Advanced Regrouping in Multiple Columns

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What does it mean to have 'multiple regroupings' in one problem?

It means you have to carry a number in more than one column. For example, carrying from the ones to the tens, AND from the tens to the hundreds.

$$168 + 257 = ?$$

$$\begin{array}{rr} & 168 \\ + & 257 \\ \hline & 425 \end{array}$$Ones: $8+7=15$. Write $5$, carry $1$. Tens: $1+6+5=12$. Write $2$, carry $1$. Hundreds: $1+1+2=4$.

$$399 + 499 = ?$$

$$\begin{array}{rr} & 399 \\ + & 499 \\ \hline & 898 \end{array}$$Ones: $9+9=18$. Write $8$, carry $1$. Tens: $1+9+9=19$. Write $9$, carry $1$. Hundreds: $1+3+4=8$.

$$87 + 95 = ?$$

$$\begin{array}{rr} & 87 \\ + & 95 \\ \hline & 182 \end{array}$$Ones: $7+5=12$. Write $2$, carry $1$. Tens: $1+8+9=18$. Write $8$ in the tens place and the $1$ in the new hundreds place.

What happens when you need to regroup from the hundreds column?

The carried digit moves to the thousands place. For example, $12$ hundreds is the same as $1$ thousand and $2$ hundreds.

$$678 + 543 = ?$$

$$\begin{array}{rr} & 678 \\ + & 543 \\ \hline & 1221 \end{array}$$Ones: $8+3=11$. Write $1$, carry $1$. Tens: $1+7+4=12$. Write $2$, carry $1$. Hundreds: $1+6+5=12$. Write $2$, carry $1$ to the thousands place.

$$99 + 99 = ?$$

$$\begin{array}{rr} & 99 \\ + & 99 \\ \hline & 198 \end{array}$$

$$456 + 789 = ?$$

$$\begin{array}{rr} & 456 \\ + & 789 \\ \hline & 1245 \end{array}$$

When solving $247 + 385$, which columns will you need to regroup in?

Both the ones column ($7+5=12$) and the tens column ($1+4+8=13$). You will regroup twice.

$$999 + 2 = ?$$

$$1001$$

$$586 + 627 = ?$$

$$1213$$

$$88 + 88 = ?$$

$$176$$

$$249 + 155 = ?$$

$$404$$

$$765 + 345 = ?$$

$$1110$$