This pizza has been cut into 4 equal parts. so each objet d’art of the pizza represents 1 out of 4 equal parts. So mathematically, we can represent each piece as $ \frac { 1 } { 4 } $. This number is called a fraction .

The number below the measure that represents the entire total of equal parts that the solid is divided into is called the denominator .

And the count on the top that represents the numeral of equal parts we are considering is called the numerator.

## What is an Improper Fraction?

Before discussing improper fraction, we first base need to understand proper fractions .

proper fractions : Fractions for which the numerator is less than the denominator are called proper fractions. For exemplar, if you order a pizza and cut it into 4 equal parts, and then eat one slice out of it, the remaining pizza can be expressed as $ \frac { 3 } { 4 } $ of the unharmed pizza. here, since 3 is less than 4, the fraction is a proper fraction .

improper fractions : Improper fractions are defined as fractions for which the numerator is greater than the denominator. Let us take an exercise of improper fraction, think you rate a pizza that has 4 slices. Your friends eat all 4 slices. And you realize you didn ’ t get any. You order another pizza. After eating 1 slice from it, you realize you are done eat. indeed, how much of the pizza did your friends and you have in all ?

Your friends beginning had all 4 slices of 1 pizza, and then you had 1 slice of the same size from the irregular pizza .

thus, the total pizza corrode is $ \frac { 5 } { 4 } $ slices of pizza. And that ’ s an improper divide with a numerator greater than the denominator .

interracial numbers : assorted numbers are equitable another room of writing fractions greater than a whole. A desegregate number has a whole contribution and a fractional separate, which is actually a proper divide .

Let ’ s take the lapp exercise from above. You and your friends ate one wholly pizza and one-fourth of a pizza. As a mix fraction, we can write this as $ 1 $ and $ \frac { 1 } { 4 } $ of a pizza or $ 1\frac { 1 } { 4 } $ of a pizza .

## Fraction Conversion

**Improper Fraction to Mixed Number**

An improper fraction can be converted to a desegregate fraction and a interracial fraction can be converted to an improper fraction .

Let ’ s say we want to convert the fraction $ \frac { 7 } { 2 } $ into a desegregate number .

mistreat 1 : Find the quotient and the remainder by dividing the numerator with the denominator .

pace 2 : The quotient will be the number of wholes for the mix phone number. The remainder will be the numerator of the fractional character and the denominator will remain the lapp .

so, the interracial number mannequin of $ \frac { 7 } { 2 } $ will be :

**Mixed Number to Improper Fraction**

Any mix count can be converted into an improper fraction .

Let ’ s say we want to convert the shuffle act $ 1\frac { 3 } { 4 } $ into an improper fraction .

measure 1 : Multiply the denominator with the unharmed. And then add the numerator to the product .

step 2 : Keep the denominator same and solve for the numerator .

therefore, the improper divide for the desegregate number $ 1\frac { 3 } { 4 } $ will be $ \frac { 7 } { 4 } $ .

## Solved Examples

**Example 1. ** **Identify the improper fractions:**

$ \frac { 1 } { 5 } $, $ 2\frac { 7 } { 5 } $, $ \frac { 3 } { 2 } $, $ \frac { 1 } { 3 } $, $ \frac { 5 } { 4 } $, $ 6 \frac { 1 } { 6 } $

**Solution: ** $ \frac { 2 } { 3 } $ and $ \frac { 5 } { 4 } $ are improper fractions as the measure of the numerator is greater than the value of the denominator for both of these fractions .

**Example 2. Write ** $ 4\frac { 2 } { 7 } $ **as an improper fraction.**

**Solution: ** Converting $ 4\frac { 2 } { 7 } $ into an improper fraction ,

$ 4 \frac { 2 } { 7 } $ = $ \frac { ( 7\times4 ) + 2 } { 7 } $ = $ \frac { 30 } { 7 } $

**Example 3. Write ** $ 2\frac { 9 } { 6 } $ **as an improper fraction.**

**Solution: ** While dividing 29 by 6, the quotient and end are 4 and 5 respectively.

so $ \frac { 29 } { 6 } $ written as a blend number is $ 4 \frac { 5 } { 6 } $ .

Converting $ 3\frac { 1 } { 5 } $ to an improper fraction :

## Practice Problems

## What are Improper Fractions? Meaning, Definition, Examples

Attend this quiz & Test your cognition.

1

### What type of fraction is $\frac{11}{4}$?

Mixed fraction Improper fraction Proper fraction unit fraction

Correct

Incorrect

Correct answer is: Improper fraction

Since the value of the numerator is greater than the denominator, the given fraction is an improper fraction.

2

### Write the mixed number $3\frac{1}{5}$ as an improper fraction.

$ \frac { 18 } { 5 } $ $ \frac { 16 } { 5 } $ $ \frac { 1 } { 15 } $ $ \frac { 14 } { 5 } $

Correct

Incorrect

Correct answer is: $\frac{16}{5}$

Converting $3\frac{1}{5}$ to an improper fraction:

$3\frac{1}{5}$ = $\frac{(5\times 3) + 1}{5}$ = $1\frac{6}{5}$

3

### Identify the improper fraction.

$ \frac { 2 } { 7 } $ $ \frac { 11 } { 22 } $ $ \frac { 14 } { 15 } $ $ \frac { 12 } { 11 } $

Correct

Incorrect

Correct answer is: $\frac{12}{11}$

The value of the numerator is greater than the value of the denominator in $\frac{12}{11}$. Therefore, it is an improper fraction.

4

### Convert $\frac{5}{2}$ into a mixed fraction.

$ 2\frac { 1 } { 2 } $ $ 1\frac { 1 } { 2 } $ $ 1\frac { 2 } { 4 } $ none of the above

Correct

Incorrect

Correct answer is: $2\frac{1}{2}$

Dividing 5 by 2, we get the quotient and the remainder as 2 and 1 respectively.

The quotient becomes the whole number, the remainder becomes the numerator of the fractional part and the denominator remains the same.

## Frequently Asked Questions

**Which are easier for calculations: improper fractions or mixed fractions?**

improper fractions are easy for arithmetic operations of addition, subtraction, generation, and division. desegregate fractions are easier to understand and represent in figures .

**Why are fractions important?**

Every quantity can not be expressed in hale numbers. Fractions are employed to indicate a certain depart or part of any detail. They are a fundamental concept in calculation and applied in algebra, ratios, and several other concepts in mathematics and early fields .

**How are decimals related to fractions?**

Fractions and decimals are both ways to represent quantities or numbers. Decimals are nothing but a different means to represent fractions whose denominator is 10 or powers of 10. For exemplar, the fraction $ \frac { 15 } { 10 } $ in decimal form is 1.5 .