Logic — the Art of Reasoning

Mathematics — the Art of Studying Patterns and Relationships Using Logic

Subtraction Without Borrowing

Uri Geva, MathVentures, a Division of Ten Ninety Document Version 2.0
Copyright © 2002–06 Uri Geva, Ten Ninety, All Rights Reserved.
This work may be redistributed under the terms of the GNU General Public License
as published by the Free Software Foundation.
This work comes with absolutely no warranty!

Its Simple and Easy

Subtracting without borrowing is very simple and easy. (It does not use either compliment arithmatic or negative numbers.) It can easily be adopted to be your everyday subtracting method. You can learn how to do it by simply following the two examples described below.

A note for the mathematically advanced reader (If you do not think of yourself to be one, skip this note):

There are other methods for performing subtraction without borrowing. Some involve the use of negative numbers and others use methods of complements, either 9-Complement or 10-Complement. The technique described here has several advantages over these methods.

Advantages:

This method is very simple.
It requires no more than the mathematical knowledge of a second or third grader. No need to know special concepts as negative numbers and complements.
Often students, who have to perform subtraction, intuitively take a short-cut – they round at least one of the numbers up or down to a number with which they feel more comfortable. This method is nothing more than a general and algorithmic description of this alternative approach.

Examples:

It's that simple!

Downloads

You can download the description of subtraction without borrowing in one or both of the following documents.

The above example is displayed as an image, which you can save to your computer.

Subtraction Without Borrowing - Light

This document contains the information described above with some graphics that is aimed at making it easier to understand the examples.

Subtraction Without Borrowing - with Detailed Mathematical Background

This document contains a mathematical discussion and detailed explanation how this procedure works. It also includes more examples.

Table of Contents