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Math for Kids23 chapters | 325 lessons

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Instructor:
*Sabrina Hairston*

Sabrina has taught a variety of subjects and grades as a substitute teacher and will complete her MAT in 2016.

In this lesson, you will learn what improper fractions are and how to recognize them. You will also learn how to convert and reduce improper fractions, and we'll review the concept of the greatest common factor.

An **improper fraction** is a fraction whose top number (numerator) is larger than the bottom number (denominator). An improper fraction isn't *wrong*, but since the numerator, which represents the parts of the whole, is larger, the fraction actually represents a whole number and a fraction.

Examples of improper fractions include:

To find the whole number in an improper fraction, we can convert, which is to change the fraction to a **mixed number**. A mixed number has both a whole number and a fraction. For example, if we convert the improper fractions mentioned earlier to mixed numbers, the mixed numbers would look like this:

How did we do that? In order to convert improper fractions to mixed numbers, there are a couple of steps you must take:

- First, divide the numerator by the denominator. This will give you a whole number answer.
- Second, write the remaining value above the denominator. This is the fraction part of your mixed number.

Let's try converting 8/7 into a mixed number. Start by dividing 8 by 7 to get 1. The number 1 then becomes our whole number. The remaining value is also 1. That remaining value is now our new numerator that goes over the denominator (7), giving us the fraction part of the our mixed number.

Sometimes, you'll end up with a mixed number whose fraction is not in the lowest terms, which means the numerator and denominator have no common factor except 1. To bring the fraction to the lowest terms, we **reduce** the fraction, like in the problem below:

Let's work through how we reduce that fraction. We begin by following the same process as before to create our mixed number. We divide 12 by 10 to get a whole number of 1. The remaining value (2) becomes our new numerator, which we place over the unchanged denominator (10). Now, we have our new mixed number:

But wait. There's more we can do here. Our new mixed number is not in the lowest terms. We can reduce it. In order to reduce our new mixed number, we find the greatest common factor (GCF) of the fraction. The GCF is the largest number that will divide evenly into both the numerator and the denominator. For our example, here the GCF is 2. So, we divide both the numerator and denominator by that number:

Don't forget to include the whole number to complete your mixed number:

Sometimes, you'll find that there is no remaining value when you've converted an improper fraction. In these cases, the answer is simply a whole number. Let's look at an example:

When we convert the improper fraction, we divide the numerator by the denominator (24 divided by 12):

But there's no remaining value. The answer is simply the whole number itself--in this case, 2.

An improper fraction is when the top number (numerator) is larger than the bottom number (denominator). To convert an improper fraction, divide the numerator by the denominator to get a whole number, then place the remaining value over the unchanged denominator. This gives you a mixed number, which has both a whole number and a fraction, though you may need to reduce the fraction to its lowest terms.

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Math for Kids23 chapters | 325 lessons

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