Adding with Digits Up to 1000

Numbers up to 1000 can have up to three digits: a hundreds digit, a tens digit, and a ones digit. For example, in \(356\) the \(3\) means 3 hundreds, the \(5\) means 5 tens, and the \(6\) means 6 ones. Adding two numbers like these is often called 3-digit addition, and it works the same way as adding smaller numbers, except now there is a hundreds column to keep track of as well.

The key idea is to keep matching place values together. Ones are added to ones, tens are added to tens, and hundreds are added to hundreds. This lesson builds on skills from Addition with Tens and Ones, extending the same column method one place value further.

Before adding, write the numbers on top of each other so that the ones digits line up, the tens digits line up, and the hundreds digits line up. Lining the digits up correctly is the most important step, since even a strong addition strategy will give the wrong answer if the columns are misaligned.

When every column adds to less than 10, there is no carrying to worry about. For example, \(213 + 154\): ones give \(3+4=7\), tens give \(1+5=6\), hundreds give \(2+1=3\), so \(213 + 154 = 367\). This is the simplest case and a good warm-up before tackling regrouping.

Regrouping happens whenever a column's total is 10 or more. Since only one digit can be written in each column, the extra amount is "carried" as an extra 1 into the next column to the left, because ten ones make one ten, and ten tens make one hundred.

Work through \(356 + 274\) one column at a time:

• Ones: \(6 + 4 = 10\). Write \(0\) in the ones place and carry \(1\) to the tens column.
• Tens: \(5 + 7 = 12\), plus the carried \(1\) makes \(13\). Write \(3\) in the tens place and carry \(1\) to the hundreds column.
• Hundreds: \(3 + 2 = 5\), plus the carried \(1\) makes \(6\). Write \(6\) in the hundreds place.

Putting the digits together gives \(356 + 274 = 630\).

Try \(487 + 365\):

• Ones: \(7 + 5 = 12\). Write \(2\), carry \(1\).
• Tens: \(8 + 6 = 14\), plus the carried \(1\) is \(15\). Write \(5\), carry \(1\).
• Hundreds: \(4 + 3 = 7\), plus the carried \(1\) is \(8\). Write \(8\).

So \(487 + 365 = 852\).

After finishing a 3-digit addition problem, it helps to check the answer is reasonable. Rounding each number and adding the rounded values gives a quick estimate; for \(356 + 274\), rounding to the nearest hundred gives \(400 + 300 = 700\), which is close to the actual answer of \(630\) and confirms nothing went badly wrong. This estimation check is explored further in Addition using Estimation.

If the numbers being added are the same or very close, strategies from Adding with Doubles Up to 1000 can make mental addition even faster than working column by column.

Two errors show up most often in 3-digit addition with regrouping. The first is misaligning digits, which mixes up place values and produces a wrong sum. The second is forgetting to add the carried 1 into the next column, which makes the answer too small by exactly 10 or 100. Slowing down and writing the carried digit clearly above the correct column avoids both mistakes.

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