 in a fraction what is the bottom number called

Within the final article, we found that integers alone are usually not adequate to completely describe the world round us—we’d like the fractions present between the integers too. (In studying that, we additionally discovered that fractions are usually not integers.) The truth is, finally, we’re going to find that even fractions gained’t absolutely fulfill our wants! However we’ll go away that for a future article—there’s nonetheless a lot to be taught concerning the fractional world first.

Particularly, right this moment we’re going to take a deeper have a look at fractions and be taught a couple of fast suggestions that can assist you perceive precisely what numerators and denominators inform you.

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What are fractions?

Earlier than we get too far into the main points of what the assorted elements of a fraction imply, let’s briefly overview their anatomy. First, a fraction is made up of two integers—one on the highest, and one on the underside.

The highest one known as the numerator, the underside one known as the denominator, and these two numbers are separated by a line. The road could be horizontal or slanted—they each imply the identical factor and easily serve to separate the numerator from the denominator. The right way to pronounce fractions in English

When you’ve identified about fractions for some time, it’s in all probability been a while because you’ve contemplated the names we use to explain them. However they aren’t precisely apparent, so it’s value spending a minute or two desirous about them.

Right here’s the fast and soiled tip that can assist you keep in mind find out how to pronounce all of them: The numerator is at all times spoken first, and also you pronounce it precisely as you pronounce the quantity. For instance, in 1/2 the numerator, 1, is simply pronounced “one;” or in 45/77 the numerator, 45, is just pronounced “forty-five.” Simple sufficient. However denominators are a bit trickier. They use the next conference:

• 2 is pronounced “half”

• 3 is pronounced “third”

• 4 is pronounced “fourth” (or “quarter”)

• 5 is pronounced “fifth”

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6 is pronounced “sixth”

• 7 is pronounced “seventh”

• 8 is pronounced “eighth”

• 9 is pronounced “ninth”

• 10 is pronounced “tenth,” and so forth.

So, for the fraction written 1/2, the denominator, 2, is pronounced “half,” and your entire fraction is subsequently “one-half.” Rather less apparent: For the fraction 45/77, the denominator, 77, is pronounced “seventy-seventh,” so your entire fraction is “forty-five seventy-sevenths.”

A straightforward solution to keep in mind that is that with the exceptions of “half” and “quarter,” the phrases used to explain the denominator of a fraction are the identical used to place issues so as—for instance, the order during which runners end a race: “third,” “fourth,” “fifth,” and so on.

What’s a denominator?

Now let’s take a more in-depth have a look at the totally different elements of a fraction. First, the underside half—the denominator. The phrase “denominator” is derived from the Latin phrase “nomen,” which suggests “identify” (and likewise exhibits up in phrases like “nominate” and “nomenclature”). And that’s just about what the denominator of a fraction does: it “names,” or signifies, the kind of fraction that’s described by the numerator (the highest half).

What does the denominator inform you?

Right here’s what I imply. The denominator of a fraction tells you what number of elements an entire is damaged into. It may be an entire pineapple, an entire music, or an entire something. If the denominator of a fraction is, say, 4, then that signifies that the entire no matter is damaged up into 4 equally-sized items. Or, if the denominator is 12, which means the entire no matter is broken-up into 12 equally-sized items. However how precisely does that “identify” the kind of fraction? Nicely, that leads us to the which means of the numerator.

What’s a numerator and what does it inform you?

The phrase numerator comes from the Latin verb “enumerate,” which we nonetheless use in English to imply “to depend.” So, the numerator of a fraction counts the variety of equally-sized items (recognized by the denominator) which might be contained within the fraction.

How, then, will we put this all collectively to grasp the which means of fractions? Right here’s the fast and soiled tip: Going again to our examples from earlier than, the fraction 1/2 means “one piece of an entire object divided into two equally sized elements.” The denominator signifies that two elements make an entire, and the numerator counts off the truth that the fraction 1/2 comprises a type of elements. Equally, the fraction 45/77 means “forty-five items of an entire object that’s divided into seventy-seven equally sized elements.”

What does it imply if the numerator is greater than the denominator?

In all of the examples thus far, the numerator has at all times been smaller than the denominator. In different phrases, in 1/2 and 45/77, 1 and 45 are smaller than 2 and 77, respectively. However what would it not imply if the numerator had been greater than the denominator? One thing like 7/4?

Nicely, let’s strive deciphering this the identical approach as earlier than. The denominator, 4, signifies that an entire is split into 4 equally sized elements, and the numerator, 7, signifies that we have now seven of these elements. So, if 4 elements make an entire, and we have now seven, then we should have an entire object plus three extra of the equally sized elements. So 7/4 is equal to 1 3/4—also referred to as “one and three-quarters”—and we now know {that a} fraction whose numerator is bigger than its denominator represents a quantity that’s larger than one. In case you’re questioning, that kind of fraction known as “improper,” whereas fractions like 1/2 with numerators less-than denominators are known as “correct.”

What does it imply if the denominator is lower than one?

To this point we’ve solely talked about fractions with denominators which might be larger than one. On the finish of the final article, I requested the “brain-teaser” query: “Why can’t the denominator of a fraction be zero?” To search out out the reply to that query, and take a peek at how fractions with denominators less-than one work, take a look at final week’s Math Dude Video Further! episode posted to YouTube and the movies part of the Math Dude’s Fb web page.

Who makes use of fractions?

Briefly: Everybody! You have in all probability used fractions with out even realizing it.

For instance your grandma bakes six cookies. She says that you simply and your two cousins can every have one, after which asks you to place the remainder in a plastic bag. Which means 3/6 of the cookies will likely be eaten and three/6 will likely be saved. As soon as the three cookies are put away, you give 1/3 of the batch to at least one cousin, 1/3 to your different cousin, and maintain 1/3 to your self. You do not even consider it as utilizing fractions to divide the batch, however that is what’s taking place!