# How to Convert a Whole Number to an Improper Fraction?

• Last Updated : 25 Apr, 2022

Numbers are mathematical figures or values that may be used for counting, measuring, and doing other arithmetic operations. Integers, whole numbers, natural numbers, rational and irrational numbers, and so on are examples of numbers. The number system is a standardized method of expressing numbers in many formats, including figures and language. It contains many sorts of numbers such as prime numbers, odd numbers, even numbers, rational numbers, whole numbers, and so on. These numbers can be represented in several ways depending on the number system used.

The number system includes several sorts of numbers, such as prime numbers, odd numbers, even numbers, rational numbers, whole numbers, and so on. These figures and words can be used to express these numbers. For example, integers like 50 and 35 stated as figures can alternatively be written as fifty and thirty-five.

### Whole numbers

The subset of numbers that includes zero and all positive integers is known as whole numbers. The overall number goes from 0 to infinity. These numbers are used in everyday computations, mostly to measure fundamental quantities. Natural numbers are made up of solely whole numbers, including zero. The numbers 0, 1, 2, 3, 4, 5,… denote the subset. The subset excludes fractions, decimals, and negative integers.

Positive integers, also known as counting numbers, are parts of whole numbers that contain zero, such as 0,1, 2, 3, 4, 5, and so on while excluding negative integers, fractions, and decimals. 10, 11, 22, 100, 1000, and so on are examples of whole numbers.

Improper Fraction

An improper fraction is a type of fraction in which the numerator exceeds or equals the denominator. Every fraction is made up of two parts: the numerator and the denominator. Proper fractions and improper fractions are the two primary types of fractions in mathematics depending on the values of the numerator and denominator. For example, 7/2 and 9/5, are improper fractions.

### How to Convert a Whole Number to an Improper Fraction?

To change a whole number into an improper fraction, the following steps are required,

• Step 1: Reduce the whole number to a proper fraction. A numerator is a whole number while the denominator is 1. For instance, if the whole number is 5, the fraction’s numerator is 5 and the denominator is 1. As a result, 5/1.
• Step 2: Now Choose any fraction that is equal to 1. When the number of numerator and denominator of a fraction are the same then the fraction is equal to 1. 4/4, 6/6, and 7/7 are a few examples.
• Step 3: At last Multiply the whole number by the fractional which is equivalent to 1. Take the improper fraction from Step 1 above. Multiply it by any fraction that equals one. This has no effect on the original improper fraction’s value. For example Multiply 5/1 by 5/5, (numerator times numerator, and denominator times denominator). 5/1 divided by 5/5 equals 25/5.

As a result, after simplifying the improper fraction, we will receive the same whole number, which is 5.

### Sample Questions

Question 1:  Identify improper fractions out of the following: 11/5, 6, 2/9, 6/3, 3/5.

Solution:

An improper fraction is a type of fraction in which the numerator exceeds or equals the denominator. Every fraction is made up of two parts: the numerator and the denominator.

from the above given fractions, 11/5, 6, and 6/3 are improper fractions. As, in 11/5, 11 > 5, 6 can be written as 6/1 where 6 > 1, and 6/3 can be simplified as 2/1 where 2 > 1.

Question 2: How to change the whole number 8 into an improper fraction?

Solution:

Here 8 is a whole number,

• Step 1: Reduce the whole number to a improper fraction. we can write it as 8/1
• Step 2: Now Choose any fraction that is equal to 1. When the number of numerator and denominator of a fraction are the same then the fraction is equal to 1. So here fraction is 8/8 as this is equal to 1 .
• Step 3: Atlast Multiply the whole number by the fractional which is equivalent of 1. Take the improper fraction from Step 1 above. Multiply it by any fraction that equals one. This has no effect on the original improper fraction’s value.

Therefore here whole number 8 , which we can write as 8/1 will be multiply by fraction which is equivalent to 1 i.e 8/8

= 8/1 × 8/8

= 64/8 ,its an improper fraction.

Question 3: How to convert 3/5 into a whole number?

Here 3/5 is not a improper fraction as numerator is less than denominator .The only fractions that can be converted into whole numbers are those with numerators that are the same as their denominators or that are an exact multiple of their denominators. Therefore 3/5 cannot be converted into whole numbers.

Question 4: How to change the whole number 10 into an improper fraction?

Solution:

Here 10 is a whole number,

• Step 1: Reduce the whole number to a improper fraction. we can write it as 10/1.
• Step 2: Now Choose any fraction that is equal to 1. When the number of numerator and denominator of a fraction are the same then the fraction is equal to 1. So here fraction is 10/10 as this is equal to 1.
• Step 3: Atlast Multiply the whole number by the fractional which is equivalent of 1. Take the improper fraction from Step 1 above. Multiply it by any fraction that equals one. This has no effect on the original improper fraction’s value. Therefore here whole number 10 , which we can write as 10/1 will be multiply by fraction which is equivalent to 1 i.e 10/10.

= 10/1 × 10/10

= 100/10 ,its an improper fraction.

Question 5: Simplify improper fractions 8/6 + 10/6 and find out the result is a whole number or not?

Solution:

Given: 8/6 + 10/6

Here with the same denominator is 6.

= 8/6 + 10/6

= (8 + 10)/6

= 18/6

Here 18/6 is an improper fraction after further simplifying,

= 18/6 = 3

Hence 3 is a whole number.

Question 6: Change the whole number 6 into an improper fraction.

Solution:

Here 6 is a whole number,

• Step 1: Reduce the whole number to an improper fraction. we can write it as 6/1.
• Step 2: Now Choose any fraction that is equal to 1. When the number of numerator and denominator of a fraction are the same then the fraction is equal to 1. So here fraction is 6/6 as this is equal to 1.
• Step 3: At last Multiply the whole number by the fractional which is equivalent to 1. Take the improper fraction from Step 1 above. Multiply it by any fraction that equals one. This has no effect on the original improper fraction’s value.

Therefore here whole number 6, which we can write as 6/1 will be multiplied by a fraction that is equivalent to 1 i.e 6/6

= 6/1 × 6/6

=  36/6, it’s an improper fraction, if simplified further it does not change the original value.

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