# Properties of Subtraction of Rational Numbers

We will learn how to use the properties of subtraction of rational numbers to find the difference of two 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)

How to use the properties to solve the subtraction of two rational numbers?

Solved examples using the properties of subtraction of rational numbers:

1. Find the additive inverse of:

(i) 2/3

(ii) -17/9

(iii) 6/-19

(iv) -5/-13

Solution:

(i) Additive inverse of 2/3 is -2/3

(ii) Additive inverse of -17/9 is 17/9.

(iii) In standard form, we write 6/-19 as 6/19.

Hence, its additive inverse is 6/19.

(iv) We may write, -5/-13 = (-5) × (-1)/(-13) × (-1) = 5/13

Hence, its additive inverse is -5/13

2. Subtract 5/7 from 4/5

Solution:

Subtract 5/7 from 4/5

= (4/5 – 5/7)

= 4/5 + (additive inverse of 5/7)

= (4/5 + -5/7)

= {28 + (-25)}/35

= 3/35

3. Subtract -3/5 from -3/4

Solution:

Subtract -3/5 from -3/4

= {-3/4 - (-3/5)}

= -3/4 + (additive inverse of -3/5)

= {-3/4 + 3/5)}, [since, additive inverse of -3/5 is 3/5]

= (-15 + 12)/20

= -3/20

4. The sum of two rational numbers is -7. If one of them is -11/3, find the other.

Solution:

Let the other number be x. Then,

x + -11/3 = -7

⇒ x = -7 + (additive inverse of -11/3)

⇒ x = (-7 + 11/3), [since, additive inverse of -11/3 is 11/3]

⇒ x = (-7/1 + 11/3)

⇒ x = (-21 + 11)/3

⇒ x = -10/3

Hence, the required number is -10/3.

5. What number should be added to -5/6 to get 13/15?

Solution:

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

-5/6 + x = 13/15

⇒ x = 13/15 + (additive inverse of -5/6)

⇒ x = (13/15 + 5/6), [since, additive inverse of -5/6 is 5/6]

⇒ x = (26 + 25)/30

⇒ x = 51/30

⇒ x = 17/10

Hence, the required number is 17/10.

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers