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Understanding the fractional inch use and measurement

inch understanding the fractional inch

In metalworking workshops from countries that have adopted the International System, as Brazil, country of professor Stefanelli, in general, the easiest way to produce parts that were designed in fractional inch is to convert the measurements in inch to millimeter . After all, machines were designed to work in the international system.

However, it is not uncommon to have into our hands a tool in inch and a part or tool for measuring. What to do, pretend you're having a convulsion doesn't solve your problem, so, continue on this page and see how easy it is!


The fraction is a way of representing a part of a whole. It is a portion of a unit which was divided into equal parts. A well known example is a pizza sliced into eight pieces or the fractional inch.


figure 1 - representation of a mixed fraction and its corresponding fractional

Generally, the fraction is represented by a pair of numbers aligned in the vertical and separator by a line divider. The number over the line is the ' numerator ' and the underneath is the ' denominator '. The example in figure 1 represents an 'mixed fraction,' which is greater than the unit, in this case, the quantity of integers is represented to the left of the dividing line (think in a entire pizza more five pieces).

The denominator express in how many parts the whole is divided. In the example of Figure 1 it was divided into eight parts. The numerator express how many shares will be considered (five). In this example, we consider a 'full' unit and another five pieces of which was divided into eight (one and five-eighths).

It is also possible to represent an integer number in fraction form 8/8, 2/2, 1/1, 128/128 are expressions of the unit (number one - 1). See, in Figure 1, the distance between 0 and 1 is an integer that is divided into eight eighths. Thus:

1 = 2/2 = 4/4 = 8/8 = 16/16 = 32/32 = 64/64 = 128/128 ... (called as apparent fraction). It is not recommended, or elegant, to express the integer number on this way.

See that 1 5/8 it's equal to 1 + 5/8 = 8/8 + 5/8 = 13/8 (keeping the denominator and summing the numerator ).

13/8 it's what we call of 'improper fraction'' (the value of the numerator is bigger than the denominator). Keeping the fraction like this is a kind of trapp armed against yourself. Always express in the mixed form (1 5/8).

The fraction must be expressed in its simplest possible form or irreducible. We know that 4/8 it's the same of 1/2 and we must express the fraction in the form of 1/2 . No intention to make someone decorate this: if both the numerator and denominator are even numbers it is possible to simplify. The same if both are divisible by three, five ... and so on.

Fractional Inch

A inch is fractioned in two halves that, in its turn, also are divided in your halves and so on successively. This is the progression that the division of fractions of inch results: 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128 , where each new term represent half on the previous one. (It's important to memorize this numerical progression)


figure 2 - inch divided in 16 fractions

It is somewhat counter-intuitive, but a greater number in the denominator decreases the size of the fraction. One way to understand this is to note that the inch is divided into a larger number of parts. In this way, if you want to reduce the fraction of the inch, go on multiplying by two the denominator (1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128) among other ways.

sum of fractions

When the sum of fractions (the sum of the value of the vernier to the scale, for example) will have even numerator, go on dividing both by two until remains an odd number - irreducible fraction (see the importance of memorazing that progression?). Example: 1/8 + 3/8 = 4/8 = 2/4 = 1/2.

tip: when summing two even numbers or two odd numbers the result always will be an even number , when summing a even number to a odd one the result always will be an odd number.

Another caution is that we can only sum fractions whose denominators are equal. It's not possible to sum 1/2 with 1/16, except if we convert fractions to the same denominator. In this way 1/2 = 2/4 = 4/8 = 8/16 that plus 1/16 results in 9/16. Go on multiplying by two the numerator and denominator until the denominator will be equal to the other.

dividing by half

Dividing a fraction by half (to determine the radius, for example) is also quite simple. If it is a mixed fraction (1 5/8, for example) to convert into an improper fraction (13/8) and multiply the denominator by two (half of 1 5/8, which is equivalent to 13/8, and is 13/16), if the fraction is 'not improper' only multiply directly the denominator by two (half of 3/4 is 3/8; half of 63/64 is 63/128)...

tip : if in the mixed fraction the integer number is an even number , it's not necessary to convert it to a improper fraction, just divide also the integer number by two.
(example: half of 2.1/4 is 1.1/8; half of 4.5/8 is 2.5/16)

measuring fractions

And finally, for those who work in decimal system and has the habit to count the marks from left to right. It's not how you do with fractions. We must 'look' to the integer fraction and locate your half (the mark is usually slightly larger than the adjacent) and repeat this process until you reach the measure, summing the fractions. The practice leads to perfection. However, usually we are under pressure.


tip : count the number traits of a full inch to the other (usually 32 or 64 - remember that you are not counting traits , but the distance between them ). If they're 16-Figure 3 - each distance is equal to 1/16 "count how many marks there are to an measure that interests to you, (the tenth-figure 3) see that the fraction is 10/16, ten is even number, simplify dividing both by two until there is an odd number in numerator. The answer is 5/8, figure 3.


figure 3 - measurement of an object in fractional inch - answer: 5/8"

That's it .
practice your knowledge of measurement of fractional inch:

Afterward , interact with the topic:
Use of vernier caliper in fractional inch - measuring and interpretating

Eduardo J. Stefanelli -