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

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  ¹⁄₂,    3  ⁴⁄₅,    7  ³⁄₄,    29  ⁸⁄₁₅

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  ¹⁄₃

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  ¹⁄₃. 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  ¹⁄₂. Ans.

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  ⁷⁄₁₁. 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  ⁴⁄₅ 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  ⁴⁄₅ can be shown as 19⁄5.

Numerically it can be shown as follows.

3  ⁴⁄₅ = 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  ⁴⁄₅ = (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  ³⁄₄ into improper fraction

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

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

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

Convert 29  ⁸⁄₁₅ into improper fraction

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

we get 29  ⁸⁄₁₅ = (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  ¹⁄₂
   2. 2  ³⁄₄
   3. 3  ¹⁄₄
   4. 4  ²⁄₃
   5. 5  ⁶⁄₇
   6. 7  ⁸⁄₉
   7. 6  ³⁄₇
   8. 9  ¹⁄₉
   9. 8  ¹⁰⁄₁₁
   10. 7  ¹¹⁄₁₃
   For Answers see at the bottom of the Page.
   
   

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   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  ¹⁄₂
      2. 6  ⁷⁄₁₀
      3. 3  ²⁄₃
      4. 3  ¹⁄₄
      5. 7  ²⁄₅
      6. 11  ¹⁄₇
      7. 3  ⁵⁄₆
      8. 6  ¹⁄₈
      9. 5  ⁷⁄₉
      10. 8  ¹⁰⁄₁₁
   2. 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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