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

Fractions are frequently referred to as numbers between numbers. Fractions are numeral values that represent a separate or a fortune of a whole. For example, look at the pizza below .
Example of fraction in real life
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.

Numerator and Denominator

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 .
Example of proper fraction in real life
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 .
Example of improper fraction in real life
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 .
Example of mixed number in real life

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 .
Fraction Conversion
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 :
Improper fraction to mixed number
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 .
Converting mixed number to improper fraction
step 2 : Keep the denominator same and solve for the numerator .
Example of mixed number as improper fraction
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 .

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