$Colorful House of Math logo$

Algebra

Geometry

Statistics and Probability

Functions

Proofs

Encyclopedia>Numbers and Quantities>Arithmetic>Addition and Subtraction>How to Subtract Using the Column Method

When you are subtracting two numbers using the column method, you subtract the number on the bottom of the column from the number above it in the column. When you subtract, you may end up in a situation where the number you are subtracting is larger than the number that you are subtracting from. In cases like these, you have to borrow (sometimes called regrouping). Below, you will find a method for subtraction without borrowing, and a method for subtraction with borrowing.

Rule

Subtraction Without Borrowing

1.: Make sure the numbers are set up according to the column method.
2.: Start with the numbers in the column furthest to the right. Subtract the bottom number from the top number, and write the answer underneath the line.
3.: Move to the next column to the left. Subtract the bottom number from the top number, and write the answer underneath the line.
4.: Keep doing this until you run out of columns. You’ve found the answer! If there’s a place that seems to be “missing” a number, you can just fill it with a $0$ .

Example 1

Calculate $46 - 42$ , $658 - 134$ and $98.43 - 61.10$

658 - 134 = 524 solved using the column method 98.43 - 61.10 = 37.33 solved using the column method

When you end up in a situation where you have to subtract more than you have, you have to borrow from the column to the left. Subtracting more than you have means that the number at the top of the column is smaller than the number below it. If the number at the top of the column you borrow from is $0$ , you have to jump another column to the left and borrow from the top number there. Then you can put a $9$ above the $0$ , and a $10$ above the column that needed to borrow to begin with. Here is a detailed explanation of how to do it:

Rule

Subtraction with Borrowing

1.: Make sure the numbers are set up according to the column method.
2.: Start like you learned in the recipe above. When the top number in the column is smaller than the bottom number, look at Item 5.
3.: Borrow a ten from the top number in the column to the left. Make a mark on the number you borrowed from, which is now one less than before.
4.: Put the $10$ you borrowed on top of the column that needed to borrow.
5.: Subtract the bottom number from $10$ , and then add the number between them.
6.: Put the number you got underneath the line.
7.: Move one column to the left.
8.: Before you subtract the bottom number from the top number in this column, remember that you borrowed one from the top number. Then you can subtract.
9.: If you end up in a situation where the number on the top is less than the number at the bottom again, you have to repeat Items 3 to 5.

Example 2

Calculate $153 - 38$ , $735.638 - 594.271$ and $90.88 - 31.90$

153 - 38 = 115 solved using the column method 735.638 - 594.271 = 141.367 solved using the column method 90.88 - 31.90 = 58.98 solved using the column method