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Converting Improper Fraction to Proper Fraction

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In this article we will explain the meaning of the following terms:

  1. Proper Fraction.
  2. Improper Fraction.
  3. Mixed Fraction.

We then explain how we can convert one kind of fraction into another type of fraction.

How to Convert an Improper Fraction to a Proper Fraction?

The answer to the above question is that it is not possible to convert an improper fraction to a proper fraction. Therefore the question of how to convert an improper fraction to a proper fraction does not arise.

On the other hand, it is possible to convert an improper fraction to a mixed fraction. This is the most common situation we face when trying to convert an improper fraction. Let us try to understand the definitions of these words in order to understand why converting improper to proper fractions is impossible.

What is a Proper Fraction?

A proper fraction is a fraction whose numerator (the number lying above) is less than the denominator (the number lying below). Some examples of proper fractions are:

  1. \frac{3}{5} – Here the numerator 3 is less than 5.
  2. \frac{1}{8} – Here the numerator 1 is less than 8.
  3. \frac{2}{19}
  4. \frac{13}{97}, etc.

What is an Improper Fraction?

An improper fraction is a fraction whose numerator (the number lying above) is greater than or equal to the denominator (the number lying below). Some examples of improper fractions are:

  1. \frac{7}{5} – Here the numerator 3 is less than 5.
  2. \frac{13}{8} – Here the numerator 1 is less than 8.
  3. \frac{27}{19}, etc.

Why is converting improper into a proper fraction impossible?

By looking at the definitions of a proper and an improper fraction it becomes clear that converting an improper fraction to a proper fraction is impossible. This is because in an improper fraction the numerator is greater than the denominator and we cannot change the value of the numerator to make it smaller than the denominator.

For example, suppose that we are given the improper fraction 16/10. Suppose that we reduce it to the lowest terms as follows, \frac{16}{10} = \frac{8}{5}.

Notice that even after we reduce the fraction to the lowest terms, it still remains improper. This illustrates why we cannot make the numerator of an improper fraction to be less than the denominator. Also, just as it is impossible to convert an improper fraction to a proper fraction, in the other direction it is also impossible to convert a proper fraction to an improper fraction.

What is a Mixed Fraction?

A mixed fraction is a fraction of the following form, W \frac{N}{D}

Here, W denotes the whole number part, N denotes the numerator and D denotes the denominator. Given any improper fraction, we can convert it into a mixed fraction. This is done by dividing the bigger number by the smaller one. Then the quotient becomes the whole number part, the remainder becomes the numerator and the divisor becomes the denominator. For example, \frac{8}{5}= 1\frac{3}{5}.

This is because when we divide 8 by 5, we get 1 as the quotient and 3 as the remainder. The divisor which is 5 becomes the denominator.

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