Lesson 2 - Comparing Like & Unlike Fractions

  


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money cut by scissorsComparing fractions is like comparing two amounts.  For example, compare these two fractions:  one-fourth of a dollar and three-fourths of a dollar?      1_4or3_4.gif (983 bytes)

Comparing like fractions, fractions with the same denominator, is easy.  Simply look at the numerator (the number on top) and see which numerator is larger.  The larger fraction is the one with the larger numerator.
    
king_tut.gif (3704 bytes)Comparing unlike fractions, or fractions with different denominators can be as easy as comparing like fractions if you know the cheat for it.  I call it, "King Tut" math.  The books all call it, "cross product." 

In my mind, I imagine the mummy of King Tut was prepared with its arms crossed in an X.  Multiply in an X manner starting from the denominators (bottom numbers) diagonally across to the other numerators (top numbers).
    
Example:

                     Compare the fractions


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Step 1:  find the product of the first denominator (5) and the second numerator (7):
Step 2:  find the product of the second denominator (8) and the first numerator (3):

Compare the products and you can quickly see which fraction is greater than, less than, or equal to the other.  Since the first cross-product is larger, the first fraction is larger.

    
Example:

Compare the fractions 3/7 and 1/2.
The first cross-product is the product of the first numerator and the second denominator: 3 × 2 = 6.
The second cross-product is the product of the second numerator and the first denominator: 7 × 1 = 7.
Since the second cross-product is larger, the second fraction is larger.

    
Need some practice?  

Extension Activities - Comparing Like & Unlike Fractions

  

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