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Subtract Fractions with Unlike Denominators

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  • Last Updated : 18 Jan, 2022

Numbers in the form of ‘m/n’ are called fractions, here n cannot be zero for the fraction to be a valid fraction. In the given fraction ‘m/n’, the variable ‘m’ is called Numerator and ‘n’ is called Denominator. Fractions are further classified on the basis of magnitude comparison of Numerator and Denominator. Cases where Numerator is smaller than Denominator i.e (m<n), such Fractions are called Proper Fractions and Cases where Numerator is greater than Denominator i.e (m>n ), such Fractions are called Improper Fractions.

Mathematical Operations like Addition and Subtraction are also performed on the Fractional forms of Numbers.

To subtract fractions with different Denominators. Follow the below steps:

Step 1: Make the denominator of both the fractions the same. For this, we will have to find the L.C.M of given numbers in the denominator.

Step 2: Multiply the numerator and denominator by the factor, which will help attain the same denominator for the given fractions.

Step 3: After attaining the same denominator, perform the required subtraction calculation as required.

Example: Consider two numbers 1/3 and 4/5. Subtract a smaller fraction from the larger one.

Solution:

Given two fractions: 1/3 and 4/5.

To perform Subtraction or even to compare the two numbers, we will need to have a common denominator for both of them.

Given First Fractional Number: 1/3

Given Second Fractional Number: 4/5

Numbers in Denominator: 3 for the first number and 5 for the second number.

We will find LCM of the numbers 3 and 5

The LCM of 3 and 5 is 15.

So, to attain 15 as the denominator, the multiplying factor for numerator and denominator for the first fractional number will be 5. Similarly, the multiplying factor for numerator and denominator for the second fractional number will be 3

First Fractional Number: (1×5)/(3×5)

= 5/15

Second Fractional Number: (4×3)/(5×3)

= 12/15

Now since the denominator is same, we will compare the numerators. Clearly, 12/15 is greater than 5/15. So, we will subtract 5/15 from 12/15.

Second Fractional Number > First Fractional Number

Second Fractional Number – First Fractional Number

(12/15) – (5/15)

= 7/15

Similar Questions

Question 1. Subtract 1/3 from 1/2.

Answer:

Numbers in Denominator: 3 for the first number and 2 for the second number.

We will find LCM of the numbers 3 & 2

The LCM of 3 & 2 is 6.

So, to attain 6 as the denominator, the multiplying factor for the numerator and denominator for the first fractional number will be 2. Similarly, the multiplying factor for the numerator and denominator for the second fractional number will be 3

First Fractional Number: (1*2)/(3*2)

= 2/6

Second Fractional Number: (1*3)/(2*3)

= 3/6

So, (1*3)/(2*3) – (1*2/3*2)

= (3/6) – (2/6)

= 1/6

Question 2. Subtract 1/4 from 1/3.

Answer: 

Numbers in Denominator: 4 for the first number and 3 for the second number.

We will find LCM of the numbers 4 & 3

The LCM of 4 & 3 is 12.

So, to attain 12 as the denominator, the multiplying factor for the numerator and the denominator for the first fractional number will be 3. Similarly, the multiplying factor for the numerator and denominator for the second fractional number will be 4

First Fractional Number: (1*3)/(4*3)

= 3/12

Second Fractional Number: (1*4)/(3*4)

= 4/12

So, [(1*4)/(3*4) – (1*3)/(4*3)]

= (4/12) – (3/12) 

= 1/12

Question 3. Subtract 1/4 from 1/2.

Answer: 

Numbers in Denominator: 4 for the first number and 2 for the second number.

We will find LCM of the numbers 4 & 2

The LCM of 4 & 2 is 4.

So, to attain 4 as the denominator, the multiplying factor for the numerator and the denominator for the first fractional number will be 1. Similarly, the multiplying factor for the numerator and denominator for the second fractional number will be 2

First Fractional Number: (1*1)/(4*1)

= 1/4

Second Fractional Number: (1*2)/(2*2)

= 2/4

So, [(1*2)/(2*2) – (1*1)/(4*1)]

= (2/4) – (1/4)

= 1/4

Question 4. Subtract 1/5 from 1/2.

Answer: 

Numbers in Denominator: 5 for the first number and 2 for the second number.

We will find LCM of the numbers 5 & 2

The LCM of 5 & 2 is 10.

So, to attain 10 as the denominator, the multiplying factor for the numerator and the denominator for the first fractional number will be 2. Similarly, the multiplying factor for the numerator and denominator for the second fractional number will be 5

First Fractional Number: (1*2)/(5*2)

= 2/10

Second Fractional Number: (1*5)/(2*5)

= 5/10

So,

= (5/10) – (2/10)

= 3/10

Question 5. Subtract 1/5 from 1/4.

Answer: 

Numbers in Denominator: 5 for the first number and 4 for the second number.

We will find LCM of the numbers 5 & 4

The LCM of 5 & 4 is 20.

So, to attain 20 as the denominator, the multiplying factor for the numerator and denominator for the first fractional number will be 4. Similarly, the multiplying factor for the numerator and denominator for the second fractional number will be 5

First Fractional Number: (1*4)/(5*4)

= 4/20

Second Fractional Number: (1*5)/(4*5)

= 5/20

So,

= (5/20) – (4/20)

= 1/20

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