Subtraction of Rational Numbers

In subtraction of rational numbers a/b and c/d, we define:

(a/b - c/d) = a/b + (-c/d) = a/b + (additive inverse of c/d)



Examples on subtraction of rational numbers are explained here step-by-step;


1. Find the additive inverse of:

(i) 5/9

(ii) -15/8

(iii) 9/-11

(iv) -6/-7


Solution:

(i) Additive inverse of 5/9 is -5/9

(ii) Additive inverse of -15/8 is 15/8.

(iii) In standard form, we write 9/-11 as -9/11

Hence, its additive inverse is 9/11

(iv) We may write, - = -6/-7 = (-6) × (-1)/(-7) × (-1) = 6/7

Hence, its additive inverse is -6/7



2. (i) Subtract 3/4 from 2/3

(ii) Subtract -5/7 from -2/5


Solution:

(i) Subtract 3/4 from 2/3

(2/3 – 3/4) = 2/3 + (additive inverse of 3/4)= (2/3 + -3/4)

= {8 + (-9)}/12

= -1/12


(ii) Subtract -5/7 from -2/5{2/5 - (-5/7)} = -2/5 + (additive inverse of -5/7)

= {-2/5 + 5/7)} (since, additive inverse of -5/7 is 5/7)

= (-14 + 25)/35

= 11/35



3. The sum of two rational numbers is -5. If one of them is -13/6, find the other.

Solution:

Let the other number be x. Then,

x + -13/6 = -5

⇒ x = -5 + (additive inverse of -13/6)

⇒ x = (-5 + 13/6) = (-5/1 + 13/6) = (-30 + 13)/6

⇒ x = -17/6

Hence, the required number is -17/6

4. What number should be added to -7/8 to get 4/9?

Solution:

Let the required number to be added be x. Then,

-7/8 + x = 4/9

⇒ x = 4/9 + (additive inverse of – 7/8)

⇒ x = (4/9 + 7/8) = (32 + 63)/72 = 95/72

Hence, the required number is 95/72

5. Evaluate 3/5 + 7/3 + -11/5 + -2/3

Solution:

Using the commutative and associative law, it follows that we may arrange the terms in any manner suitably. Using this rearrangement property, we have:

3/5 + 7/3 + -11/5 + -2/3

= (3/5 + -11/5) + (7/3 + -2/5)

= {(3 + (-11)}/5 + {7 + (-2)}/3

= -8/5 + 5/3

= (-24 + 25)/15

= 1/15

6. Simplify: (4/7 + -8/9 + -5/21 + 1/3)

Solution:

Using the rearrangement property, we have:

4/7 + -8/9 + -5/21 + 1/3 = (4/7 + -5/21) + (-8/9 + 1/3)

= {12 + (-5)}/21 + {-8 + 3}/9

= (7/21 + -5/9)

= {21 + (-35)}/63

= -14/63

= -2/9

7. What should be subtracted from -5/7 to get -1?

Solution:

Let the required number be x. Then,

-5/7 – x = -1

⇒ -5/7 = x - 1

⇒ x = (-5/7 + 1)

= (-5 + 7)/7

= 2/7

Hence, the required number is 2/7.

These are the basic examples on subtraction of rational numbers discussed above.



Rational Numbers

What is Rational Numbers?

Representation of Rational Numbers on the Number Line

Addition of Rational Numbers

Subtraction of Rational Numbers

Multiplication of Rational Numbers

Division of Rational Numbers

To Find Rational Numbers

Worksheet on Rational Numbers

Worksheet on Representation of Rational Number on a
   Number Line

Worksheet on Addition and Subtraction of Rational
   Number

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers

8th Grade Math Practice

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