Addition

Add Three-Digit Numbers With Carrying

Add 386 + 247 column by column, carrying in both the ones place (6+7=13) and the tens place (8+4+1=13) to get 633.

carry A carry propagates when a column sum is 10 or more: write the ones digit and carry 1 to the next column. This can happen in multiple columns in the same problem.
regrouping A carry is a form of regrouping: 10 ones become 1 ten, or 10 tens become 1 hundred. Each carry moves 1 group to the column on the left.

Example

Add 386 and 247 with carries across columns.

highlighted = computed this step

Step 1 — Set up

Line up the addends by place value.

xxxx386+247x□□□\begin{array}{rrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\&3&8&6\\+&2&4&7\\\hline\\\phantom{x}&\square&\square&\square\end{array}
Line up hundreds, tens, and ones.hundredstensones386247+Add 386 and 247 from right to left.If a column reaches 10 or more, move one group to the next place.

Step 2 — Ones column

Ones: 6 + 7 = 13, write 3, carry 1.

xx1x386+247x□□3\begin{array}{rrrr}\phantom{x}&\phantom{x}&\hl{1}&\phantom{x}\\&3&8&6\\+&2&4&7\\\hline\\\phantom{x}&\square&\square&\hl{3}\end{array}
Ones make 13: write 3 ones and carry 1 ten.hundredstensones386247+3carry 11Ones: 6 + 7 = 1313 ones = 3 ones + 1 ten; write 3.

Step 3 — Tens column

Tens: 8 + 4 + carry 1 = 13, write 3, carry 1.

x11x386+247x□33\begin{array}{rrrr}\phantom{x}&\hl{1}&1&\phantom{x}\\&3&8&6\\+&2&4&7\\\hline\\\phantom{x}&\square&\hl{3}&3\end{array}
Tens make 13 with the carried 1: write 3 tens and carry 1 hundred.hundredstensones386247+3carry 113carry 11Tens: 8 + 4 + carry 1 = 1313 tens = 3 tens + 1 hundred; write 3.

Step 4 — Hundreds column

Hundreds: 3 + 2 + carry 1 = 6, write 6.

x11x386+247x633\begin{array}{rrrr}\phantom{x}&1&1&\phantom{x}\\&3&8&6\\+&2&4&7\\\hline\\\phantom{x}&\hl{6}&3&3\end{array}
Hundreds make 6 with the carried 1.hundredstensones386247+3carry 113carry 116Hundreds: 3 + 2 + carry 1 = 66 hundreds stay in the hundreds column; write 6.

Step 5 — Result

Read the complete answer: 633.

xxxx386+247x633,sum=633\begin{array}{rrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\&3&8&6\\+&2&4&7\\\hline\\\phantom{x}&6&3&3\end{array},\quad \text{sum}=633
Read the completed sum: 633.hundredstensones386247+carry 11carry 11633Result: 386 + 247 = 633Each written digit stayed in its own place-value column.