Fractions

=Fractions= //A fraction is a part of a whole//

Slice a pizza, and you will have fractions:
The bottom number tells how many slices the pizza was **cut into**. || media type="youtube" key="vjjv1CVjwso" height="315" width="420"Watch this video clip for a simple explanation. ==
 * [[image:http://www.mathsisfun.com/images/fractions/pie-1-2.jpg width="120" height="120"]] || [[image:http://www.mathsisfun.com/images/fractions/pie-1-4.jpg width="120" height="120"]] || [[image:http://www.mathsisfun.com/images/fractions/pie-3-8.jpg width="120" height="120"]] ||
 * 1/2 || 1/4 || 3/8 ||
 * **(One-Half)** || **(One-Quarter)** || **(Three-Eighths)** ||
 * The top number tells how many slices you **have**
 * The top number tells how many slices you **have**

Imagine that you ordered a full pizza with six silces. The [|fraction]that represents the whole pizza is 6/6 which is the same as the integer After all, we ordered 1 whole pizza so it makes sense that all 6 slices are the same as 1.

You eat 1 of the slices and there are now 5 slices left. The [|fraction] 5/6 now represents the slices of this pizza.

The **numerator** is the number that is at the top of the fraction and represents how many 'things' we have. In our examples, the numerator represents how many slices of pizza are left. The **denominator** is the number that is at the bottom of the fraction and represents how many 'things' make up the whole. In other words, how many slices were in 1 whole pizza--6. Therefore, 6 is the denominator in our example.


 * Everything above** the division symbol is the **numerator** and must be treated as if it were one number, and **everything below** the division symbol is the **denominator** and also must be treated as if it were one number.



Basically, the **numerator** tells you how many part we are talking about, and the **denominator** tells you how many parts the whole is divided into. So a fraction like **6/7** tells you that we are looking at six (**6**) parts of a whole that is divided into seven (**7**) equal parts.

>> ===Comparing Fractions=== >> 1. To compare fractions with the same denominator, look at their numerators. The larger fraction is the one with the larger numerator. For example 6/10 is larger then 5/10. >> 2. To compare fractions with the same numerator but different denominators, the larger fraction is the one with the smallest denominator. For example 1/2 is larger then 1/3. >> 3. To compare fractions with different denominators and numerators you need to convert to a common denominator. We will look at this later. The following document provides an excellent introduction to fractions. Click on the link and work your way through this.



Now try the following worksheets on comparing fractions. The answers are also provided for you to check your work.

=Equivalent Fractions=

There are many ways to write a fraction of a whole. Fractions that represent the same number are called equivalent fractions. This is basically the same thing as equal ratios. For example, 2/4, and 4/8 are all equivalent fractions. To find out if two fractions are equivalent, use a calculator and divide. If the answer is the same, then they are equivalent. Some fractions may look different, but are really the same, for example:

It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called //**Simplifying**//, or //**Reducing**// the Fraction
 * 4/8 ||  || 2/4 ||   || 1/2 ||
 * (Four-Eighths) ||  || Two-Quarters) ||   || (One-Half) ||
 * [[image:http://www.mathsisfun.com/images/fractions/pie-4-8.jpg width="120" height="120"]] ||  || [[image:http://www.mathsisfun.com/images/fractions/pie-2-4.jpg width="120" height="120"]] ||   || [[image:http://www.mathsisfun.com/images/fractions/pie-1-2.jpg width="120" height="120"]] ||

//**Watch the following video for the basics of fractions.**// The attached pdf show equivalent fractions

= = =**//Now try these exercises with answers here // **= = = he video has an excellent explanationmedia type="youtube" key="UzArYZYx67g" height="315" width="420" = =

//**The following PDF has some good exercises for you to try with answers here  The first two pages concentrate on equivalent fractions.**//


 * [[image:http://www.mathsisfun.com/numbers/images/fraction-number-line-thumb.gif width="189" height="94" link="http://www.mathsisfun.com/numbers/fraction-number-line.html"]] ||  || ==Fractions on the Number Line. Click on the link and try this activity[|Fractions number line]==

where you can see many common fractions and their simpler version. ||

=media type="youtube" key="VxpbMg_WASs" height="315" width="420" =

//**Proper fraction**//

 When the numerator is less than the denominator, we call the expression a proper fraction. These are some examples of proper fractions.

