Introduction to Regrouping (Carrying)

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$$529 + 164 = ?$$

$$\begin{array}{rr} & 529 \\ + & 164 \\ \hline & 693 \end{array}$$Ones: $9+4=13$. Write $3$, carry $1$. Tens: $1+2+6=9$. Hundreds: $5+1=6$.

Why do we carry a '$1$' when the sum is, for example, $15$?

Because $15$ ones is the same as $1$ ten and $5$ ones. The $1$ ten is 'carried' over to be added with the other tens.

$$315 + 415 = ?$$

$$\begin{array}{rr} & 315 \\ + & 415 \\ \hline & 730 \end{array}$$Ones: $5+5=10$. Write $0$, carry $1$. Tens: $1+1+1=3$. Hundreds: $3+4=7$.

$$68 + 7 = ?$$

$$\begin{array}{rr} & 68 \\ + & 7 \\ \hline & 75 \end{array}$$Ones: $8+7=15$. Write $5$, carry $1$. Tens: $1+6=7$.

What does it mean to 'regroup' in addition?

When the sum of a column is $10$ or more, you bundle a group of $10$ and move it as a '1' to the next higher place value column.

What is another word for 'regrouping'?

A common word is 'carrying' or 'carrying over'.

In the problem $28 + 15$, what is the sum of the digits in the ones column ($8+5$)?

The sum is $13$.

When the ones column adds up to $13$, what two things do you do?

1. Write the $3$ (from the ones place of $13$) in the answer's ones place. 2. Carry the $1$ (from the tens place of $13$) to the top of the tens column.

$$28 + 15 = ?$$

$$\begin{array}{rr} & 28 \\ + & 15 \\ \hline & 43 \end{array}$$Ones: $8+5=13$. Write $3$, carry $1$ to the tens column. Tens: Add the carried $1$ to the other tens: $1+2+1=4$.

$$147 + 236 = ?$$

$$\begin{array}{rr} & 147 \\ + & 236 \\ \hline & 383 \end{array}$$Ones: $7+6=13$. Write $3$, carry $1$. Tens: $1+4+3=8$. Hundreds: $1+2=3$.

If the sum of your ones column is $19$, what digit do you write in the answer's ones place?

You write the $9$.

If the sum of your ones column is $19$, what number do you carry to the tens column?

You carry the $1$, which represents $1$ ten.