Best Overview of Fractions | Math Review

Fractions

Welcome to this Mometrix video on fractions. Fractions can be simple or complex. In this video, we’ll cover different types of fractions and how to add fractions with different denominators.

So what is a fraction? A fraction is a part of a whole, which means a fraction can never be a whole number. Think of it like this:

Our circle is divided into eight equal pieces. Let’s say three pieces were filled in. That would mean ⅜ of the circle is filled in.

The top number, 3 (three) is called the numerator. The bottom number, 8 (eight) is called the denominator.

When saying fractions out loud, the denominator will usually be spoken as the ordinal version of the number. You would say “eighth” instead of “eight”, or “third” instead of “three”.

2 = half
3 = third
4 = quarter or fourth
5 = fifth
6 = sixth
7 = seventh
8 = eighth
9 = ninth
10 = tenth

As you can see, there are a couple of exceptions. If the denominator is 2, you would say “half”, and if the denominator is four, you might say “quarter” instead of “fourth”.
Hopefully, that helps you to understand how fractions are defined, and also how to actual say them out loud.. But there are different types of fractions. Let’s take a look at those.

First, we have proper fractions. A proper fraction always has a numerator that is smaller than the denominator. Our example of ⅜ that we used before is a proper fraction. The denominator, 3, is smaller than the denominator, 8. Some other examples of proper fractions include ⅘, \(\frac{5}{9}\), and \(\frac{23}{50}\).

An improper fraction is the opposite of a proper fraction, in that the numerator is larger than the denominator.

So, while \(\frac{3}{8}\) is a proper fraction, \(\frac{8}{3}\) is an improper fraction. Improper fractions are always equal to or greater than 1. That means \(\frac{9}{9}\) is also an improper fraction since it equals 1.

There are also mixed fractions, which contain a whole number and a proper fraction. Here’s an example:

2\(\frac{3}{4}\)

Note that the whole number, 2, is followed by the proper fraction, \(\frac{3}{4}\).

We also have equivalent fractions. Equivalent fractions are two different fractions that name the same number.

For example:

\(\frac{6}{8}\) and \(\frac{3}{4}\) look different, but they’re the same. ¾ is just a simplified version of \(\frac{6}{8}\). To simplify \(\frac{6}{8}\), you just divide the numerator and denominator by 2.

Now that we know the different types of fractions, we can explore how to add them.

If two fractions have the same denominator, adding is a breeze. You just add the numerators together, and that gives you the answer. For example:

\(\frac{1}{4} + \frac{2}{4} = \frac{3}{4}\)

Simple. But what happens if the denominators are different? Well, in that case, you have to convert the denominators to be the same. So let’s go back to our circle with the equation:

\(\frac{3}{8} + \frac{1}{2} = x\)

You can’t simplify \(\frac{3}{8}\) into any fraction that would easily add with \(\frac{1}{2}\), so we have to look at the \(\frac{1}{2}\). We can see that half of the circle has four parts. That converts to \(\frac{4}{8}\). So the equation now becomes:

\(\frac{3}{8} + \frac{4}{8} = \frac{7}{8}\)

Subtraction works the same way. If you’re subtracting fractions with the same denominator, you can just subtract the top numbers:

\(\frac{3}{4} – \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\)

Notice I simplified \(\frac{2}{4}\) to \(\frac{1}{2}\). Simplifying numbers just makes them easier to work with.

But if you’re subtracting with a different denominator, you have to make the denominators match. For example:

\(\frac{3}{8} – \frac{1}{4} = x\)

We can convert 14 to 28, then our equation looks like this:

\(\frac{3}{8} – \frac{2}{8} = \frac{1}{8}\)

Those problems were pretty easy because they had the same denominator or were easy to convert. But let’s look at one more equation that’s a little trickier:

\(\frac{3}{4} + \frac{6}{7}\)

Wow. These numbers are nothing alike. But there is a way to solve the problem. It involves multiplying the numerators and denominators, like this:

\(\frac{3 \times 7}{4 \times 7} + \frac{6 \times 4}{7 \times 4}\)

Notice how you’re calculating this. You’re multiplying the numbers that are across from each other diagonally and placing them in the NUMERATOR position. Then, you’re simply multiplying the denominator.
The equation yields this answer:

\(\frac{21}{28} + \frac{24}{28} = \frac{45}{28}\)

We only add the top number, the numerator, together. We don’t add the denominator. With this calculation, we’ve found the “least common denominator.” The least common denominator is the smallest common number between denominators. Anytime you perform a calculation with different denominators, you must find the least common denominator to solve the problem.

So that’s our look at fractions. I hope this overview was helpful.

See you guys next time!

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