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Add multi-digit whole numbers

The understanding centers on combining whole-number quantities by coordinating corresponding place-value units: ones with ones, tens with tens, and so on. When a column totals ten or more, the learner composes a unit of the next place and records the remainder, preserving the value of the sum; expanded form, place-value charts, and estimation support interpretation and error checking alongside the standard algorithm. The scope is multi-digit whole numbers, including numbers through commonly used large place values, not decimals, signed numbers, or abstract generalizations.

Detailed Explanation: Add multi-digit whole numbers

Line up the numbers by place value: ones under ones, tens under tens, hundreds under hundreds, and so on. Then add from right to left. If a column totals 1010 or more, regroup: write the ones digit and carry the extra ten to the next column.

Example:

47,586+26,739\begin{array}{r} 47{,}586\\ + 26{,}739\\ \hline \end{array}

  1. Ones: 6+9=156+9=15. Write 55 in the ones place and carry 11 ten.

  2. Tens: 8+3+1=128+3+1=12. Write 22 in the tens place and carry 11 hundred.

  3. Hundreds: 5+7+1=135+7+1=13. Write 33 in the hundreds place and carry 11 thousand.

  4. Thousands: 7+6+1=147+6+1=14. Write 44 in the thousands place and carry 11 ten-thousand.

  5. Ten-thousands: 4+2+1=74+2+1=7. Write 77.

So,

47,586+26,73974,325\begin{array}{r} 47{,}586\\ + 26{,}739\\ \hline 74{,}325 \end{array}

Therefore, 47,586+26,739=74,325\boxed{47{,}586+26{,}739=74{,}325}.

To check, round the numbers:

47,586≈48,000,26,739≈27,00047{,}586\approx 48{,}000,\qquad 26{,}739\approx 27{,}000

Since 48,000+27,000=75,00048{,}000+27{,}000=75{,}000, the exact answer 74,32574{,}325 is reasonable.

Learn by doing: Add multi-digit whole numbers

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

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