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Add using the standard algorithm

The standard algorithm represents addition of multi-digit whole numbers by aligning equal place values and combining digits from right to left, regrouping whenever a place-value total reaches ten; it applies to addends through the millions, including cases requiring regrouping across several places or zeros. It connects written computation to the base-ten structure of numbers and helps prevent errors such as misaligning digits, while more advanced extensions to decimals, fractions, or arbitrary-sized numbers are not included.

Detailed Explanation: Add using the standard algorithm

Line up the numbers so that digits with the same place value are in the same column. Start adding in the ones column and move left. When a column totals 1010 or more, write the ones digit and regroup by carrying 11 to the next column.

Example: Add 3,786,459+2,947,6833,786,459+2,947,683.

First, align the place values:

+3,786,459+ 2,947,683\begin{array}{r} \phantom{+}3,786,459\\ +\ 2,947,683\\ \hline \end{array}

Add from right to left:

  1. Ones: 9+3=129+3=12. Write 22 in the ones place and carry 11.
  2. Tens: 5+8+1=145+8+1=14. Write 44 and carry 11.
  3. Hundreds: 4+6+1=114+6+1=11. Write 11 and carry 11.
  4. Thousands: 6+7+1=146+7+1=14. Write 44 and carry 11.
  5. Ten-thousands: 8+4+1=138+4+1=13. Write 33 and carry 11.
  6. Hundred-thousands: 7+9+1=177+9+1=17. Write 77 and carry 11.
  7. Millions: 3+2+1=63+2+1=6. Write 66.

The completed addition is:

+3,786,459+ 2,947,683+6,734,142\begin{array}{r} \phantom{+}3,786,459\\ +\ 2,947,683\\ \hline \phantom{+}6,734,142 \end{array}

Therefore, 3,786,459+2,947,683=6,734,142\boxed{3,786,459+2,947,683=6,734,142}.

Learn by doing: Add using the standard algorithm

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

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