Subtraction of Rational Numbers with Different Denominator

# Subtraction of Rational Numbers with Different Denominator

Learn about the Subtraction of Rational Numbers with Different Denominators from here. Get to know the detailed procedure to follow while solving Problems on Subtraction of Rational Numbers having Different Denominators. Check out a few examples explaining step by step and get a good hold of the concept and learn to solve problems on your own.

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## How do you Subtract Rational Numbers with Different Denominator?

Follow the guidelines listed below to Subtract Rational Numbers with Different Denominator. They are in the following fashion

Step 1: Check out whether the Denominator is Positive or not. If either of the Denominators is negative rearrange them so that denominators become positive.

Step 2: Obtain the Denominators of Rational Numbers in the earlier step.

Step 3: Determine the Least Common Multiple of the Denominators of the given Rational Numbers.

Step 4: Express the Rational Numbers in terms of a Common Denominator using the LCM Obtained.

Step 5: Write a Rational Number whose numerator is the difference of numerators of rational numbers obtained in the earlier step and denominator is the LCM obtained in the earlier steps.

Step 6: Rational Number obtained in step 5 is the required rational number. Simplify if it is required.

### Solved Examples on Subtracting Rational Numbers with Different Denominator

1. Subtract 9/5 from 5?

Solution:

Given Rational Numbers are 5/1 and 9/5

Since the denominators aren’t the same find the LCM of Denominators.

LCM(1, 5) = 5

Express the Rational Numbers given using the LCM Obtained.

5/1 = 5*5/1*5 = 25/5

9/5 = 9*1/5*1 = 9/5

Subtracting we get 25/5 -9/5

= 16/5

Therefore, 5-9/5 = 16/5

2. Find the Difference of 4/3 and 6/5?

Solution:

Find the LCM of the Denominators 3, 5

LCM(3, 5) = 15

Express the Rational Numbers with Common Denominator using the LCM obtained.

4/3 = 4*5/3*5 = 20/15

6/5 = 6*3/5*3 = 18/15

difference = 20/15 – 18/15

= 2/15

Therefore, Difference of 4/3 and 6/5 is 2/15.

3. Simplify 4/12-5/-6?

Solution:

Since one of the denominators isn’t positive change it to positive by rearranging it.

5/-6 =5*(-1)/-6*(-1)

= -5/6

Find the LCM of the Denominators 12, 6

LCM(12,6) = 12

Express the Rational Numbers in terms of a Common Denominator using the LCM obtained.

4/12 = 4*1/12*1 = 4/12

-5/6 = -5*2/-6*2 = -10/12

Subtracting the Rational Numbers Obtained we get

= 4/12-(-10/12)

= 14/12

= 7/6

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