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For some people the word "Fractions" is not a happy word. Many people don't like adding fractions,or subtracting fractions because it has always been very confusing or frustrating. Here are 10 proven tips,tricks, or helpful information that can help everyone understand a little bit better.
For each tip or trick I will give the pros of the tip or trick,and the con of every tip or trick.

7 Shortcuts for solving fractions

Tip 1. Adding fractions without using a Least Common Multiple

This trick has been around for a long time and can be very helpful if you don't want to calculate a least common multiple. (LCM)

Step 1. Multiple the denominators (the red arrow) in order to calculate the denominators

Step 2. Multiply the numerator of the first fraction with the denominator of the second fraction,and then multiply the numerator of the second fraction with the denominator of the first fraction. (Some people call this the criss-cross method) Follow the black and blue lines.

Step 3. Add these two solutions together to calculate the numerator
            3 x6 =18  1 x4 =4  and 18+4 = 22 (This will be the numerator).

Step 4. Reduce the final answer.



Step 1. Multiply the denominators together 
(4 x 5 =20 ) This gives you a common denominator.

Step 2. Divide the common denominator by the original denominators to determine your multipler.
20/4=5
20/5=4

Step 3. Multiply the numerator (top) by the factor from step 2.
2x5 =10
 20    20
3x4=12
​ 20    20
Step 4. Calculate your numerator (top) by adding the numerators from step 3. Put your common denominator underneath.  Simplify.
10 +12 =22
     20      20

Pros: You don't have to find a least common multiple. Works with proper and improper fractions.


Cons: You can easily confuse the steps.

Tip 3.Dividing Fractions Using Keep Change Flip

Most people find that this tip makes dividing fractions much easier. You keep the first fraction,change the sign from division to multiplication, and finally flip the last fraction (create a reciprical)
Keep the first fraction the same
Change the division sign to multiplication
Flip the last fraction
Pros: Gives you a systematic method for dividing fractions. 



Cons: It can be confusing with mixed numbers.  Remember to use the circle trick first!

Tip 4. What is the name of the bar of a fraction?

Impress your friends and teachers with this fact. The bar used with fractions is called the Vinculum
Vinculum
Denominator
Numerator.
Think of the vinculum as a division sign. It is a line that separates the numerator and the denominator.
Step1.
Step2.
Step3.
Step4.

Tip 5.Use the Ladder Method to find the LCM and GCF

​Find the Lowest Common Multiple (LCM) and the Greatest Common Factor ( GCF) of 16 and 24
Step 1. Divide each number by the same prime number and draw a line around the two new numbers. 
Step 2. Repeat step 1 until the numbers are no longer divisible by the same prime number.
Step 3. Circle the left column of prime numbers.Multiply the numbers you circle to find your  GCF
2x2x2 = 8

X
+
+
X
I call this the Circle Method. It is helpful when creating an improper fraction.

Step 1. Start at the bottom of the fraction. Multiply the denominator times the whole number.
Step 2. Then add the product from step 1, to the numerator.

Tip 7. Memorize decimal equivalents of common fractions

Most people know their times tables and understand how much time they save when doing calculations. In the same way by memorizing this list of fractions can be a real time saver and help you with fractions and decimals. 
1/4 = .25
1/2 = .5
3/4 = .75
1/3 = .333~
1/5 = .2
2/5 = .4




Tip 6. Use the Circle Method to create an Improper Fraction

3/5 = .6
4/5 = .8
1/8 = .125
3/8 = .375
5/8 = .625
7/8 = .875




This method is a modified version of tip number 1. It is a mixture of adding fractions the traditional method, and the criss-cross method. The picture looks confusing, here goes the explanation:
Pros: Gives you a systematic method for creating improper fractions. Easy to understand


Cons: It can be confusing with mixed numbers. Some people will add the numbers first and then multiple,which will result in an error.
Pros: Saves you time and it improves your number sense.



Cons: It takes some work to memorize the decimals equivalents of the fractions.  Make some flashcards!!!
thumbs up fraction tips
thumbs down fraction tips
thumbs up fraction tips
thumbs down fraction tips
Pros  You don't have to calculate the Least Common Multiple and then figure out how many times the denominators go in to this number. You are able to shorten the number of steps involved when adding fractions.

Cons  Many people get confused about which numbers to cross multiple. Many people just learn the trick, but don't really understand what they are doing.
thumbs up fraction tips
thumbs down fraction tips
thumbs up fraction tips
thumbs down fraction tips
thumbs up fraction tips
thumbs down fraction tips

Tip 2. Adding fractions without using a GCM

add fractions without a LCM
Multiply the numbers you circle to find your  GCF 2x2x2 = 8
Step 4b.Draw an L around the prime numbers and the reamaining numbers. Multiply all the numbers in the L for your LCM
2x2x2x1x2x3= 48
Multiply all the numbers in the L for your LCM 2x2x2x1x2x3= 48
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