Skill: Add two 2-digit numbers with regrouping

Explanation and Free Practice Resources

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.

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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 $(47+38)$ .

Write the numbers so the place values line up:

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

1. Add the ones.

7+8=15

Fifteen ones means $1$ ten and $5$ ones:

15=10+5

Write the $5$ in the ones place and regroup the $1$ ten into the tens place:

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

2. Add the tens, including the regrouped ten.

4+3+1=8

Write $8$ in the tens place:

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

Therefore,

\boxed{47+38=85}

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

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Addition - Whole Number 2 digit + 2 digit, With Carry

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