Add multi-digit whole numbers Addition of multi-digit whole numbers is understood as combining quantities while preserving place-value units: ones are combined with ones, tens with tens, and so on, with each group of ten regrouped into the next place. The standard algorithm is justified by this structure and checked through estimation, expanded form, or properties of addition for several-digit numbers, including numbers in the millions; decimals, negative numbers, and more abstract generalizations are outside this scope.
Detailed Explanation: Add multi-digit whole numbers To add multi-digit whole numbers:
Line up the numbers by place value : ones under ones, tens under tens, hundreds under hundreds, and so on.Add from right to left , starting with the ones.If a column adds to 10 10 10 regroup : write the ones digit in that column and carry the tens digit to the next column.
Example:
3 , 758 , 496 + 2 , 684 , 759 \begin{array}{r}
3,758,496\\
+2,684,759\\
\hline
\end{array} 3 , 758 , 496 + 2 , 684 , 759 ​ ​ Add each place-value column from right to left:
Ones: 6 + 9 = 15 6+9=15 6 + 9 = 15 5 5 5 1 1 1 Tens: 9 + 5 + 1 = 15 9+5+1=15 9 + 5 + 1 = 15 5 5 5 1 1 1 Hundreds: 4 + 7 + 1 = 12 4+7+1=12 4 + 7 + 1 = 12 2 2 2 1 1 1 Thousands: 8 + 4 + 1 = 13 8+4+1=13 8 + 4 + 1 = 13 3 3 3 1 1 1 Ten-thousands: 5 + 8 + 1 = 14 5+8+1=14 5 + 8 + 1 = 14 4 4 4 1 1 1 Hundred-thousands: 7 + 6 + 1 = 14 7+6+1=14 7 + 6 + 1 = 14 4 4 4 1 1 1 Millions: 3 + 2 + 1 = 6 3+2+1=6 3 + 2 + 1 = 6
So,
3 , 758 , 496 + 2 , 684 , 759 6 , 443 , 255 \begin{array}{r}
3,758,496\\
+2,684,759\\
\hline
6,443,255
\end{array} 3 , 758 , 496 + 2 , 684 , 759 6 , 443 , 255 ​ ​ The sum is 6 , 443 , 255 \boxed{6,443,255} 6 , 443 , 255 ​
You can check that the answer is reasonable by estimating:
3 , 758 , 496 ≈ 3 , 800 , 000 and 2 , 684 , 759 ≈ 2 , 700 , 000 3,758,496\approx3,800,000
\qquad\text{and}\qquad
2,684,759\approx2,700,000 3 , 758 , 496 ≈ 3 , 800 , 000 and 2 , 684 , 759 ≈ 2 , 700 , 000 Since 3 , 800 , 000 + 2 , 700 , 000 = 6 , 500 , 000 3,800,000+2,700,000=6,500,000 3 , 800 , 000 + 2 , 700 , 000 = 6 , 500 , 000 6 , 443 , 255 6,443,255 6 , 443 , 255