Improper Fraction

A fraction is a numerical quantity that represents a part of a proportion or an amount of something or a collection. A fraction comprises a numerator and a denominator. For example, if one watermelon is cut into half, then the fraction for each of the halves will be represented as  ½; where 1 is the numerator and 2 is the denominator. Improper fraction is more useful than mixed fractions when doing calculations. In this article, we will be discussing what are improper fractions and how they can be solved.

Improper Fraction

As defined above, a fraction with the numerator value greater than the denominator is known as an improper fraction. For instance, a fraction of 10/3 has 10 in the numerator which is greater than the denominator 3. Similarly, other examples of improper fractions are 100/3, 25/4, and 99/2. The main difference between proper and improper fraction is that the value of the numerator is higher than the denominator in the latter.

The two solutions of improper fractions provided below can further explain the steps involved.

Simplification of Improper Fractions

Different fractions have their own benefits and understanding. A mixed fraction is definitely easier to understand when referring to day to day items, quantities, or other comparisons. But in terms of doing mathematical calculations, a mixed fraction can be more confusing than any other types of fractions. Moreover, in order to attempt mathematical calculations, the first step involves simplifying these mixed fractions to a proper or improper fraction. An improper fraction is more useful than mixed fractions when doing calculations such as addition and subtraction.


1.Convert the Improper Fraction 7/4 Into a Mixed Fraction.


Following are the steps mentioned below to convert an improper fraction into a mixed fraction:

Step 1: Use the division method to solve the improper number to get a mixed fraction

Step 2: When we divide 7 by 4, we get 1 whole part and 3 as a remainder.

Step 3: The remainder, 3, becomes the numerator along with 4 as the denominator. ¾ is considered as a proper fraction when we look at the mixed fraction number obtained.

Step 4: The last step is to combine the whole number with the proper fraction, which in this case

is 1 and 3/4. These two-part together make the mixed fraction 1¾.

From here you can conclude, that the mixed fraction for the improper fraction 7/4 is 1¾.

2. Convert the Mixed Fraction 5⅗ Into an Improper Fraction.


Following are the steps mentioned below to convert a mixed fraction into an improper fraction:

Step 1: Unlike the above-mentioned example, the conversion of a mixed fraction to an improper fraction involves multiplication.

Step 2: The first multiplication has to take place between the denominator and the whole number. In the example given above, 5 is the whole number, as well as 5, is the denominator.

Therefore, the product of the two becomes 25.

Step 3: This product will then be added with the numerator, i.e, 25 +3 = 28.

Step 4: The product when added with the numerator value of the mixed fraction, becomes the new numerator for the improper fraction. That being said, it means, 28 is the numerator for the improper fraction.

Step 5: In the case of the denominator, the value remains the same for an improper fraction as given by the mixed fraction. Remember, not to change the value of the denominator when converting from mixed to an improper fraction. Therefore, in this case, the denominator remains 5.

Step 6: The last step is to combine the numerator and denominator together to get an improper fraction. 28/5 becomes the new improper fraction for the mixed fraction of 5⅗.

Note: The denominator value is lesser than the numerator and therefore it can easily be distinguished as an improper fraction.

FAQ (Frequently Asked Questions)

1. How Many Types of Fractions are There?

There are many types of fractions:

1. Unit Fraction: A unit fraction is a fraction that has 1 as the numerator. Some examples of unit fractions are 1/4, 1/5, ⅙, and 1/8.

2. Proper Fraction: A proper fraction is the one that has a numerator value lesser than the denominator. For example, 3/9, 5/17, 2/5 are some examples of proper fractions.

3. Improper Fraction: The definition of an improper fraction is that when a fraction has the numerator greater than the denominator. Some examples of improper fractions are 5/3, 10/7, 15/4, and 31/7.

4. Mixed Fraction: A mixed fraction consists of a proper fraction along with a whole number. For instance, 1¾, 7⅘, and 21¼ are some examples of a mixed fraction.

2. How Can Improper Fractions Be Simplified?

Answer: A fraction with the numerator value greater than the denominator is known as an improper fraction. An important feature of an improper fraction is that when the numerator is divided by the denominator, then it does not lead to a whole number. Whenever an improper fraction exists, it can only be simplified to a mixed fraction through the method of division. The method to simplify improper fractions is division.