Fractions

Greatest Common Factor =Greatest Common Factor = //The highest number that divides exactly into two or more numbers.//

//It is the "greatest" thing for simplifying fractions!//

Let's start with an Example ...

 * === Greatest Common Factor of 12 and 16 ===
 * 1) Find all the **Factors** of each number,
 * 2) Circle the **Common** factors,
 * 3) Choose the **Greatest** of those ||   || [[image:http://www.mathsisfun.com/numbers/images/gcf.gif width="298" height="140"]] ||

So ... what is a "Factor" ?
Factors are the numbers you multiply together to get another number:

A number can have many factors:

Factors of 12 are **1, 2, 3, 4, 6** and **12** ...

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

(Read how to find [|All the Factors of a Number] . In our case we don't need the negative ones.)

What is a "Common Factor" ?
Let us say you have worked out the factors of two numbers:

Example: Factors of 12 and 30

 * Factors of 12 are **1, 2, 3, 4, 6** and **12** ||
 * Factors of 30 are **1, 2, 3, 5, 6, 10, 15** and **30** ||

Then the **common** **factors** are those that are found in both lists:
 * <span style="color: #000000; color: #000088; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;">Notice that **1, 2, 3** and **6** appear in both lists?
 * <span style="color: #000000; color: #000088; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;">So, the **common factors** of 12 and 30 are: **1, 2, 3** and **6**

<span style="color: #000000; display: block; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;">It is a //common// factor when it is a factor of two or more numbers.

(It is then //"common to"// those numbers.)

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GCF Games



[|Greatest Common Factor Math Game]

<span style="color: #2bd497; font-family: Impact,Charcoal,sans-serif; font-size: 150%;">[|GCF Practice]

<span style="font-family: Arial Black,Gadget,sans-serif; font-size: 200%;">Divisibility Rules



<span style="background-color: #000000; color: #ff00ff; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 200%;">Least common multiple(Common Denominators) To find the least common multiple of 2 numbers, first we list all the multiples of each number and find which number (not 0) is shared between the 2 numbers and is the lowest.

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LCM games <span style="font-family: Impact,Charcoal,sans-serif; font-size: 200%;">[|Pirate Game]



<span style="background-color: #00ffff; color: #0000ff; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 300%;">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**.**-Denominator** ||
 * = [[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**-Numerator**
 * = The top number tells how many slices you have**-Numerator**

<span style="background-color: #00ffff; color: #993300; display: block; font-family: qarmic,Verdana,sans-serif; font-size: 20px; text-align: center;">Numerator / Denominator <span style="display: block; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px; text-align: center;">We call the top number the **Numerator**, it is the number of parts you have. We call the bottom number the **Denominator**, it is the number of parts the whole is divided into. You just have to remember those names! (If you forget just think "Down"-ominator) media type="custom" key="28841022"

Videos  Khan Academy Introduction to fractions  media type="custom" key="28931050" Math Antics media type="custom" key="29520141" align="center"

Khan Academy-Fractions as a division problem

<span style="color: #eb3757; font-family: Comic Sans MS,cursive; font-size: 200%;">Fractions on Number lines

<span style="color: #3914cf; font-family: Arial Black,Gadget,sans-serif; font-size: 190%;">[|Fractions on a number line]



<span style="color: #333122; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 180%;">[|Fraction models]







Fraction Flags



Equivalent Fractions

**//Equivalent Fractions//**//have the same value, even though they may look different.// <span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;"> These fractions are really the same: <span style="color: #a06000; display: block; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 17.48px; text-align: center; vertical-align: middle;">12 = 24 = <span style="color: #a06000; display: block; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 17.48px; text-align: center; vertical-align: middle;">48 <span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;">**Why are they the same?** Because when you multiply or divide **both** the top and bottom by the same number, the fraction keeps it's value. <span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;"> The rule to remember is: <span style="color: #000088; display: block; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 17px; text-align: center;">//"Change the bottom using multiply or divide,// <span style="color: #000088; display: block; font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 17px; text-align: center;">//And the same to the top must be applied"// <span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;">Here is why those fractions are really the same:
 * ||  ||   ||   || [[image:http://diysolarpanelsv.com/images/equivalent-fractions-clipart-6.png width="708" height="373" caption="Image result for equivalent fractions"]] ||



Dividing



<span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;"> Choose the number you divide by carefully, so that the results (both top and bottom) stay <span style="background-color: rgba(180,230,255,0.2);">[|whole numbers]. <span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;"> If we keep dividing until we can't go any further, then we have <span style="background-color: rgba(180,230,255,0.2);">[|simplified] the fraction (made it as simple as possible).

Videos

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Interactive



<span style="background-color: #ff0000; color: #ffff00; display: block; font-size: 20px; text-align: center;">Equivalent Fractions Games



Fraction Monkeys

Hooda-Number Eaters



Creature Capture







Drop Zone



Legend of Dick and Dom

Dolphin Equivalent fractions



Tony's Pizza Shop



<span style="background-color: #ffff00; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 200%;">Simplifying Fractions <span style="background-color: #ffff00; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 200%;">media type="custom" key="25071652"

**Here are the two rules:**

<span style="color: #0000ff; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 130%;">1) You can divide the numerator and the denominator by any number... as long as you use the same number for both! For example, you can't divide the numerator by 3 and the denominator by 5.

