Add 3-digit numbers with regrouping

Addition of two three-digit whole numbers is understood as combining corresponding hundreds, tens, and ones, with ten units of one place composed as one unit of the next place whenever a column total reaches 10 or more. Place-value drawings, expanded form, and the standard algorithm represent the same regrouping structure; a carried digit is a newly composed place-value unit, not an extra number to append. The scope is limited to whole numbers with three-digit addends and does not include decimals or more advanced generalizations.

Detailed Explanation: Add 3-digit numbers with regrouping

Line up the numbers by place value:

Ones under ones
Tens under tens
Hundreds under hundreds

Example:

\begin{array}{r} 368\\ +257\\ \hline \end{array}

1. Add the ones

8+7=15

Write the $5$ in the ones place. Regroup the $10$ ones as $1$ ten, so carry $1$ to the tens place.

2. Add the tens

6+5+1=12

Write the $2$ in the tens place. Regroup the $10$ tens as $1$ hundred, so carry $1$ to the hundreds place.

3. Add the hundreds

3+2+1=6

Write the $6$ in the hundreds place.

\begin{array}{r} 368\\ +257\\ \hline 625 \end{array}

So, $\boxed{368+257=625}$ . The carried $1$ represents a newly made ten or hundred from regrouping.

Learn by doing: Add 3-digit numbers with regrouping

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

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