# CLASS-7ZERO PROPERTIES OF SUBTRACTION OF RATIONAL NUMBER

ZERO PROPERTIES OF SUBTRACTION OF RATIONAL NUMBER -

Only the right identity exists for subtraction. The properties of zero in the context of the subtraction of rational numbers can be summarized as follows:

Properties of Zero in Subtraction of Rational Numbers -

1. Subtracting Zero:-

Subtracting zero from any rational number does not change the value of that number. For any rational number (a − 0) = a

2. Zero Minus a Number:-

Subtracting a rational number from zero gives the additive inverse (negative) of that number. For any rational number (0 − a) = −a

3. Number Minus Itself:-

Subtracting any rational number from itself always results in zero. For any rational number a(a − a) = 0

Illustrations and Examples:-

A)  Subtracting Zero:-         (a − 0) = a

5

1.  If, a = ---------- then

6

5                       5

a − 0 = ---------- − 0 =  -----------

6                       6

3

2.   If, a− ----------, then

4

3                          3

So,   a − 0 = − ---------- − 0 =  − ----------

4                          4

B) Zero minus a number:-

(0 − a) = −a

4

1.  If,    a = ----------, then

5

4                    4

0 − a = 0 − ---------- =  − ----------

5                    5

3

2.  If,   a− ---------, then

7

3                3

0 − a = 0 − (− ---------) = ----------

7                7

C) Number minus itself :-                (a − a) = 0

4

1.  If a = ----------, then

7

4                 4

a − a ---------- − ----------- = 0

7                 7

5

2.  If a− -----------, then

9

5                     5

a − a− ----------- − (− ----------)

9                      9

5                 5

=  − ----------- + ----------- =  0

9                9

Summary:-

These properties are fundamental when working with rational numbers and subtraction. They illustrate how zero interacts with other rational numbers under subtraction, maintaining consistency with the broader properties of arithmetic operations. Understanding these properties can help simplify and solve various mathematical problems involving rational numbers.