HELP WITH FRACTIONS -
CONVERSION FROM IMPROPER TO
MIXED AND MIXED TO IMPROPER

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Go to
Help With Fractions
through Fun Games.

For details, see near
the bottom of this page.

Please study
Fractions
if you have not already done so.

There we studied about
half, quarter, three fourth
with examples and exercises.

Also study Fractions Made Easy.

There we studied about
concept of fraction in general
with examples and exercises.

Here, we will see definitions of proper fractions,
improper fractions and mixed fractions.

We will also see problems on
conversion from improper fractions to mixed fractions
and mixed fractions to improper fractions.

Proper, Improper and Mixed fractions

         A fraction in which Numerator is less than the
        Denominator is called a proper fraction.

Examples of proper fraction :
1⁄3, 2⁄5, 3⁄7, 13⁄17

        The value of a proper fraction is always less than one.

        A fraction in which Numerator is greater than
        or equal to the Denominator
        is called an improper fraction.

Examples of improper fraction :
4⁄3, 7⁄2, 12⁄12, 29⁄11

        improper fractions have values
         greater than or equal to 1.

         A combination of a whole number and a
        proper fraction is called a mixed fraction.

Examples of mixed fraction :
2  12,   3  45,   7  34,   29  815





Conversion of improper to mixed fractions :
Help With Fractions

         An improper fraction with numerator greater than its
        denominator can be converted into a mixed fraction,
        with a whole number and a proper fraction.

        Let us convert the improper fractions
        in the examples above to mixed fractions.

Solved Example 1 of Help With Fractions:
Improper to Mixed Fraction

Convert 4⁄3 into mixed fraction.

The denominator is 3 which means
each unit is divided into 3 equal parts.

The numerator shows that there are 4 such parts.

4 parts = 3 parts + 1 part
= 1 unit in full + 1 part
out of 3 parts in another unit

Numerically it can be shown as follows.

4⁄3 = (3 + 1)⁄3 = 3⁄3 + 1⁄3= 1 + 1⁄3 = 1  13

or we can show the division of 4 by 3,
using the Long Division method.


                        Dividend
           Divisor   3 )   4   ( 1   Quotient    
                           3
                          ---
                           1   Remainder 
                          ---  

          

        4⁄3 = 1  13. Ans.

        Dividend⁄Denominator
        = Quotient + Remainder⁄Denominator



Solved Example 2 of Help With Fractions:
Improper to Mixed Fraction

Convert 7⁄2 into mixed fraction.


                        Dividend
           Divisor   2 )   7   ( 3   Quotient    
                           6
                          ---
                           1   Remainder 
                          ---  

          

        Using the formula
        Dividend⁄Denominator
        = Quotient + Remainder⁄Denominator

        7⁄2 = 3  12. Ans.

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Solved Example 3 of Help With Fractions:
Improper to Mixed Fraction


Convert 29⁄11 into mixed fraction.

Now we will directly find the answer
by long division method.


                        Dividend
           Divisor   11 )   29   ( 2   Quotient    
                            22
                           ---
                             7   Remainder 
                           ---  

          

        Using the formula
        Dividend⁄Denominator
        = Quotient + Remainder⁄Denominator

        29⁄11 = 2  711. Ans.

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Conversion of mixed to improper fractions :
Help With Fractions

Solved Example 4 of Help With Fractions:
Mixed to Improper Fraction

Convert 3  45 into improper fraction

The denominator of the mixed fraction is 5.
The whole number 3 of the mixed
fraction tells us to take 3 units
containing 5 parts each.
i.e. 5 + 5 + 5 = 15 parts.
The numerator 4 of the prper fraction
4⁄5 tells us to take
4 parts of another unit of 5 parts.
Thus we have 15 + 4 = 19 parts altogether.
Thus 3  45can be shown as 19⁄5.

Numerically it can be shown as follows.

3  45= 3 + 4⁄5 = 5⁄5 + 5⁄5 + 5⁄5 + 4⁄5
= (5 + 5 + 5 + 4)⁄5
= (3 x 5 + 4)⁄5 = 19⁄5

Thus, 3  45= (3 x 5 + 4)⁄5. Ans.

We can formulate like this:

        Whole Number  (Numerator⁄Denominator)
         = (Whole Number x Denominator
             + Numerator)⁄Denominator

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Solved Example 5 of Help With Fractions:
Mixed to Improper Fraction

Convert 7  34 into improper fraction

Applying the Formula
Whole Number  (Numerator⁄Denominator)
= (Whole Number x Denominator + Numerator)⁄Denominator

we get7  34= (7 x 4 + 3)⁄4 = 31⁄4. Ans.

Solved Example 6 of Help With Fractions:
Mixed to Improper Fraction


Convert 29  815 into improper fraction

Applying the Formula
Whole Number  (Numerator⁄Denominator)
= (Whole Number x Denominator + Numerator)⁄Denominator

we get29  815= (29 x 15 + 8)⁄15 = 443⁄15. Ans.

Exercise on Help With Fractions :
Conversion from improper to mixed
and mixed to improper fractions

Problems on Help With Fractions :

  1. Convert the following imroper
    fractions to mixed fractions
    1. 9⁄2
    2. 67⁄10
    3. 11⁄3
    4. 13⁄4
    5. 37⁄5
    6. 78⁄7
    7. 23⁄6
    8. 49⁄8
    9. 52⁄9
    10. 98⁄11
            
  2. Convert the following mixed
    fractions to imroper fractions
      1. 2  12
      2. 2  34
      3. 3  14
      4. 4  23
      5. 5  67
      6. 7  89
      7. 6  37
      8. 9  19
      9. 8  1011
      10. 7  1113
    For Answers see at the bottom of the Page.

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    The following links will take you to Help
    With Fractions on other topics of Fractions

    Equivalent Fractions

    Comparing Fractions

    Adding Fractions

    Subtracting Fractions

    Multiplying Fractions

    Dividing Fractions

    Simplifying Fractions

    Fraction word Problems

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    Help With Fractions

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    Answers to Exercise on Help With Fractions :
    Conversion from improper to mixed
    and mixed to improper fractions

    Answers to Problems on Help With Fractions :

    1.  
      1. 4  12
      2. 6  710
      3. 3  23
      4. 3  14
      5. 7  25
      6. 11  17
      7. 3  56
      8. 6  18
      9. 5  79
      10. 8  1011
        1. 5⁄2
        2. 11⁄4
        3. 13⁄4
        4. 14⁄3
        5. 41⁄7
        6. 71⁄9
        7. 45⁄7
        8. 82⁄9
        9. 98⁄11
        10. 102⁄13

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