Question

please answer me urgently please urgent answer me ​

Answer 1

Answer:

Step-by-step explanation:

Question 1.

Additive inverse of any number x is the number which when added to x results in 0.

For $2/-9$

It can be written as -2/9

Assuming y be the additive inverse of it. So, by definition:

-2/9 + y = 0

y = 2/9 (Answer)

Question 2.

Verify -(-a) = a

Here, a = -19/21

L.H.S would be -[-(-19/21)] = -[19/21] = -19/21

This is equal to R.H.S

Hence proved.

Question 3

The numbers 1 and -1 are their own reciprocals

Question 4

Rational numbers are not closed under Division.

This is because of the possibility of division by zero. Zero is a rational number and division by zero is undefined.

Question 5

To find out rational numbers between 0 and 1, the basic way is to add/subtract a fraction the value of which is between 0 and 1.

Let that fraction be 1/4

so, first rational number will be 0+1/4 = 1/4

Second rational number will be 1-1/4 = 3/4

Question 6

There are infinite number of rational numbers between two numbers.

Question 7

Reciprocal of -2

Reciprocal of any number is calculated by dividing 1 with that number.

So, here reciprocal of -2 will be 1/(-2) which is equal to -1/2

Question 8

Simplify $\frac{7}{6} *\frac{-3}{28}$

Dividing the 6 in denominator with 3 in numerator. And, dividing 28 in denominator with 7 in numerator.

$\frac{1}{2} *\frac{-1}{4}$

Multiplying numerator and denominators respectively.

$\frac{1}{2} *\frac{-1}{4} =\frac{-1}{8}$

Question 9

The denominator of a rational number cannot be Zero.

This is because division by zero is undefined.

Question 10

Zero is the additive identity of a rational number. This is because adding it to them does not change the result.

a+0 = 0+a = a

Question 11

Commutative property states that

a+b = b+a

Two rational numbers can be added in any order.