# Converting mixed numbers and improper fractions

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Fraction are very commonly used and very important form of representation of numbers. Fraction is usually written in the “p/q” form. Here ‘p’ is the numerator and 'q' is the denominator. The denominator of a fraction cannot be equal to zero i.e. q not equal to zero. Fraction where the numerator is lesser than the denominator p < q is called as a proper fraction. A fraction where the numerator is greater than the denominator is called as improper fraction p > q. An improper fraction can be converted to a mixed fraction. A mixed fraction is the combination of a whole number and a proper fraction.

Example 1: Convert the mixed number 1¾ to improper fraction?
Solution: The number is a mixed number 1¾   where 1 is the whole number part and ¾ is the proper fraction as the numerator is lesser than the denominator i.e. 3 < 4.
The mixed number can be now converted to improper fraction.
Therefore, 1¾   = (4*1 + 3)/ 4 = (4 + 3)/4 = 7/4
This gives 7/4 which is an improper fraction as 7 > 4.
Hence, the mixed fraction gives 1¾ can be expressed as 7/4.

Question: Multiple choice question (Pick the correct option.)
Convert the mixed number 6½ into improper fraction?
a)    13/2                b) 7/2              c) 11/2                        d) None of these.

Correct answer: option a.
The mixed number 6½ can be now converted to improper fraction.
Therefore, 6½    = (6*2 + 1)/2 = (12 + 1)/2 = 13/2.
This gives 13/2 which is an improper fraction.