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Many times after adding fractions,multiplying fractions, or dividing fractions, you are left with a fraction that needs to be simplified or reduced. 

  • This method of simplifying a fraction involves using a factor tree in order to reduce the fraction. 
  • Here are the steps for reducing or simplying a fraction using a factor tree.



factor tree is a diagram that helps you find the prime factors of a number. You find the factor of a number, and then the factors of that number until you can’t factor anymore. The end result of the factor tree is all the prime factors of the original number.

Step 1. Make a factor tree for the top number ( numerator) and the bottom number ( denominator).

Step 2. Underline prime numbers on your factor tree.

Step 3. Make a list of the prime numbers for your numerator and denominator.

Step 4. Cancel common factors found on the numerator and the denominator

Step 5. Multiply the remaining factors.

Let's look at an example from the video:

Simplify or Reduce the fraction     16
                                                                    120
























Simplifying Fractions

Step 1. Set up a factor tree for your numerator and your denominator Your numerator is the top number of your fraction and denominator is the bottom number
Step 2. Underline the prime numbers on both factor trees. Prime numbers are only divisible by itself and 1
Step 3. Make a list of the prime numbers for your numerator and your denominator
Step 5. Multiply any remaining factors found in the numerator and denominator. 
Step 4. Cross out common factors.There is not a 5 or 3 on the numerator so they are not crossed out.

Making a factor Tree for 16
Making a factor Tree for 120
Making a factor Tree  for 16
Making a factor Tree
2x2x2x2/2x2x2x5x3
Making a factor Tree
2/5x3

Simplify a fraction = Reducing a Fraction to Lowest Terms

Simplyfing a Complex Fraction

Definition of a Complex Fraction

A complex fraction is a fraction with a fraction within a fraction. In other words the denominator,numerator,or both contain a fraction.

How do you simplify a Complex Fraction ?

I feel the easiest method for simplifying a complex fraction is to rewrite the fraction as a division problem by using, Change,Keep,Flip

Example 1  Simplify the following Complex Fraction


complex fraction/5+7/11/5/12
Lets look at the parts of this complex fraction
5+7/11/5/12 definition complex fraction
Numerator
You can think of the vinculum  as a division sign
Denominator
12/11/5/12
Step 1 Simplify the numerators if you can. In this problem add 5+7=12 and then change the fraction into a division problem. See step 2.
Step 2  Rewrite the division problem to a multiplication problem by using the "Keep,Change,Flip Method"
Keep the first fraction the same
Change the sign
Flip the last fraction/ Create a reciprocal
12/11 x 12/5 =144/55 keep change flip
12/11 x 12/5 =144/55 multiply the complex fraction straight across
Step 3  Multiply straight across in order to get the complex fraction in the simplest form

Simplify a complex fraction that includes a variable

simplify x/2 + 1/x/x^2 +2x
Step 1.  
keep change flip rewrite the division problem to a multiplication problem
simplify the numerator x/2 + 1/2
Step 2.  
Step 3.  
x
x
x^2 +2/2x x 1/x^2 +2x = x^2 +2/2x(x^2 +2x)
Simplify this complex fraction that has an  exponent
Simplify the numerator using the common denominator 2x
​Rewrite the equation using Keep,Change,Flip
Keep the first fraction the same
Change the sign
Flip the last fraction/ Create a reciprocal
Step 4  Multiply straight across in order to get the complex fraction in the simplest form
Questions answered in this video...

How do you simplify a complex question?

What is a complex fraction?

How do you simplify 5+7/11/5/12?

How do you simplify x/2 +1/x/x^2 +2x?


Simplifying Complex Fractions
fraction calculator
Common Core Standard: 4.NF.1
To simplify a fraction means to reduce a fraction to its lowest terms. 
A fraction is in lowest terms when the numerator and denominator have no common factor other than one.