137+5+1=13. Write 33 and carry 11.
  • Thousands: 8+6+1=158+6+1=15. Write 55 and carry 11.
  • Ten-thousands: 5+7+1=135+7+1=13. Write 33 and carry 11.
  • Hundred-thousands: 4+2+1=74+2+1=7.

The completed addition is:

458,763+276,589735,352\begin{array}{r} 458{,}763\\ +276{,}589\\ \hline 735{,}352 \end{array}

So,

458,763+276,589=735,352.458{,}763+276{,}589=735{,}352.

Check that the answer is reasonable by estimating:

459,000+277,000≈736,000.459{,}000+277{,}000\approx736{,}000.

Since 735,352735{,}352 is close to 736,000736{,}000, the answer makes sense.

Learn by doing: Add multi-digit whole numbers

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    Addition - Whole Number 4 digit + 3 digit - Column, With Carry

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