Audio GED Prep Mathematics Lesson 2


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Lesson Summary:

Audio GED Prep Mathematics Lesson 2


Definition of a fraction/parts of a fraction

A fraction shows a part of a whole. They are usually shown by a top number, called the numerator, and a bottom number, called the denominator. Between the numerator and the denominator, there is a slash, either a straight line(—) or a slash (/).

The denominator shows how many parts are in a whole, (1) and the numerator shows how many parts you have. There are several ways that you will see fractions used. The reciprocal of a fraction is when you switch the numerator and the denominator. For example, 3/4 and 4/3 are reciprocals.

Types of fractions

First, there are simple fractions. In simple fractions, the numerator is smaller than, or equal to the denominator, meaning that you have a part of a whole, or exactly one whole thing.

Then, there are complex fractions, in which the numerator is larger than the denominator. You can write these out like a normal fraction, or write them as a mixed number, which consists of an integer and a fraction side by side. If you have a complex fraction, you have at least one whole thing or more, and part of another whole.

Simplifying fractions/equivalent fractions

Sometimes, a fraction can be simplified. This means that it could be written as a fraction that has a smaller numerator and denominator without changing its value. If both numbers of a fraction can be divided by the same number, then the fraction can be simplified.

This means that there are many fractions that are equal to the same part of a whole. For example, if you divide a whole into four parts, and you have two parts out of the whole (2/4), that is the same as diving a whole into two parts and having one of the two parts. (1/2). Both 2/4 are ½ are exactly half of the whole or 50%. You can divide both 2 and 4 by 2 to get 1 and 2 respectively. If you cannot divide the numbers of a fraction by the same number, then the fraction is as simple as possible. For example, the fraction 7/8 cannot be divided by the same number, and so is completely simplified.

Converting fraction to mixed number/vice versa

Sometimes, it will be useful to convert a fraction to a mixed number or from a mixed number back into a fraction.

For sake of ease, first simplify the fraction if possible. To convert a fraction to a mixed number, you must first see if the numerator is greater than the denominator.If it is not, then you cannot create a mixed number because you do not have more than one whole.

If the numerator is greater, then subtract the denominator from the numerator. For example, if the fraction 9/8 then you subtract 9 – 8 = 1. The result is you new numerator. You then put a large number one next to the fraction to show one whole unit. So, 9/8 becomes 1 1/8.

Then, you need to check if the numerator is still greater than the denominator. In this case, it is not, and so you are done. If, however, you have the fraction 17/8, you would get 1 9/8. Because the numerator is still larger, repeat the process and add another whole unit. In this case, you would get 2 1/8. Now that the numerator is larger than the denominator, you are done.

You can also think about it as dividing the numerator by the denominator, and leaving the remainder as the denominator. This works best when you have very large numerators.

When you want to reverse this process, you have to follow another process. Simply multiply the integer, or large number by the denominator and then add this number to the numerator. For the example 2 1/8, this would be 2 x 8 = 16, and then 1 + 16 = 17. You then have the complex fraction 17/8.

Adding and Subtracting Fractions

In order to add or subtract fractions, you have to make sure they have the same denominator. If they do not have the same denominator, you need to find a common denominator. It is best to try to find the lowest common denominator to make things easier. In order to find this, you multiply the top and the bottom number by the same things. An easy way to find this is to multiply both number in one fraction by the denominator of the other fraction, and vice versa.

1/2 + 1/3 = x

3/6 + 2/6 = x

5/6 = x

3/4 – 1/5 = x

15/20 – 4/20 = x

11/20 = x

Multiplying and Dividing Fractions

To multiply fractions, all you have to do is multiply the numerators to create a new numerator and then you multiply the denominators to get a new denominator. Then you should simply the fraction.

3/4 x 4/5

3 x 4 = 12

4 x 5 = 20



To divide fractions, the easiest way to make this happen is the multiply by the reciprocal of the second fraction. A reciprocal is when your switch the numerator and the denominator.

(7/10)/(4/5) = x

(7/10) x (5/4) = x

35/40 = x

7/8 = x


An allegory is a story in which the characters, settings, or events have a deeper symbolic meaning such as George Orwell’s “Animal Farm”.
©2015 Franz Amussen, All Rights Reserved

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