An improper fraction has a top number (or numerator) which is larger than the bottom number (or denominator). Fractions typically represent parts of a whole, but improper fractions represent an amount greater than the whole. This can be misleading and needs further explanation. In this OneHowTo article we explain how to convert improper fractions to mixed numbers or a mixed fraction to get a figure better demonstrating the amount it represents.
First, it's very important to know what proper fractions, improper fractions and mixed fractions are. To do this, you should try to remember that the "numerator" is the number that appears on top of the fraction and the "denominator" is the one below. So:
- Proper fraction: the numerator is smaller than the denominator
- Improper fraction: the numerator is greater than or equal to the denominator
- Mixed number: a number accompanied by a proper fraction
Bear in mind that all improper fractions can be expressed with an equivalent mixed fraction and this conversion is exactly what we will be talking about in this OneHowTo article.
So, let's take a look at an example to make it easier to understand how to convert improper fractions to mixed numbers. Let's say you want to convert the improper fraction 9/4 into a mixed number.
The first thing you do is divide the numerator (the top number, the larger number) by the denominator (the bottom number, the smaller number). In our example we have to divide 9 by 4.
With the sum worked out, you should note down the quotient and remainder of the division. This is key to forming the mixed fraction.
You should end up with a mixed fraction, followed by a fraction that is formed by the remainder of the dividing number (the original denominator). So, in the example, in the results of our sums with the mixed fraction, we can see that the integer will be 2 (the quotient of the division) and the fraction 1/4 (the leftover bits from our calculation):
9/4 = 2 1/4
If you want to reverse the sum, i.e. you want to convert a mixed number into an improper fraction, keep the denominator and then multiply the mixed fraction's whole number by the denominator. Afterwards, add the numerator to get the numerator of the improper fraction.
So, in the example, 4 is the denominator. You multiply 2 by 4 and you will add 1. That means that the improper fraction will be 9/4.
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