<span style="color: #ff0000; display: block; font-family: Comic Sans MS,cursive; font-size: 130%; text-align: center;">2) You need to get the numerator and denominator as small as possible.

<span style="color: #993300; display: block; font-family: qarmic,Verdana,sans-serif; font-size: 20px; text-align: center;">Simplifying Fractions Games Soccer Fruit Shoot Baseball



Visual Fractions



Fraction Slider game-Can you beat my score of 45?



<span style="color: #13de70; display: block; font-family: "Arial Black",Gadget,sans-serif; font-size: 160%; text-align: center;">Estimating sums and differences of fractions

[|Chose one video to watch]



Adding and Subtracting fractions with like denominators media type="custom" key="27056118"

<span style="background-color: #ff00ff; color: #00ffff; display: block; font-size: 26px; text-align: center;">Adding and subtraction fraction games



<span style="font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 150%;"> Or Stellar Spellers. Very cool.

Fruit Splat-Addition Fruit Splat-Subtraction

Catapult game Speedway

<span style="background-color: #00ffff; color: #6600cc; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 210%;">Adding and Subtracting fractions with unlike denominators <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">Let's try this: <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">1/2 + 1/3 <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">The main rule of this game is that we can't do anything until the denominators are the same! <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">We need to find something called the least common denominator (LCD)... It's really just the LCM of our denominators, 2 and 3. <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">The LCM of 2 and 3 is 6. So, our LCD 6. <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">We need to make this our new denominator... <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">Change the 1/2:

<span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">Change the 1/3:

<span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">1/2 + 1/3 = 3/6 + 2/6 <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">Now we can do it! <span style="color: #ff0000; display: block; font-family: "Comic Sans MS",cursive; font-size: 16.9px; text-align: center;">(3+2)/6 = 5/6

Videos

Shmoop



Khan Academy

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<span style="color: #1c18d1; font-family: Arial Black,Gadget,sans-serif; font-size: 180%;">[|Khan Academy Lesson -Adding fractions with unlike denominators]

Khan Academy-Subtracting fractions with unlike denominators



<span style="color: #db0e71; font-family: Comic Sans MS,cursive; font-size: 170%;">Modeling adding and subtracting with unlike denominators





Games Math Play

<span style="color: #0000aa; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 140%;">This one gets harder as you go....



<span style="background-color: #404040; color: #ff0000; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 200%;">Challenging! City under Siege



<span style="background-color: #ffff00; color: #ff00ff; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 200%;">Modeling Fractions



<span style="color: #993300; font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 200%;">Mixed Numbers and Improper Fractions media type="custom" key="25019616" <span style="color: #ff0000; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 130%;">Multiply the whole number part by the fraction's denominator.

<span style="color: #ff0000; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 130%;">Add that to the numerator

<span style="color: #ff0000; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 130%;">Then write the result on top of the denominator.

Games Matching <span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;">

<span style="font-family: Verdana,Arial,Tahoma,sans-serif; font-size: 15px;">

<span style="color: #444011; font-family: Impact,Charcoal,sans-serif; font-size: 220%;">Fraction Review



<span style="background-color: #fafad2; color: #800080; font-family: Impact,Charcoal,sans-serif; font-size: 200%;">Adding and subtracting mixed numbers

media type="custom" key="25071706" Subtracting Mixed numbers-video Adding and subtracting mixed numbers practice

Adding mixed numbers with regrouping

Subtracting mixed numbers with regrouping



Practice for adding and subtracting with regrouping

Games

Math Baseball

Dig It



Fishy fractions



<span style="font-family: &#39;Arial Black&#39;,Gadget,sans-serif; font-size: 200%;">Word problems

<span style="color: #555565; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 200%;">Multiplying and dividing Fractions

Khan Academy-Multiplying whole number times a fraction video



Multiplying a fraction by a whole number



Multiplying 2 fractions



Area of Rectangles

Multiplying Mixed Numbers



Multiplication as scaling

Multiplication of Fractions-Tiling media type="custom" key="29648749" align="center"

Division of fractions videos

Dividing whole numbers by fractions

Dividing fractions by whole numbers



<span style="color: #555565; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 200%;">[|Math Playground] Math Play

Count on



Dividing Fractions Multiplying fractions is easy: you multiply the top numbers and multiply the bottom numbers. For instance:

Then, you simplify if possible. That's it!

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[|Flocabulary] -If you don't have headphones you can read the close captioning



Moonshot



[|Math Games models]







All fraction skills Game

<span style="color: #555565; font-family: &#39;Comic Sans MS&#39;,cursive; font-size: 200%;">Ratios media type="custom" key="29183009"

[|Shmoop-Unit Rates]

Games





[|Ratio rumble]



Ratio Design Challenge

<span style="color: #25a4b5; font-family: Impact,Charcoal,sans-serif; font-size: 190%;">Unit Rates media type="custom" key="29167921"







Equal ratios and proportions

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[|Equal Ratios]

[|Ratio pairs]



Ratio Tables