Regrouping and Column Math For Arithmetic

When kids are learning two-digit addition and subtraction, one of the concepts they'll encounter is regrouping, which is also known as borrowing and carrying, carry-over, or column math. This is an important mathematics concept to learn, because it makes working with large numbers manageable when calculating math problems by hand.

Getting Started

Before tackling carry-over math, it's important to know about place value, sometimes called base-10. Base-10 is the means by which numerals are assigned place value, depending on where a digit is in relation to the decimal. Each numeric position is 10 times greater than its neighbor. Place value determines a digit's numerical value. 

For example, 9 has a greater numerical value than 2. They are also both single whole numbers less than 10, meaning their place value is the same as their numerical value. Add them together, and the result has a numerical value of 11. Each of the 1s in 11 has a different place value, however. The first 1 occupies the tens position, meaning it has a place value of 10. The second 1 is in the ones position. It has a place value of 1.

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Free Printable 3-Digit Subtraction Worksheets

By Deb Russell

Place value will come in handy when adding and subtracting, especially with double-digit numbers and larger figures.

Addition

Addition is where the carry-over principle of math comes into play. Let's take a simple addition question like 34 + 17. 

• Begin by lining up the two figures vertically, or on top of one another. This is called column addition because 34 and 17 are stacked like a column.
• Next, some mental math. Start by adding the two digits that occupy the ones place, 4 and 7. The result is 11. 
• Look at that number. The 1 in the ones place will be the first numeral of your final sum. The digit in the tens position, which is 1, must be then placed on top of the other two digits in the tens position and added together. In other words, you must "carry over" or "regroup" the place value as you add. 
• More mental math. Add the 1 you carried over to digits already lined up in the tens positions, 3 and 1. The result is 5. Place that figure in the tens column of the final sum. Written out horizontally, the equation should look like this: 34 + 17 = 51.

Subtraction

Place value comes into place in subtraction as well. Instead of carrying over values as you do in addition, you will be taking them away or "borrowing" them. For example, let's use 34 - 17.

• As you did in the first example, line up the two numbers in a column, with 34 on top of 17.
• Again, time for mental math, beginning with the digits in the ones position, 4 and 7. You can't subtract a larger number from a smaller one or you'd wind up with a negative. In order to avoid this, we must borrow value from the tens place to make the equation work. In other words, you're taking a numerical value of 10 away from the 3, which has a place value of 30, in order to add it to the 4, giving it a value of 14. 
• 14 - 7 equals 7, which will occupy the ones place in our final sum. 
• Now, move to the tens position. Because we took away 10 from the place value of 30, it now has a numerical value of 20. Subtract the place value of 2 from the place value of the other figure, 1, and you get 1. Written out horizontally, the final equation looks like this: 34 - 17 = 17.

This can be a hard concept to grasp without visual helpers, but the good news is that there are ​many resources for learning base-10 and regrouping in math, including teacher lesson plans and student worksheets.