# Subtraction With Regrouping

by on December 20, 2011

You may not be familiar with the term “regrouping”.  You may remember it being called subtraction with “borrowing”.  We have gone away from calling it borrowing and tend to call it regrouping now, simply because that is exactly what the numbers are doing; they are regrouping themselves between columns.  The idea of “borrowing” implies that we are going to return something, when in fact the number never gets returned to its original column!

So, what exactly is Subtraction with Regrouping?  Once your child has had an opportunity to learn his Subtraction facts, and once he has practiced some Column Subtraction without regrouping, he will move on to Subtraction with Regrouping.  This type of subtraction is when we take two 2-digit numbers (or larger), and line them up one on top of the other in a column.  When you look at the Ones column, the digit on the top is smaller than the digit on the bottom, which makes that column difficult to solve without regrouping into the next column.

Let me explain.  We always begin subtracting in the Ones column, or the column furthest to the right.  If we had the problem 63 – 35 (written up and down in column format of course!), we would begin by trying to subtract the numbers in the Ones column, which are 3 – 5.  Since 3 – 5 is not possible, we have to “go next door” to the Tens column and ask for help.  I always tell kids that the Tens column is very generous, and that he is always willing to give up a bundle of ten, even if it’s his last one!  So, your child would look in the Tens column, and “take” one from the Tens column by striking the 6 and writing a 5 above it (the Tens column had one taken from him, so he is left with 5 instead of 6).  Now ask your child to take that number that he just got from the Tens column and bring it back home to the Ones column.  I like to have kids write a small “1” to the left of the number in the Ones column (the 3) to show that they now have 13 in the Ones column.  Now, your child has 13 – 5 in the Ones column, which is possible to subtract.  He would write the answer or “difference” of 8 under the equals sign.  Next, he would look at the Tens column, which now reads 5 – 3.  He would subtract these two numbers and print 2 under the equals sign.  He should see a final answer of 28.

What to watch for: When children begin subtraction with regrouping, they want to flip the numbers around so the subtraction “works”.  Using our previous example, a child will often write the answer of “2” in the Ones column, because he simply flipped the 3 and the 5 in the Ones column to make 5-3 instead of 3-5.

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• As always, playing math games at home is a great way to reinforce math skills learned in school.