Chapter 1 Rational Numbers

**NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1**

**Question 1.**

**Using appropriate properties find:**

**(i) **−25×35+52−35×16

**(ii) **25×(−37)−16×32+114×25

**Solution.**

**Question 2.**

Write the additive inverse of each of the following:

**Solution.**

**(i)** 28

Additive inverse of 28 is 28

**(ii)** −59

−6−5=65

Additive inverse of −6−5 is −65

**(iii) **−6−5

−6−5=65

Additive inverse of −6−5 is −65

**(iv)** 2−9

Additive inverse of 2−9 is 29

**(v)** 19−6

Additive inverse of 19−6 is 196

**Question 3.**

Verify that – (-x) = x for :

**(i)** x=1115

**(ii)** x=−1317

**Solution.**

**Question 4.**

Find the multiplicative inverse of the following:

**Solution.**

**Question 5.**

Name the property under multiplication used in each of the following:

**(i) **−45×(1)=1×−45=−45

**(ii) **−1317×−27=−27×−1317

**(iii) **−1929×29−19=1

**Solution.**

**(i)** 1 is the multiplicative identity

**(ii)** Commutativity of multiplication

**(iii)** Multiplicative inverse.

**Question 6.**

Multiply 613 by the reciprocal of −716

**Solution.**

Reciprocal of −716 is −167

Now,

613×−167=6×(−16)13×7=−9691

**Question 7.**

Tell what property allows you to compute : 13×(6×43) as (13×6)×43

**Solution.**

Associativity.

**Question 8.**

Is the 89 multiplicative inverse of −118 ? Why or why not?

**Solution.**

−118=−98

Now, 89×−98=−1≠1

So, No ; 89 is not the multiplicative inverse of −118(=−98) because the product of 89 and -13(-) and −118(=−98) is not 1.

**Question 9.**

Is 0.3 the multiplicative inverse of 313 ? Why or why not?

**Solution.**

Yes ; 0.3 is the multiplicative inverse of 103 because

310×103=3×1010×3=3030=1

**Question 10.**

Write :

**(i)** The rational number that does not have a reciprocal.

**(ii)** The rational numbers that are equal to their reciprocals.

**(iii)** The rational number that is equal to its negative.

**Solution.**

**(i)** The rational number ‘0′ does not have a reciprocal.

**(ii)** The rational numbers 1 and (-1) are equal to their own reciprocals.

**(iii)** The rational number 0 is equal to its negative.

**Question 11.**

**Fill in the blanks :**

**(i)** Zero has**……….**reciprocal.

**(ii)** The numbers**……….**and**………**are their own reciprocals.

**(iii)** The reciprocal of – 5 is.**………….**

**(iv)** Reciprocal of 1x, where x≠0

**(v)** The product of two rational numbers is always a.**………**

**(vi)** The reciprocal of a positive rational number is**……….**

**Solution.**

**(i)** Zero has no reciprocal.

**(ii)** The numbers 1 and -1 are their own reciprocals.

**(iii)** The reciprocal of – 5 is −15

**(iv)** Reciprocal of 1x, where x≠0 is x.

**(v)** The product of two rational numbers is always a rational number.

**(vi)** The reciprocal of a positive rational number is positive.

**NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2**

**Question 1.**

Represent these numbers on the number line.

**(i) **74

**(ii) **−56

**Solution.**

**(i)** 74

We make 7 markings of distance 14 each on the right of 0 and starting from 0. The seventh marking represents 74

**(ii)** −56

We make 5 markings of distance 16 each on the right of 0 and starting from 0. The seventh marking represents −56

**Question 2.**

Represent −211,−511,−911 on the number line.

**Solution.**

We make 9 markings of distance 111 each on the left of 0 and starting from 0.

The second marking represents −211 the fifth marking represents −511 and the ninth marking represents −911

**Question 3.**

Write five rational numbers which are smaller than 2.

**Solution.**

Five rational numbers which are smaller than 2 are 1, 12,0, -1, −12

**Question 4.**

Find ten rational numbers between −25 and 12

**Solution.**

**Question 5.**

Find five rational numbers between:

**Solution.**

**Question 6.**

Write five rational numbers greater than -2.

**Solution.**

Five rational numbers greater than -2 are:

−32, -1, −12, 0, 12

There can be many more such rational numbers

**Question 7.**

Find ten rational numbers between 35 and 34

**Solution.**