Partial sums represent addition of whole numbers within 1,000 by decomposing each addend into hundreds, tens, and ones, adding corresponding place-value parts, and combining those results. This reasoning shows why regrouping may be needed when a partial sum reaches 10 or more units of a place and connects written computation to place value; it does not include general algorithms for larger numbers or algebraic summation.
To use partial sums, break each number into hundreds, tens, and ones. Then add matching place values and combine the results.
Example: Add .
The partial sums and show regrouping because tens make hundred, and ones make ten. Therefore,
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