Chapter 1: Rational Numbers

Solution:-

False.

Because, the reciprocal of -1 is -1 and reciprocal of 1 is 1.

Solution:-

False.

The reciprocal of-1 is -1.

Solution:-

False.

The correct form is for any rational number x, (x) × (-1) = – x.

Solution:-

False.

Because, for rational numbers x and y, if x < y then x – y is a negative rational number.

Example, let x = 2 and y = 3

Then,

= X – y

= 2 – 3

= -1

Solution:-

True.

For example,

Let x = – 1/3 and y = -2/3

Then,

= x + y

= (-1/3) + (-2/3)

= -1/3 – 2/3

= -3/3

= – 1

Solution:-

False.

Between any two rational numbers there are infinite rational numbers.

Solution:-

False.

Rational numbers are closed under addition, subtraction and multiplication.

Solution:-

False.

Subtraction of rational number is not commutative.

Let x and y are any two rational number,

Then, x – y ≠ y – x

Solution:-

False.

Express each of the given rational numbers with 4 as the common denominator.

Now,

-¾ = [(-3×1)/ (4×1)] = (-3/4)

-2/1 = [(-2×4)/ (1×4)] = (-8/4)

Then,

-3/4 > -8/4

Hence,

-¾ > -2

So, -¾ is greater than -2.

Solution:-

True.

Because, 0/1 is a rational number.