//**Improper fraction**//

 An improper fraction occurs when the numerator is greater than or equal to the denominator. These are some examples of improper fractions:

**//Mixed number//**

 When an expression consists of a whole number and a proper fraction, we call it a mixed number. Here are some examples of mixed numbers:

We can convert a mixed number to an improper fraction. First, multiply the whole number by the denominator of the fraction. Then, add the numerator of the fraction to the product. Finally, write the sum over the original denominator. In this example, since three thirds is a whole, the whole number 1 is three thirds plus one more third, which equals four thirds. Convert 1-1/3 to an improper fraction:

=Simplifying Fractions= //To simplify a fraction, divide the top and bottom by the **highest number** that//

//can divide into both numbers exactly.//

Simplifying (or //reducing//) fractions means to make the fraction as simple as possible. Why say four-eighths ( 4/8 ) when you really mean half ( 1/2 ) ?
 * || (Four-Eighths)4/8 ||  || (Two-Quarters)2/4 ||   || (One-Half)1/2 ||   ||
 * || [[image:http://www.mathsisfun.com/images/fractions/pie-4-8.jpg width="120" height="120"]] ||  || [[image:http://www.mathsisfun.com/images/fractions/pie-2-4.jpg width="120" height="120"]] ||   || [[image:http://www.mathsisfun.com/images/fractions/pie-1-2.jpg width="120" height="120"]] ||

How do I Simplify a Fraction ?
There are two ways to simplify a fraction:

Method 1
Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc).

Example: Simplify the fraction 24/108 :

 * || ÷ 2 ||  || ÷ 2 ||   || ÷ 3 ||   ||
 * [[image:http://www.mathsisfun.com/images/left-up-over-arrow.gif width="75" height="25"]] [[image:http://www.mathsisfun.com/images/left-up-over-arrow.gif width="75" height="25"]] [[image:http://www.mathsisfun.com/images/left-up-over-arrow.gif width="75" height="25"]] ||
 * 24 ||  || 12 ||   || 6 || = || 2 ||
 * 108 ||^  || 54 ||^   || 27 ||^   || 9 ||
 * [[image:http://www.mathsisfun.com/images/left-under-over-arrow.gif width="75" height="25"]] [[image:http://www.mathsisfun.com/images/left-under-over-arrow.gif width="75" height="25"]] [[image:http://www.mathsisfun.com/images/left-under-over-arrow.gif width="75" height="25"]] ||
 * || ÷ 2 ||  || ÷ 2 ||   || ÷ 3 ||   ||
 * || ÷ 2 ||  || ÷ 2 ||   || ÷ 3 ||   ||

Method 2
Divide both the top and bottom of the fraction by the [|Greatest Common Factor], (you have to work it out first!). =Greatest Common Factor= //The highest number that divides exactly into two or more numbers.//

Let us start with the last word:
 * Greatest Common Factor** is made up of three words
 * //Greatest//,
 * //Common// and
 * //Factor//

What is a "Factor" ?
Factors are the numbers you multiply together to get another number: Sometimes we want to find ALL the factors of a number: The factors of 12 are **1,2,3,4,6** and **12** ...

... because **2** × **6** =12, or **4** × **3**= 12, or **1** × **12** = 12.

What is a "Common Factor" ?
Example: Then the **//common// factors** are those that are found in both numbers:
 * The factors of 12 are **1, 2, 3, 4, 6** and **12** ||
 * The factors of 30 are **1, 2, 3, 5, 6, 10, 15** and **30** ||
 * Notice that **1,2,3** and **6** appear in both lists?
 * So, the **common factors** of 12 and 30 are: **1, 2, 3** and **6.**

Here is another example: Example: What are the common factors of 15, 30 and 105?
 * The factors of 15 are **1, 3, 5,** and **15** ||
 * The factors of 30 are **1, 2, 3, 5, 6, 10, 15** and **30** ||
 * The factors of 105 are **1, 3, 5, 7, 15, 21, 35** and **105** ||

The factors that are common to all three numbers are **1, 3, 5** and **15** In other words, the **common factors** of 15, 30 and 105 are **1, 3, 5** and **15**

What is the "Greatest Common Factor" ?
It is simply the **largest** of the common factors. In our previous example, the largest of the common factors is 15, so the **Greatest Common Factor** of 15, 30 and 105 **is 15** The "Greatest Common Factor" is the largest of the common factors (of two or more numbers) Watch the following clip for a review of this.media type="youtube" key="7P7zT-iuH80" height="315" width="420"

Finding the Greatest Common Factor
=There are three basic steps:=
 * =find all **factors** of both numbers=
 * =then select the ones that are **common** to both, and=
 * =then choose the **greatest**.=

