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How to subtract a fraction from a whole number?

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  • Last Updated : 01 Jun, 2022

A fraction is a numerical figure that represents a part of a whole.. A fraction is made up of two parts: the numerator and the denominator. Here the fraction is divided into two parts the upper part of the fraction represents the numerator, while the denominator is the lower part of the fraction. For example, 5/8 is a fraction. In this case, the numerator is 5, and the denominator is 8. Natural numbers are a set of counting numbers starting with 1. On the other hand, natural numbers with zero (0) form a set known as whole numbers. Zero, on the other hand, is an undefined identity that represents a null set or no result at all. Whole numbers are basically numbers that do not contain any fractions, decimals, or even negative integers. Whole numbers are the set of positive numbers and zeroes. Alternatively, whole numbers are a set of non-negative integers. The set of whole numbers in mathematics is given as {0, 1, 2, 3, 4, 5, …} which is denoted by the symbol W.

W = {0, 1, 2, 3, 4, 5, 6, 7 …}

How to subtract a fraction from a whole number? 

Solution: 

To subtract a fraction from whole number. We have to follow some steps,

  • Step 1: Make the denominator 1 to convert the whole number to a fraction.
  • Step 2: Compare the denominators and take lcm to make them like fractions.
  • Step 3: In last subtract the numerators of fraction 

Example: Let’s learn how to subtract x – y/z,

Solution: 

Follow the above steps,

Step 1: Make the denominator 1 and convert the whole number to a fraction. Therefore here above, convert x into fraction; we can write it as x /1 in fraction.

Step 2: Compare the denominators and take lcm to make them like fractions. Now its x/1 – y/z, we will take the lcm of denominators  z and 1, the lcm is z so that the fractions will be = (xz – y) /z

Step 3: In the last subtract the numerators of the fraction, so the fraction will be,

= (xz – y)/z

Sample Questions

Question 1: Subtract 5 whole number from 3/4?

Solution: 

Follow the above steps,

Step 1: Make the denominator 1 to convert the whole number to a fraction. Therefore here above whole number is 5, we can write it as 5/1 in fraction.

Step 2: Compare the denominators and take lcm to make them like fractions. Now its 3/4 – 5/1, we will take lcm of denominators 4 and 1, the lcm is 4, so the fractions will be = (3 – 20) /4

Step 3: In last subtract the numerators of fraction

Now = (3 – 20) /4

= -17/4

Question 2: Subtract 3/2 from 8?

Solution: 

We can write whole number 8 as 8/1 in a fraction, and another number we have 3/2, now subtract 3/2 from 8/1.

= 8/1 – 3/2 

By taking lcm of 1 and 2, we have 2,

= {(8 × 2) – (3 × 1)}/2

= (16 – 3)/2

= 13/2 

Question 3: Subtract 25 from 10/8?

Solution: 

We can write whole number 25 as 25/1 in a fraction, and another number we have 10/8, now subtract 25 from 10/8.

= 25/1 – 10/8

By taking lcm of 1 and 8, we have 8,

= {(25 × 8) – (10 × 1)}/8

= (200 – 10)/8

= 190/8 

= 95/4

Question 4: Subtract 1/5 from 4?

Solution: 

We can write whole number 4 as 4/1 in a fraction, and another number we have 1/5, now subtract 1/5 from 4/1.

= 4/1 – 1/5 

By taking lcm of 5 and 1, we have 5,

= {(4 × 5) – (1 × 5)}/5

= (20 – 5)/5

= 15/5

= 3

Question 5: Subtract 100 from 10/8?

Solution: 

We can write whole number 100 as 100/1 in a fraction, and another number we have 10/8, now subtract 100 from 10/8.

= 10/8 – 100/1

By taking lcm of 8 and 1, we have 8,

= {(10 × 1) – (100 × 8)}/8

= (10 – 800)/8

= -790/8

= -395/4

Question 6: Subtract 5/3 from 55?

Solution:  

We can write whole number 55 as 55/1 in a fraction, and another number we have 5/3, now subtract 5/3 from 55/1.

= 55/1 – 5/3

By taking lcm of 1 and 3, we have 3,

= {(55 × 3) – (1 × 3)}/3

= (165 – 3)/3

= 162/3

= 54

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