This understanding involves decomposing each two-digit addend into tens and ones, combining like place values, and determining the sum when the ones digits total fewer than ten and the tens digits also total fewer than ten. The learner connects expanded notation, place-value models, and the standard vertical algorithm, understanding why each digit remains in its place; cases requiring composing a new ten, larger numbers, and more general algorithms are outside this scope.
To add two 2-digit numbers without regrouping:
Example: Find .
Break apart the numbers:
Add like place values:
Now combine the tens and ones:
You can also use the vertical method. Line up the tens and ones:
23
+ 45
----
68
The ones digits are in the same column, so . The tens digits are in the same column, so . Since neither sum is or more, no new ten needs to be made. Therefore, .
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