Chapter 1: Rational Numbers

Solution:-

No, we cannot find a rational number whose multiplicative inverse is –1.

Solution:-

The five rational numbers between 0 and 1 are, 1/6, 2/6, 3/6, 4/6, 5/6.

Solution:-

1/5 and -1/5 are the rational number whose absolute value is 1/5.

Solution:-

From the question it is given that,

The length of rope = 40 m

The length of one piece of rope = 10/3

Let us assume the total number of pieces be y.

So,

(10/3) y = 40

y = (40 × 3)/10

y = 120/10

y = 12 pieces

∴The number of pieces cut from the rope are 12.

Solution:-

From the question it is given that,

The length of rope = 5½ m = 11/2 m

The total number of pieces = 12

Let us assume the length of one piece of rope be y.

So,

12y = 11/2 m

y = (11/2) × (1/12)

y = 11/24

∴The length of one piece of rope 11/24.

Solution:-

The LCM of the denominators 7, 8, 2 and 5 is 280

∴ 8/7 = [(8×40)/ (7×40)] = (320/280)

(-9/8) = [(-9×35)/ (8×35)] = (-315/280)

(-3/2) = [(-3×140)/ (2×140)] = (-420/280)

(2/5) = [(2×56)/ (56×56)] = (112/280)

Now, 320 > 112 > 0 > -315 > -420

Hence, ⇒ 8/7 > 2/5 > 0 > -9/8 > -3/2

Descending order 8/7, 2/5, 0, -9/8, -3/2

Solution:-

0 ÷ (2/3) = 0 × (3/2)

= 0/2

= 0

Solution:-

Given, a winter day the temperature at a place in Himachal Pradesh was –16°C.

Formula, (C/5) = (F – 32)/9

Where, C = -16^o

Then,

(-16^o/5) = (F – 32)/9

(-16^o/5) × 9 = F -32

(-144/5) = F – 32

F = 32 – (144/5)

F = (160 – 144)/5

F = 16/5

F = 3.2 ^oF

Solution:-

Additive inverse of 7 = – 7

Multiplicative inverse of 7 = 1/7

Then,

Sum of additive inverse and multiplicative inverse of 7 = -7 + (1/7)

= (-49 + 1)/7

= – 48/7

Solution:-

Additive inverse of -1/3 = 1/3

Multiplicative inverse of -1/3 = -3/1

Then,

The product of additive inverse and multiplicative inverse of 1/3 = 1/3 × (-3)

= -1