Thursday, March 4, 2021

What is a fraction?


Update, 12 Nov 2012: Do you want to explore fractions rather than just read about them? We have developed interactive tools that allow students to explore and compare fractions with like and unlike denominators using graphical, visual models:

* A fraction is written with one number “over” another number. For example, ½ and ¾ are fractions.

* The top number is called the numerator, and the bottom number is called the denominator.

* The top number “represents” the parts of something, and the bottom number represents how many parts there are in that whole thing. For example, if a candy bar has 10 total pieces of the same size, and you eat three of those pieces, you could say you ate “three tenths” of that candy bar. The “3” would be written on top, because that is how many “parts” you ate. The “10” would be written on the bottom, because that is how many pieces there are in the “whole” candy bar.

* An easy way to remember this is that fractions represent “parts of the whole” where “of” means “over” in math terms.

Now, look at this circle:

What fraction of this circle is shaded purple?

The answer is three fourths, which would be written as a “3” on top and a “4” on the bottom of a fraction. That is because there are three “parts” that are shaded purple, and there are four parts in the “whole” thing. The bottom number in a fraction represents how many “total parts” there are in the “whole” object, while the top number in the fraction represents how many parts of the whole you’re talking about.

Now, look at this circle:

What fraction of this circle is shaded purple?

Even though three “parts” of eight parts in the “whole” object are shaded, the answer is not three eighths. This was kind of a trick question, but teachers are sure to throw something like this at you.

You see, in order for the whole to be represented by the bottom number in a fraction, all the pieces have to be the same size. In this picture, four of the pieces are big, and the other four pieces (the ones at the sides) are small.

If every piece were truly an “eighth,” they would all be the same size. You can’t have some of the “eighths” being bigger than some of the other “eighths.” All the “eighths” should be the same size, hence the fact that they all have the same name, “eighths.”

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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