Chapter 8: Rational Numbers

Solution:-

(7/-8) [<] (8/9)

Negative rational number is less than positive rational number.

Solution:-

(3/7) [>] (-5/6)

Negative rational number is less than positive rational number.

Solution:-

(5/6) [<] (8/4)

The LCM of 6 and 4 is 12

∴ (5/6) = [(5 × 2)/ (6 × 2)] = (10/12)

and (8/4) = [(8 × 3)/(4 × 3)] = (24/12)

Now, 10 < 24

⇒ (10/12) < (24/12)

Hence, (5/6) < (8/4)

Solution:-

(-9/7) [<] (4/-7)

Let us write (4/-7) with a positive denominator.

= (4/-7)

= [(4 × (-1))/ (-7 × -1)]

= (-4/7)

So, (-9/7) < (-4/7)

Solution:-

(8/8) [=] (2/2)

(8/8) divide both denominator and numerator by 8

Then, 1/1 = 1

(2/2) divide both denominator and numerator by 2

Then, 1/1 = 1

Therefore, 1 = 1

Solution:-

The reciprocal of 0 does not exist.

Solution:-

The reciprocal of 1 is 1.

Reciprocal of 1 = (1/1) = 1

Solution:-

(-3/7) ÷ (-7/3) = 9/49.

(-3/7) ÷ (-7/3)

= (-3/7) × (3/-7)

= (-3 × 3)/ (7 × -7)

= -9/-49

Solution:-

0 ÷ (-5/6) = 0.

We know that, division of zero by any number is zero.

Solution:-

0 × (-5/6) = 0.

We know that, multiplication of zero by any number is zero.