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Wednesday, November 18, 2020

NCERT Class VIII Mathematics Chapter 1 Rational Numbers

CHAPTER 1: RATIONAL NUMBERS


Rational number: A number ‘r’ is called a rational number, if it can be written in the form ofwhere p and q are integers and q≠0.


EXERCISE 1.1


1. Using appropriate properties find.


(i)

Solution:

[Using commutative property]

[Using distributive property]


(ii)

Solution:

            [Using commutative property]

[Using distributive property]


2. Write the additive inverse of each of the following.

(i) (ii) (iii)

(iv) (v)

Answer:

(i) Additive inverse of is

(ii) Additive inverse of is

(iii) Additive inverse of is

(iv) Additive inverse of is

(v) Additive inverse of is


3. Verify that – (– x) = x for.


(i) x =

Solution:

We have, x =x =

= 0 and 

= 0

⸫The additive inverse of is  

=

– (– x) = x.


(ii) x =

Solution:

We have, x =x =

= 0 and 

= 0

⸫The additive inverse of is  

– (– x) = x.


4. Find the multiplicative inverse of the following.

(i) – 13 (ii) (iii) (iv) (v) (vi) – 1 

Answer:

(i) Multiplicative inverse of –13 is

(ii) Multiplicative inverse of is

(iii) Multiplicative inverse of is 5

(iv) Multiplicative inverse ofis

 (v) Multiplicative inverse ofis

(vi) Multiplicative inverse of –1 is –1

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

(i)

Answer: 1 is the multiplicative identity.


(ii)

Answer: Commutative property.

 

(iii)

Answer: Multiplicative Inverse property.


6. Multiply by the reciprocal of .

Solution:

The reciprocal ofis.

Now,


7. Tell what property allows you to compute as

Solution:

By using associative property of multiplication, a× (b×c) = (a×b) ×c


8. Is the multiplicative inverse of ? Why or why not?

Solution:

is not the multiplicative inverse of .


9. Is 0.3 the multiplicative inverse of? Why or why not?

Solution:

⸫0.3 is the multiplicative inverse of .


10. Write.


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

Answer: 0


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

Answer: 1 and –1


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

Answer: 0


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, where x ≠ 0 is ________.

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

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

Answer:

(i) No (ii) 1, –1

(iii) (iv) x

(v) Rational Number (vi) Positive


EXERCISE 1.2


1. Represent these numbers on the number line. 

(i)

Solution:

Here, P is

(ii)

Solution:

Here, M is

2. Represent , , on the number line.

Solution:

Here, B = , C = and D =

3. Write five rational numbers which are smaller than 2.

Answer: 1,, 0.

4. Find ten rational numbers betweenand.

Solution:

Now, 

–8< –7<–6<–5<–4< –3<–2<–1<0<1<2<10

The required numbers are

5. Find five rational numbers between.

(i) and

Solution:

Now,

60<61<62<63<64<65<72

The required numbers are

(ii) and

Solution:

Now,

–9<–8<–7<–6<–5<–4<10

The required numbers are 

and

(iii) and

6. Write five rational numbers greater than    –2.

Answer

Five rational numbers greater than –2 = –1, 0,, 1,

7. Find ten rational numbers between and .

Solution:

Now,

48<49<50<51<52<53<54<55<56<57<58<60

The required numbers are




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