SIMPLIFYING FRACTIONS Fraction Simplification and Equality

Some Fractions are Created Equal  Fractions represent a part of a whole number  They are made of numerators and denominators  Sometimes fractions with different numerators and denominators can be equal to one another. Numerator Denominator

Equal Fractions  These two rectangles are the same size, but they are divided into a different number of pieces  If we shade one piece on the first rectangle, it is the same as shading two pieces on the second rectangle. Thus, the fractions 1/4 and 2/8 are EQUAL!  1/4 2/8

Equal Fractions  You can see examples of this in real life every day!  Check out these pizzas! They are all the same size but are divided into different numbers of equally sized pieces 1/4 of a pizza = 2/8 of a pizza = 3/12 of a pizza THESE FRACTIONS ARE ALL EQUAL

Simplify or Reduce?... That is the question.  We have seen that 1/4 = 2/8 = 3/12  When we are given a fraction containing larger numbers (3/12) and we are asked to simplify or ‘reduce’, which is the correct terminology?...  We already said that 3/12 = 1/4, did we reduce or simplify this number?...

Simplify or Reduce?... That is the question.(ctd.)  We SIMPLIFIED it! Although the numbers in the numerator and denominator are smaller than they were before, these numbers alone don’t make up the overall number.  The RATIO between the two stayed the same and therefore the number cannot be ‘reduced’. It is SIMPLIFIED.

Simplifying Fractions  Usually, fractions are easiest to understand in their simplest form.  To get to the simplest form you must SIMPLIFY them, if necessary.  Example: What is the simplified form of:

Simplifying Fractions  To simplify a fraction you must be able to divide both the numerator and the denominator by the SAME number.  Can you think of a number by which both 36 and 27 are divisible?  How about 3?  Divide 27 by 3 and get 9  Divide 36 by 3 and get 12 =

Simplifying Fractions  So now we have, but is this number in the simplest form yet?  Are there any numbers that go into both 9 and 12?  How about 3?  Divide 9 by 3 and get 3 =  Divide 12 by 3 and get 4  Thus, we have:  = = OR = ¾ is the simplest form of this fraction!

Prime Factorization  Another way to think about simplifying fractions is through Prime Factorization:  In prime factorization, you reduce the numerator and the denominator into their lowest factors. Then you can cancel out pairs of numbers appearing in both the numerator AND the denominator.  Check out these fractions that we have simplified using Prime Factorization: = = = = = = =

Challenge Problem!  Simplify this fraction:

Challenge Problem!  Simplify this fraction: = = = OR = = = =

Great Job! Keep practicing!