Lesson 3: Improper Fractions and

Mixed Fractions

1. Fraction Types:  Proper Fractions ,  Improper Fractions ,  Mixed Fractions.
2. Converting Mixed Fractions to Improper Fractions.
3. Example of Changing Mixed Fractions to Improper Fractions.
4. Converting Improper Fractions to Mixed Fractions.
5. Example of Changing Mixed Fractions to Improper Fractions.
6. Practice Game.

 FRACTION TYPES

There are 3 different types of fractions:

• Proper Fractions

       Numerator < Denominator
       Proper fractions have the numerator part smaller than the denominator part,
       for example , or  .

• Improper Fractions

        Numerator > Denominator or Numerator = Denominator,
        Improper fractions have the numerator part greater or equal to the denominator part,
        for example or .

• Mixed Fractions

        A mixed fraction is a whole number plus a fraction, for example 2or 123 .
        Mixed Fractions are sometimes called mixed numerals or mixed numbers.

CONVERTING MIXED FRACTIONS TO IMPROPER FRACTIONS

Consider the mixed fraction  1 . It reads as "one whole and two fifths".

      There are 5 fifths in 1 whole.
 

      And there are 2 fifths in , giving 5 + 2 = 7 fifths altogether.

i.e.  1 = 

TO CALCULATE THE NUMERATOR when converting  mixed to improper fractions:
 

• Multiply the whole number of the mixed fraction by the denominator
• Add on the numerator of the fraction part

Example:

Write the mixed fraction 2  as an improper fraction.

SOLUTION:

                     There are 2 x 3 thirds in 2 wholes .

                                                               There are 2 thirds in  .
                                                                                                    2 x 3 + 2 = 8 thirds altogether.
 
 
 2 =  = 

 CONVERTING IMPROPER FRACTIONS TO MIXED FRACTIONS

 Let us convert to the improper fraction.
 Do you still remember what the vinculum mean?
The fraction (or seven halves) means "7 divided by  2".

TO CHANGE THE IMPROPER fraction to a mixed fraction DIVIDE
the numerator by the denominator
 

• The quotient (i.e. the result of division) is the whole number part of the mixed fraction
• The remainder is the numerator of the fraction part of the mixed fraction

  Thus , or 7 divided by 2, is  3 remainder 1, so =  3 
 

Example:

Write the fraction  as a mixed fraction.

SOLUTION:

   =  2  (because 11 divided by 4 is 2 remainder 3).

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