Adding with regrouping
Adding with regrouping (also called carrying) is the technique used in 4th grade math when the sum of digits in any column is 10 or more: write down the ones digit and carry the tens digit to the next column to the left. In Saxon Math Intermediate 4, Chapter 1, this process is reinforced as students add two- and three-digit numbers. Understanding regrouping connects place value to arithmetic and is the foundational skill underlying all multi-digit addition and subtraction algorithms.
Key Concepts
Property When we add, we sometimes have to regroup because we cannot have a number larger than 10 as the sum of any place value.
Example For $39 + 14$: add ones $9+4=13$. Write down the 3 and carry the 1 ten. Then add tens $1+3+1=5$. Your total is 53. For $68 + 24$: add ones $8+4=12$. Write 2, carry the 1 ten. Add tens $1+6+2=9$. The sum is 92.
Explanation You can't fit two digits in the ones place! If you have 13 ones, it’s like having too many coins. You trade ten 1 dollar bills for one 10 dollar bill and carry that new ten over to its proper column.
Common Questions
What is regrouping in addition?
Regrouping (or carrying) means that when the digits in one column add up to 10 or more, you keep only the ones digit in that column and carry the tens value to the next column to the left.
How do you add with regrouping step by step?
First add the ones column. If the sum is 10 or more, write the ones digit below and write the tens digit above the next column. Then add the tens column including the carried digit, and repeat for each column.
What is an example of adding with regrouping?
For 39 + 14: add the ones 9 + 4 = 13. Write 3 in the ones place and carry 1 to the tens. Then add tens: 1 + 3 + 1 = 5. The answer is 53.
Why do we regroup when adding?
Because each place value column can only hold one digit (0-9). When a column sums to 10 or more, the tens portion must move to the next column to maintain correct place value representation.
When do 4th graders learn to add with regrouping?
In Saxon Math Intermediate 4, regrouping in addition is introduced in Chapter 1, Lessons 1-10, and practiced throughout the year with progressively larger numbers.
How is addition regrouping related to subtraction regrouping?
Addition carries (moves value left) when a column overflows, while subtraction borrows (moves value right) when a column does not have enough. Both processes preserve place value balance and use the same column-by-column logic.