Mathemagician: The All-Knowing Guide to All Things Math

Basic Math - Unit II Lesson I: Intro to Fractions

Introduction
Imagine this: you and a friend watch the door, awaiting for that pizza you ordered not too long ago. The time comes eventually and you come to answer the door. The pizza is now in your hands and you sit it down on the counter to your friends' excited look. Let's flashback to when you told your friend while you had ordered that pizza that you both would split it evenly. Simple enough, right? One pizza split with two friends. 1 / 2. Huh..that sounds familiar, 1 / 2...but what could that mean? Ah, of course—fractions! Eureka! Anyways, I'm still going to secretly take 3/4 of that pizza, sorry! No hard feelings, right?

Essential Question: What are fractions in math and how are they to be represented?

Fractions. Who doesn't love 'em? Well, if you must know, fractions are a small or tiny part, amount, or proportion of something. That something could be like a pizza that we had previously mentioned before. But, how do they work? Let's look at the basics first, and then we can go do some math magic with them later on!

What Is The Numerator?

Fractions have two different parts associated to them. These parts include the numerator—the very top of a fraction; and the denominator—the very bottom of a fraction. Let's start with the numerator. For starters, the numerator is the number above the line in a fraction which describes how many parts indicated by the denominator (what we will learn about later in this lesson) are taken. For example, let's take that slice of pizza. Well, there's 8 slices of pizza cut by the one who made the pizza in the first place. I secretly took 5 slices instead of the 4 I was supposed to grab. Now, if we use subtraction, we can determine the amount of pizza left. Unfortunately, my friend will have to deal with the fact that he's going to get less pizza—3 slices to be exact.

Now, let's put that into a fraction. Using what we have learned about the numerator (thus far), we can determine that the amount of pizza that I have taken is 5/8. The numerator being 5, the number of parts of the pizza I have taken, and the denominator being 8. So, what does that 8 represent. . .well, I'm glad you asked as that is what we will get into next!

What Is The Denominator?

Well, fractions have two different parts associated with them, as I've previously mentioned. The denominator is the one below the numerator and the line in a normal fraction, indicating the total number of parts, or the whole. So, let's go back to the pizza analogy. We already know that the 5 slices are the number of slices that I have taken—and the 8? Well, using the definition of what a denominator is we can simply determine that the 8 represents the total amount of slices of the pizza—the whole amount if you will.

Well, there you go—we've covered the entire fraction! Let's recap: the numerator is the top of the fraction and is the number of parts taken from the denominator, and the denominator is the total number of parts which can also be known as the whole unit. Great, you're a fraction expert! But. . .we're not done yet. Hold your horses, 'cause you will be strapped in for a LOT of fraction lessons in the near future. We can focus on adding, subtracting, multiplying, and diving fractions down the line—but for now, let's focus on the fractions and how they compare to the rest of the whole part (denominator).

Equivalent Fractions

So, you know earlier about how I would take 3/4 of the pizza (sorry about that by the way)? Well, I got this handy-dandy pizza cutter and, hiyah! Now, that same pizza has 8 slices! Shouldn't there be more pizza? Wrong! First of all, the Law of Conservation of Mass states that matter cannot be created nor destroyed. Also, this is where equivalent fractions come into play! Picture a pizza cut up into four slices—like if you were playing four corners. I slashed through that pizza and now it looks almost like a spider web.