Whole numbers within 1,000 can be decomposed into hundreds, tens, and ones or into other addends in multiple equivalent ways, such as . This understanding connects place value, regrouping, and the part–part–whole relationship, emphasizing that changing the partition does not change the total and supporting flexible addition, subtraction, and multiplication; more general decompositions of larger numbers are outside this scope.
To decompose a number means to break it into parts that add to the same total. You can use hundreds, tens, and ones, or regroup some parts to make different addends.
Example: Decompose in different ways.
Start with the place-value parts:
So,
Regroup one ten as ones. Now there are tens and ones:
Regroup one hundred as ones. Now there are hundreds and ones:
Each way has the same total:
The parts change, but the whole number stays the same.
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