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Add two 2-digit numbers with regrouping

The learner understands that adding two two-digit whole numbers combines ones with ones and tens with tens, and that ten ones can be composed as one ten; if the tens total reaches ten, ten tens can likewise be composed as one hundred. Place-value drawings, expanded notation, and the standard written method represent the same composition process, preventing the misconception that a regrouped digit is simply “carried” without changing its value.

Detailed Explanation: Add two 2-digit numbers with regrouping

To add two 2-digit numbers, add the ones first, then the tens. If there are 10 or more ones, regroup 10 ones as 1 ten.

Example: Add (47+38)(47+38).

Write the numbers so the place values line up:

47+38\begin{array}{r} 47\\ +38\\ \hline \end{array}

1. Add the ones.

7+8=157+8=15

Fifteen ones means 11 ten and 55 ones:

15=10+515=10+5

Write the 55 in the ones place and regroup the 11 ten into the tens place:

47+385\begin{array}{r} 4\cancel{7}\\ +3\cancel{8}\\ \hline 5 \end{array}

2. Add the tens, including the regrouped ten.

4+3+1=84+3+1=8

Write 88 in the tens place:

47+3885\begin{array}{r} 47\\ +38\\ \hline 85 \end{array}

Therefore,

47+38=85\boxed{47+38=85}

The regrouped 11 is not just a number to “carry.” It represents 1 new ten, made from the 10 ones in (15)(15) ones.

Learn by doing: Add two 2-digit numbers with regrouping

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    Base 10 Blocks - Adding - Picture to Answer, With Carry - Tens and Ones

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