Learn a quick tip to help you understand exactly what the numerator and denominator of a fraction tell you.
What Is a Denominator?
Now let’s take a closer look at the different parts of a fraction. First, the bottom part—the denominator. The word “denominator” is derived from the Latin word “nomen,” which means “name” (and also shows up in words like “nominate” and “nomenclature”). And that’s pretty much what the denominator of a fraction does: it “names,” or indicates, the type of fraction that is described by the numerator (the top part).
What Does the Denominator Tell You?
Here’s what I mean. The denominator of a fraction tells you how many parts a whole is broken into. It can be a whole pineapple, a whole song, or a whole anything. If the denominator of a fraction is, say, 4, then that indicates that the whole whatever is broken up into 4 equally-sized pieces.
Or, if the denominator is 12, that means the whole whatever is broken-up into 12 equally-sized pieces. But how exactly does that “name” the type of fraction? Well, that leads us to the meaning of the numerator…
What Is a Numerator and What Does It Tell You?
The word numerator comes from the Latin verb “enumerate,” which we still use in English to mean “to count.” So, the numerator of a fraction counts the number of equally-sized pieces identified by the denominator that are contained in the fraction. How then do we put this all together to understand the meaning of fractions? Here’s the quick and dirty tip: Going back to our examples from before, the fraction 1/2 means “one piece of a whole object divided into two equally sized parts.” The denominator indicates that two parts make a whole, and the numerator counts off the fact that the fraction 1/2 contains one of those parts. Similarly, the fraction 45/77 means “forty-five pieces of a whole object that is divided into seventy-seven equally sized parts.”
What Does It Mean if the Numerator is Bigger than the Denominator?
In all the examples so far, the numerator has always been smaller than the denominator. In other words, in 1/2 and 45/77, 1 and 45 are smaller than 2 and 77, respectively. But what would it mean if the numerator were bigger than the denominator? Something like 7/4?
Well, let’s try interpreting this the same way as before. The denominator, 4, indicates that a whole is divided into four equally sized parts, and the numerator, 7, indicates that we have seven of those parts. So, if four parts make a whole, and we have seven, then we must have a whole object plus three more of the equally sized parts. So 7/4 is equivalent to 1 3/4—also known as “one and three-quarters”—and we now know that a fraction whose numerator is greater than its denominator represents a number that is greater-than one. In case you’re wondering, that type of fraction is called “improper,” whereas fractions like 1/2 with numerators less-than denominators are called “proper.”
What Does It Mean if the Denominator is Less than One?
So far we’ve only talked about fractions with denominators that are greater-than one. At the end of the last article, I asked the “brain-teaser” question: “Why can’t the denominator of a fraction be zero?” To find out the answer to that question, and take a peak at how fractions with denominators less-than one work, check out last week’s Math Dude Video Extra! episode posted to YouTube and the videos section of the Math Dude’s Facebook page.
That’s all the math fun we have time for today. But before I go, here’s a “brain-teaser” problem for you to think about until next time:
How can you tell if one fraction is bigger or smaller than another?
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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!