Example:
Common Factor ||~ //Example Simplified// //Fraction// ||
 * ~ Two Numbers ||~ All Factors ||~ Common Factors ||~ Greatest
 * 9 and 12 || **9**: 1,3,9
 * 12**: 1,2,3,4,6,12 || 1,3 || **3** || 9/12 » 3/4 ||

And another example:
Common Factor ||~ //Example Simplified// //Fraction// ||
 * ~ Two Numbers ||~ All Factors ||~ Common Factors ||~ Greatest
 * 6 and 18 || **6**: 1,2,3,6
 * 18**: 1,2,3,6,9,18 || 1,2,3,6 || **6** || 6/18 » 1/3 ||

Example: Simplify the fraction 8/12 :
1. The largest number that goes exactly into both 8 and 12 is 4, so //the Greatest Common Factor is 4//.

2. Divide both top and bottom by 4: And the answer is: 2/3 Watch the following you tube clip for an explanation of how to simplfy fractionsmedia type="youtube" key="8JrORrjqLWs" height="315" width="420"
 * || ÷ 4 ||  ||
 * [[image:http://www.mathsisfun.com/images/left-up-over-arrow.gif width="75" height="25"]] ||
 * 8 || = || 2 ||
 * 12 ||^  || 3 ||
 * [[image:http://www.mathsisfun.com/images/left-under-over-arrow.gif width="75" height="25"]] ||
 * || ÷ 4 ||  ||
 * || ÷ 4 ||  ||

You should now be able to complete the last worksheet if you have not already done so.

[|**Factors Millionaire Game**] Before adding and subtracting fractions, students must understand basic facts about factors and divisibility. This fun game can be used to reinforce these important math concepts. [|**Factors and Multiples - Jeopardy Game**] In this interactive jeopardy game, students will practice finding the greatest common factor (GCF) and the least common multiple (LCM) of two or more numbers. [|**Soccer Math Game - Simplifying Fractions**] In this fun soccer game,students will practice reducing fractions to the simplest form. [|**Baseball Math Game - Simplifying Fractions**] This is a fun baseball math game about game about simplifying fractions. Students will have to first hit a homerun to be able to see and answer a math problem. [|**Football Math Game - Adding Fractions**] In this game, students will practice adding and subtracting fractions with common and different denominators. [|**Changing Fractions and Decimals to Percents**] Young students can use this fun millionaire game to practice changing decimals and fractions to percents. [|**Fractions, Decimals, Percents**] In this jeopardy game, students will convert fractions to decimals and percents and vice-versa. [|**Multiplying Fractions Game**] In this fun and interactive soccer game, students will test their ability to multiply different fractions. [|**Multiplying Fractions Millionaire Game**] How many points can you earn? Practice multiplying fractions by playing this fun game alone, with a partner, or in two teams. [|**Soccer Math - Dividing Fractions Game**]
 * ==MATH FRACTION GAMES click on the link [|Various Games]== ||
 * Do you want to play fun and interactive math fraction games? Click on the following links or pictures to play these exciting games about fractions.

Do you know how to divide fractions? Show your friends how many points you can score when playing this fun game. [|**Math Basketball - Dividing Fractions Game**] Dividing fractions does not have to be boring anymore. Play this fun and interactive game and score as many points as possible. [|**Fractions Jeopardy Game**] This online jeopardy game is is a fun way to review the four operations with fractions: addition, subtraction, multiplication, and division. [|Adding and Subtracting Fractions Board Game] [|Adding and Subtracting Fractions With Noah] This [|**Fraction Jeopardy Game**] has two rounds and three categories: fractions, decimals, and percents. The points are doubled in round two. Have fun earning points!

Identifying Fractions Game. Use the link attached
> **Game Description:** A fun [|fraction game]--this game forces you to guide each ball into the correct container. Each fraction ball has a fraction on it and your job is to guide the ball into the correct container. For instance, if the fraction ball has the fraction ½ on it then you must drop that ball into the container that is half full.[|Identifying Fractions] || = =

=Fresh Baked Fractions from Funbrain= The word on the street is that Fraction Jackson is a dog who loves pie (pi?). If you answer 24 problems correctly, you can put your name on Jackson's list of Master Pie Bakers.
 * [[image:http://www.funbrain.com/fract/fresh2.gif width="304" height="96" caption="FunBrain.com Fresh Baked Fractions"]] ||  ||

[|FunBrain]