math-fractions

In woodworking, there is one tool more widely used than any other…the ruler, whether it be made of plastic, wood or metal.  It can be 12 inches long, 36 inches or even longer.  It can be a straight edge, a T-square, a triangle scale, a tape measure or any number of measuring devices.  There are many to choose from.  The majority of those sold here in the United States follow the English system of measurements, which include inches and fractions of an inch.  The addition and subtraction of fractions can sometimes be a source of confusion.  I will attempt to help you sort this out.

Okay, class in now in session.  There are a lot of people who really dislike math.  I guess they could be called the arithmetic impaired.  Fractions can be a tricky business, but this can be overcome by following a few simple rules.

Rule #1. Make sure the denominators are the same In a fraction, you have two numbers: the numerator (the top number) and the denominator (the bottom).  When adding or subtracting fractions, you need to make sure the denominators are the same.  If they are the same, then your calculations will be easier to do.  If they are not, then you will have to go to Rule #2.

Rule #2. Converting denominators to match Let’s assume that you have two fractions: ½ and ¼.  We can easily tell that the denominators are different, so we have to convert.  “Which one do we convert”, you ask?  We must change the lower number, in order to match the higher number.  So, the 2 must become a 4.  In order to accomplish this, we need to multiply both the top and bottom number of ½ by 2.  This will turn the numerator from 1 to 2 and the denominator from 2 to 4.  Now we have the fractions ¼ and 2/4.  We can now go to the third and final rule.

Rule #3. Adding or Subtracting the fractions When adding fractions, the order of the fractions do not matter.  If you want to play it safe, then follow the same rule as subtracting fractions.  For subtraction, you always place the larger fraction first.  In this case, the larger fraction is 2/4.  Next, you subtract the smaller fraction from the larger.  Remember, when subtracting or adding fractions, you will only be using the numerators.  In your final answer, the denominator will always be the same as the others. So, 2/4 + ¼ will equal ¾.

As long as you follow these rules, you should not have any problems with adding or subtracting fractions.  As a quick reference, I have attached a chart below using 1/16 ” increments.  Hopefully, this will help you in your next woodworking project.