One half..One fourth..One third..what are they?  They're fractions!

A fraction describes a part of a whole when the whole is cut into into equal parts!! Fractions can also be parts of a group. For example, if there is a group of fruit: 3 oranges and 4 apples, what fraction of the group are apples? Four sevenths. There are seven parts, and four apples. What is the fraction for the oranges?  Three sevenths.  They are fractions that are not one whole, it's just a part of the whole.

There is the denominator which is the bottom number which gives the number of parts in the whole. There is the numerator which is the top number that tells how many parts are showing.    

There are several different types of fractions. Such as, equivalent fractions. They are fractions that are equal. There's also improper fractions which have a denominator that is greater than or equal to the numerator.  Most of the time,  you need to make them a regular fraction so it's easier to work with. Another type of fraction is a mixed number.  A mixed number is a fraction that that is associated with whole numbers and regular fractions. 

The example below shows three halves which is an improper fraction, also as a mixed number which is one and one half.

To change an improper fraction to a mixed number:

Reducing fractions make fractions easier to understand. It may be hard to picture what 25/75 might look like. But, if you reduce this fraction, you’ll find out it’s a fraction you are very familiar with.

To reduce a fraction to simpler terms we must divide the numerator and the denominator by the (GCF) Greatest Common Factor. This is also called simplifying the fraction.

Example:

Using a Common Factor

In the fraction 25/75 we can divide both the numerator and the denominator by 5

25 ÷ 5 = 5

75 ÷ 5 = 15

Therefore we get the fraction 5/15 but this can be reduced further by dividing by 5

5 ÷ 5 = 1

15 ÷ 5 = 3

The reduced fraction is 1/3

Using a Greatest Common Factor

Using the same example, 25/75, the greatest common fraction is 25, 5 x 5

25 ÷ 25 = 1

75 ÷ 25 = 3

The reduced fraction is 1/3

With Like Denominators

3/8 + 5/8= ? Do you know how to do this addition problem with fractions? If you don't, then keep on reading. Adding with like denominators is easy. Like denominators are fractions with the same denominators. To add like denominators you add the numerators together and you keep the denominators the same. So if you were doing this problem: 2/6 + 3/6, the answer would be 5/6.

With Unlike Denominators

You might think that adding with unlike denominators is really hard. Well if you read our directions, and follow them carefully, then you will be great at adding fractions with unlike denominators! First, in adding unlike denominators, you have to change both fractions so they are equivalent or equal, and they both have the same denominator. Here are the steps:

1. Figure out the LCD or the Least Common Denominator of the denominators for the problem 3/6 + 4/5 The multiples of 6 are: 6,12,18,24,30,36. The multiples of 5 are, 5,10,15,20,25,30,35 ............ 30 is the lowest multiple for both.

2. Then, take the fraction and multiply the denominator by what it's multyplied by to get the LCD. In the fraction 3/6, you would multiply 6 (the denominator) x 5 to get the LCD of 30. Since you multiplied the denominator x5, you have to multiply the numerator x5. Since 3x5 = 15, the new numerator is 15.

So, 3/6 is now changed into the equivalent fraction 15/30

3. Then, subtract the two fractions. 15/30- 24/30= 9/30

3. Then do the same with the other fraction and add the two fractions!!!!

Here is a problem you might want to do, so you can make sure you understand how to add fractions with unlike denominators: 2/3 + 2/9 = ?

With Like Denominators

Do you know how to do this problem: 5/10 - 3/10= ? If you don't, read on. When you subtract with like denominators they are the same denominators. In the problem I gave you, you really just subtract the 3 from the 5. Just ignore the denominator right now. So this is the solved equation without the denominators 5-3=2. Then once you have done that add the denominator to each number, so that it looks like this: 5/10 - 3/10= 2/10. That is how you subtract fractions with like denominators. Just for practice do this problem: 5/6 - 2/6 = . If you don't know how to do this problem do the steps over till you do. If you do know how to do this problem see the test and see how many you get right.

With Unlike Denominators

Here is another problem. Let's see if you know how to do this: 3/4 - 5/8= . If you don't know how to do this problem, read on. The first thing you have to do is make the denominators the same. You have to find what is called the Least Common Denominator (LCD) . In this problem, the LCD is 8. In this problem, you would multiply just the 3/4 fraction so that the denominator is 8. Here is a rule applies to every fraction equation: whatever you do to the bottom you must do to the top. So 3/4 would turn in to 6/8. After you have done that you can solve the problem. So the equation would look like this when it is solved: 6/8 - 5/8= 1/8. For extra practice do this problem: 5/12 - 1/3. If you don't quite understand this go through the steps again. If you do understand how to do these kinds of problems, then you can go and take the quiz.

There's two ways you can multiply fractions.  The first way I am going to show you is changing the fractions into decimals.  Say you had a problem that was 4/5 × 3/4=  .  The first thing you have to do is change the fractions to decimals.  So the fraction 4/5 will turn into 0.8 .  The fraction 3/4 would turn into 0.75.  Then you would line them up as if you were doing a regular multiplication problem.  The problem right now is 0.8 × 0.75.  when you figure this out on paper the answer would be

Another way to do it is leave the fraction the way it is and multiply it side by side.  Say you had another problem that you didn't know how to turn it into a decimal.  Sort of like this one: 5/9 × 7/18 =   .  You first thing you have to do is set your fractions like this one:

5× 18
9   20

Now, if the numbers diagonal from each other have a GCF then reduce them as low as they can go. So now the problem will look like this:

1 × 2
1    4

When you are multiplying now you multiply the top, then the bottom.  So the top, when it is all multiplied would be 2 and the bottom would be 4.  So the answer is 2/4 which can reduce to 1/2.   If you need extra practice go and take the test, see how you do.

Dividing by a fraction is simple! Take for instance this example.

2/7 ÷ 2/5

Step 1. Change the sign from division to multiplication

2/7 x 2/5

Step 2. Invert the fraction after the multiplication sign

2/7 x 5/2

Equivalent fractions are two fractions that are the same amount.  Here are some examples of some equivalent fractions:

All of these fractions are equal.  They all take up the same amount of the whole.You might think that the only way to show fractions are in the form of circles, but they are not always shown on circles.  You can show fractions in rectangles too.  Below is an example of equivalent fractions that are in the form of rectangles.

1 Whole		1 Whole
2 Halves		2 Halves
4 Fourths		4 Fourths
8 Eighths		8 Eighths