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A fraction consists of two numbers (as \[\frac{a}{b}\]), a numerator and a denominator. The number written at the top is the numerator, and the one written at the bottom is the denominator. Mathematicians came up with three types of fractions, named as proper fractions (or the fraction less than one and greater than 0, with numerator less than denominator), the improper fraction (or a fraction more than one or equal to one with a numerator greater than or equal to the denominator), and a mixed fraction (a combination of a whole number and proper fraction). This article contains a brief description of the improper fractions and performing various operations on them.

Whenever the numerator of the fraction is lesser than the denominator, the fraction is lesser than one. For example, \[\frac{1}{2}\] , \[\frac{9}{13}\], etc.

On the other hand, whenever the numerator of the fraction is greater than the denominator, it is a fraction more than 1. Some examples of the fractions that are greater than 1 are as follows: \[\frac{5}{2}\], \[\frac{25}{20}\], etc.

And then there are mixed fractions too. Mixed fractions contain both a whole number and a proper fraction, like, \[8\tfrac{1}{10}\], \[4\tfrac{1}{5}\], etc.

There are several number line fractions greater than 1. Here is a simple example to help you understand more about its representation.

Let us consider the below example of three whole pizzas (each divided into four parts) and a pizza from which one piece is taken away.

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Now, you can represent the number of pieces of pizza with you in the form of fractions. The denominator here will be the total number of pieces making a pizza, which is 4. Now the total pieces of pizza in all are 15, representing the numerator.

This gives us the fraction \[\frac{15}{4}\], which is an improper fraction.

For converting a fraction more than one to a mixed fraction, here are the steps that you must follow:

Divide the numerator of the given fraction by its denominator.

First, write the whole number answer received (which is also the quotient of the division).

Now write the fraction with the remainder as the numerator and the denominator staying the same.

For Example:

Convert \[\frac{13}{4}\] to a mixed fraction.

Solution:

Divide the numerator by denominator, 13 ÷ 4 = 3 with a remainder of 1. This can also be written as 3 R 1.

Now write two and then write the remainder one above the denominator 4.

= 3\[\frac{1}{4}\]

Here are the steps that you must follow to convert a mixed fraction to an improper fraction:

Multiply the whole number part of the given fraction with the denominator of the fraction.

Add the resultant to the numerator.

Then write the resultant of the sum on the numerator part and keep the denominator the same as earlier.

For Example:

Convert 3\[\frac{4}{5}\]to an improper fraction.

Solution:

Multiply the whole number part of the fraction with the denominator:

3 x 5 = 15.

Now add the resultant to the numerator:

15 + 4 =19.

Write the resultant part above the earlier denominator:

\[\frac{19}{5}\]

To represent a fraction greater than one on a number line, follow the mentioned steps:

Write a fraction greater than 1 in the form of a mixed fraction.

Now start from the whole number part of the mixed fraction.

Divide the section between the mentioned whole number and the following whole number in equal parts, as stated in the denominator.

Now count the parts for the number as mentioned in the numerator.

Mark that on the number line to complete the representation.

Q1: Convert \[\frac{17}{3}\] to a mixed fraction.

Ans. \[\frac{17}{3}\] = 17 ÷ 3 = 5 with a remainder 2.

= 5 R 2

= 5\[\frac{2}{3}\]

Q2: Convert 2\[\frac{4}{9}\] to an improper fraction.

Ans. Multiply the whole number part of the fraction with the denominator:

2 x 9 = 18.

Now add the resultant to the numerator:

18 + 4 = 22.

Write the resultant part above the earlier denominator:

\[\frac{22}{9}\]

Q3: Represent \[\frac{61}{5}\] on a number line.

Ans. \[\frac{61}{5}\] = 12 R 1

= 12\[\frac{1}{5}\]

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FAQ (Frequently Asked Questions)

1. Explain Fraction and Their Types.

Ans. A fraction is represented as a/b . For example, ½ .

As it is divided into two parts, the upper part, say ‘a,’ is termed as a numerator. The lower part of a fraction, say ‘b,’ is known as the denominator. A numerator refers to the number of parts available, and a denominator means the parts a whole is divided into.

There are three types of fractions, which are as mentioned below:

**Proper Fraction –**The numerator here is less than the denominator, and the resultant fraction is lesser than. For example, 1/2, 9/13, etc.**Improper Fraction -**The numerator part is greater than or equal to the denominator. The fraction is greater than or equal to 1. For example, 5/2, 25/20, etc.**Mixed Fraction -**Mixed fractions contain both a whole number and a proper fraction, like, 8 1/10, 4 1/5, etc.

2. Which is Better Out of a Mixed Fraction and an Improper Fraction While Doing Calculations?

Ans. There is a myth that improper fractions are bad, but that is false. Improper fractions are better than mixed fractions when it comes to mathematics and doing some calculations or solving equations.

Improper fractions are preferred over mixed fractions for calculations because mixed fractions are confusing when written in the formulas. People often get confused about whether to add or multiply the two parts.

For example, while performing 1 + 2 1/4,

The answer gets confusing as:

Is it required to be 1 + 2 + ¼ = 3 1/4

Or it should be 1 + 2 x ¼ = 1 1/2

But, in the case of the improper fractions, the calculation is straightforward, as:

1 + 9/4 = 4/4 + 9/4 = 13/4

However, mixed fractions are more preferred for everyday usages, like 2 1/4 sausages, etc.