Improper Fraction

A fraction in which the numerator is greater than or equal to the denominator. 7/2 and 9/5, for example, are improper fractions. There are two parts to every fraction: the numerator and the denominator. Proper fractions and improper fractions are the two primary forms of fractions in mathematics depending on the numerator and denominator values.

They are always equal to or larger than 1 in terms of numbers. A mixed fraction, on the other hand, is a fraction represented as a combination of a natural number and a proper fraction. It’s a truncated version of an improper fraction. 314, 125are mixed fractions, for example. A mixed fraction is always bigger than 1 in terms of numbers. Any improper fraction can also be expressed as a mixed fraction.

In general, mixed fractions are easier to understand and compare in real life than improper fractions.We can simply convert any improper fraction to a mixed number or a mixed fraction to an improper fraction.

Converting Improper Fractions to Mixed Numbers

The denominator of an improper fraction’s mixed fraction form is always the same as the original fraction’s denominator. Because mixed numbers are the simplest form of improper fractions, it is critical to master this conversion. We must follow the methods outlined below to convert an incorrect fraction to a mixed number:

• Step 1- Divide the numerator with the denominator.

• Step 2: Calculate the quotient and remainder values.

• Step 3- To represent a fraction as a mixed number, arrange the values of the quotient, remainder, and divisor in the following order:

quotient=emainder/divisor 

Let’s look at an example of how to convert improper fractions to mixed numbers quickly and easily. Let’s assume you have a 13/4 as an improper fraction. The first step is to divide 13 by 4 to arrive at a solution. The quotient is 3 with a residual of 1. The numerator will be 1, the denominator will be 4, and the full number will be 3. As a result, we have a mixed fraction of 314.

Let’s take another example and solve it. We have an improper fraction here: 9/2. When we divide 9 by 2, we get 4 as the quotient, with 1 as the remainder. We’ll go through the same procedure once more. The numerator will be 1, the denominator will be 2, and the full number will be 4. As a result, we have a mixed fraction of 4.1/2

How Do You Solve Improper Fractions?

Solving improper fractions entails applying mathematical operations to them and simplifying the resultant number. In mathematics, there are four basic arithmetic operators: addition, subtraction, multiplication, and division. The only difference between calculating an improper fraction and solving any other appropriate fraction is that we must simplify the solution and put it in mixed numbers.

Let’s figure out how to solve the improper fraction 4/3 + 7/3.

Step 1: The denominator for both fractions is the same. As a result, we’ll just add the numerators 4 and 7 together. We get 11. As a result, when improper fractions are added together, we obtain 11/3.

Step 2: We may simplify the improper fraction by dividing 11 by 3 to produce 3 as a whole, 2 as a numerator, and 3 as a denominator.

3.2/3 is the correct answer.

Adding Mixed Numbers

To combine the mixed numbers, turn each one to an improper fraction first. After that, add the improper fractions together and express the solution in the simplest way.

Example :.3.2/5 + 4.1/5 = 17/5+21/5 =(17+21)/5 =38/5 =735.

Subtracting Mixed Numbers :

To remove the mixed numbers, rewrite each one as an improper fraction first. Subtract the incorrect fractions from the answer and express it in the simplest manner possible.

Example :

9.1/6   –  5.2/6= 5.5/6 – 3.2/6 =  23/6 = 3.5/6 .

Multiplying Mixed Numbers

Rewrite each mixed number as an improper fraction before multiplying them. After that, multiply the improper fractions and put the answer in the simplest form.

Example :

2.2/3 . 5.2/5 = 8/3 . 27/5 = 5.2/5

Dividing Mixed Numbers

Divide the mixed numbers by rewriting each one as an improper fraction first. Then multiply the first fraction by the multiplicative inverse of the second fraction to divide the improper fractions.

Example :

312 423 = 7/2143

The multiplicative inverse of 14/3 is 3/14.

7/2 . 3/14 =

21/28=

3/4 

Conclusion :

Improper fractions are actually easier to utilise in mathematics than mixed fractions. People, on the other hand, grasp mixed numbers better in everyday situations.So, it is important that you know how to convert from one form to the other.We must know how to do all the arithmetic operations  of improper fractions or mixed fractions.