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## NCERT Solutions for class 8 maths chapter 1 rational numbers exercise 1.1

**NCERT Class 8 Maths Chapter 1 – Rational Numbers **is a very important chapter and it is good to get the right guidance so that you can perform well in your exams.

The **class 8th maths chapter 1 exercise 1.1 **is all about the basic introduction to rational numbers along with the different properties of these rational numbers.

A rational number is a category of real numbers which are written in the p/q form and q is not equal to 0. So, any of the fractions which have no zero denominators are called rational numbers.

### All Questions And Their Solutions For Class 8th Maths Chapter 1 Exercise 1.1

**Using appropriate properties find:**

**(i) -2/3 × 3/5 + 5/2 – 3/5 × 1/6**

**Solution:**

-2/3 × 3/5 + 5/2 – 3/5 × 1/6

=-2/3 × 3/5– 3/5 × 1/6+ 5/2 (by commutativity)

=3/5 (-2/3 – 1/6)+ 5/2

=3/5 ((- 4 – 1)/6)+ 5/2

=3/5 ((–5)/6)+ 5/2 (by distributivity)

=– 15 /30 + 5/2

=– 1 /2 + 5/2

=4/2

=2

**(ii) 2/5 × (- 3/7) – 1/6 × 3/2 + 1/14 × 2/5**

**Solution:**

2/5 × (- 3/7) – 1/6 × 3/2 + 1/14 × 2/5

=2/5 × (- 3/7) + 1/14 × 2/5 – (1/6 × 3/2) (by commutativity)

=2/5 × (- 3/7 + 1/14) – 3/12

=2/5 × ((- 6 + 1)/14) – 3/12

=2/5 × ((- 5)/14)) – 1/4

=(-10/70) – 1/4

=– 1/7 – 1/4

=(– 4– 7)/28

=– 11/28

**Write the additive inverse of each of the following:**

(i) 2/8 (ii) -5/9 (iii) -6/-5=6/5 (iv) 2/-9=-2/9 (v) 19/-16=-19/16

**Solution:**

(i) 2/8

Additive inverse of 2/8 is – 2/8

(ii) -5/9

Additive inverse of -5/9 is 5/9

(iii) -6/-5=6/5

Additive inverse of 6/5 is -6/5

(iv) 2/-9=-2/9

Additive inverse of -2/9 is 2/9

(v) 19/-16=-19/16

Additive inverse of -19/16 is 19/16

**Verify that: -(-x)=x for.**

(i) x=11/15

(ii) x=-13/17

**Here is Solution For=> (i) x=11/15**

We have, x=11/15

The additive inverse of x is – x (as x + (-x)=0)

Then, the additive inverse of 11/15 is – 11/15 (as 11/15 + (-11/15)=0)

The same equality 11/15 + (-11/15)=0, shows that the additive inverse of -11/15 is 11/15.

Or, – (-11/15)=11/15

i.e., -(-x)=x

**Here is Solution For=> (ii) -13/17**

We have, x=-13/17

The additive inverse of x is – x (as x + (-x)=0)

Then, the additive inverse of -13/17 is 13/17 (as 11/15 + (-11/15)=0)

The same equality (-13/17 + 13/17)=0, shows that the additive inverse of 13/17 is -13/17.

Or, – (13/17)=-13/17,

i.e., -(-x)=x

**Find the multiplicative inverse of the**

(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × (-3/7) (v) -1 × (-2/5) (vi) -1

**Solution For NCERT Class 8th Maths Chapter 1 Exercise 1.1 Question No. 4 :**

(i) -13

Multiplicative inverse of -13 is -1/13

(ii) -13/19

Multiplicative inverse of -13/19 is -19/13

(iii) 1/5

Multiplicative inverse of 1/5 is 5

(iv) -5/8 × (-3/7)=15/56

Multiplicative inverse of 15/56 is 56/15

(v) -1 × (-2/5)=2/5

Multiplicative inverse of 2/5 is 5/2

(vi) -1

Multiplicative inverse of -1 is -1

**Name the property under multiplication used in each of the following.**

(i) -4/5 × 1=1 × (-4/5)=-4/5

(ii) -13/17 × (-2/7)=-2/7 × (-13/17)

(iii) -19/29 × 29/-19=1

**Solution:**

(i) -4/5 × 1=1 × (-4/5)=-4/5

Here 1 is the multiplicative identity.

(ii) -13/17 × (-2/7)=-2/7 × (-13/17)

The property of commutativity is used in the equation

(iii) -19/29 × 29/-19=1

Multiplicative inverse is the property used in this equation.

**Multiply 6/13 by the reciprocal of -7/16**

**Solution:**

Reciprocal of -7/16=16/-7=-16/7

According to the question,

6/13 × (Reciprocal of -7/16)

6/13 × (-16/7)=-96/91

**Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3**

**Solution:**

1/3 × (6 × 4/3)=(1/3 × 6) × 4/3

Here, the way in which factors are grouped in a multiplication problem, supposedly, does not change the product. Hence, the Associativity Property is used here.

**Is 8/9 the multiplication inverse of**

? Why or why not?

**Solution:**

=-7/8

[Multiplicative inverse ⟹ product should be 1]

According to the question,

8/9 × (-7/8)=-7/9 ≠ 1

Therefore, 8/9 is not the multiplicative inverse of.

**If 0.3 the multiplicative inverse of**

? Why or why not?

**Solution:**

=10/3

0.3=3/10

[Multiplicative inverse ⟹ product should be 1]

According to the question,

3/10 × 10/3=1

Therefore, 0.3 is the multiplicative inverse of

**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 that does not have a reciprocal is 0. Reason:

0=0/1

Reciprocal of 0=1/0, which is not defined.

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

Reason:

1=1/1

Reciprocal of 1=1/1=1 Similarly, Reciprocal of -1=– 1

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

Reason:

Negative of 0=-0=0

**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 1/x, where x ≠ 0 is.

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

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

**Solutions**:

(i) Zero has no reciprocal.

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

(iii) The reciprocal of – 5 is -1/5.

(iv) Reciprocal of 1/x, 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.

## Exercise 1.1 Class 8 maths rational numbers examples

Some examples are 1/6, 4/7, 7/8 etc.

Even the number 0 is a rational number when represented in forms like 0/1, 0/3, etc but 2/0, 1/0, etc are not considered as rational numbers as they will give the infinite value.

While providing the **class 8 maths chapter 1 exercise 1.1, **our teachers followed all the guidelines and syllabus properly so that students can gain enough confidence to solve similar kinds of questions on their own.

The students who are looking to become experts in class 8 maths and want to become higher scorers should practice the **NCERT Solutions for Class 8 Maths **on a regular basis without missing any chapters.

The **maths class 8-chapter 1 exercise 1.1 **mainly deals in revising all the concepts of properties of rational numbers that students would have learned during the course of the chapter.

### Download Class 8 rational number chapter 1 exercise 1.1 ncert solutions

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