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Adding and Regrouping Place Values

This lesson covers adding and regrouping place values in multi-digit numbers. It explains why regrouping works, walks through carrying extra ones into the tens column and extra tens into the hundreds column, and includes worked examples with diagrams and common mistakes to avoid.

What Does Regrouping Mean in Addition?

When you add multi-digit numbers, sometimes the digits in one column add up to \(10\) or more. Since only one digit can fit in each place value spot, you have to "regroup" the extra amount into the next column to the left. This is often called carrying, and it is one of the most important skills for adding larger numbers correctly.

Regrouping works because of how our number system is built: every place value is worth ten times the value of the place to its right. That means \(10\) ones can always be traded for \(1\) ten, and \(10\) tens can always be traded for \(1\) hundred, and so on.

Reviewing Place Value Before You Add

Before regrouping makes sense, you need to be comfortable telling which digit sits in the ones, tens, and hundreds spot of a number. If you want a refresher, look back at Identifying the Place Value of a Digit or organize numbers using a place value table before you start adding.

Step-by-Step: Adding with Regrouping

Follow the same routine every time you add multi-digit numbers with regrouping:

Line up the numbers by place value, ones under ones, tens under tens, and so on.
Start adding from the ones column, the smallest place value, and work left.
If a column's sum is \(9\) or less, write it directly under that column.
If a column's sum is \(10\) or more, write only the ones digit of that sum, and carry the tens digit up to the top of the next column.
Add the carried digit into the next column's sum before moving on.

Example 1: Regrouping the Ones

Add \(48 + 27\). In the ones column, \(8 + 7 = 15\). Write the \(5\) in the ones place of the answer and carry the \(1\) ten to the top of the tens column. Then add the tens column: \(1 + 4 + 2 = 7\).

So \(48 + 27 = 75\).

Example 2: Regrouping Twice (Ones and Tens)

Add \(358 + 267\). Ones column: \(8 + 7 = 15\), write \(5\), carry \(1\) ten. Tens column: \(1 + 5 + 6 = 12\), write \(2\), carry \(1\) hundred. Hundreds column: \(1 + 3 + 2 = 6\).

So \(358 + 267 = 625\). Notice how the carry moved twice, first from the ones into the tens, then from the tens into the hundreds.

Why Regrouping Works

Regrouping is just a fast way of trading equal value. If the ones column gives a sum like \(15\), that really means \(1\) ten and \(5\) ones, since \(15 = 10 + 5\). Writing out the expanded form of multi-digits can help you see this trade happening: \(48 = 40 + 8\) and \(27 = 20 + 7\), so \(48 + 27 = (40+20) + (8+7) = 60 + 15 = 60 + 10 + 5 = 75\). The extra \(10\) from the ones simply becomes another ten.

Common Mistakes to Avoid

Forgetting to write the carried digit above the next column, then losing track of it.
Adding the carried digit into the wrong column instead of the one directly to its left.
Writing both digits of a two-digit column sum instead of carrying the extra ten.
Misaligning digits because the numbers were not lined up by matching place value first.

Quick Practice Tip

Before adding, say each number out loud by place value (for example, "three hundred fifty eight"). This habit keeps your columns lined up correctly and makes it easier to spot when a sum needs regrouping.

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