Class 8 Exam  >  Class 8 Notes  >  NCERT Solution (Ex 1.1) - Chapter 1: Rational Number, Maths, Class 8

NCERT Solution (Ex 1.1) - Chapter 1: Rational Number, Maths, Class 8 PDF Download

Exercise 1.1 (Rational Number)

Question 1:
Using appropriate properties find:

Answer:

(i)


 [Using associative property]


[Using associative property]

(II)


[Using associative property]

 
[Using distributive property]

Question 2:
Write the additive inverse of each of the following:
(i) 2/8
(ii) -5/9
(iii) -6/-5
(iv) 2/-9
(v) 19/-6

Answer 2:
We know that additive inverse of a rational number

 

(i) Additive inverse of 2/8 is -2/8
(ii) Additive inverse of -5/9 is 5/9
(iii) Additive inverse of  -6/-5 is -6/5
(iv) Additive inverse of 2/-9 is 2/9
(v) Additive inverse of19/-6  is 19/6

Question 3:
Verify that -(-x)= x for:
(i)x= 11/15
(ii)x= 13/17

Answer 3:
(i) Putting x= 11/15  in  -(-x) =x

Hence, verified.

(ii)

Hence, verified.

Question 4:
Find the multiplicative inverse of the following:

Answer 4:
We know that multiplicative inverse of a rational number 

 (i) Multiplicative inverse of  - 13 is -1/13

(ii) Multiplicative inverse of -13/19 is -19/13

(iii) Multiplicative inverse of 1/5 is 5

(iv) Multiplicative inverse of 

(v) Multiplicative inverse of

(vi) Multiplicative inverse of -1 is 1/-1

Question 5:
Name the property under multiplication used in each of the following:

Answer 5:
(i) 1 is the multiplicative identity.
(ii) Commutative property.
(iii) Multiplicative Inverse property.

Question 6:
Multiply 6/13 by the reciprocal of -7/
16
Answer 6:
The reciprocal of -7/16 is -16/7
According to the question,

Question 7:
Tell what property allows you to compute

Answer 7:
By using associative property of multiplication, a x (b x c) = (a x b) x c.

Question 8:
Is 8/9 the multiplicative inverse of  
 Why or why not?

 

Answer 8:
Since multiplicative inverse of a rational number a is

Therefore, 

But its product must be positive 1.
Therefore, 8/9 is not the multiplicative inverse of 

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

Answer 9:
Since multiplicative inverse of a rational number a is

Therefore, 

Therefore, Yes 0.3 is the multiplicative inverse of  

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.

Answer 10:
(i) 0
(ii) 1 and -1
(iii) 0

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FAQs on NCERT Solution (Ex 1.1) - Chapter 1: Rational Number, Maths, Class 8

1. What are rational numbers?
Ans. Rational numbers are numbers that can be represented in the form of p/q, where p and q are integers and q is not equal to 0. In other words, rational numbers are the numbers that can be expressed as the ratio of two integers.
2. How can we identify if a given number is a rational number or not?
Ans. To identify if a given number is a rational number or not, we need to check if it can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. If a number can be expressed in this form, then it is a rational number.
3. What is the difference between a rational number and an irrational number?
Ans. Rational numbers can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. Irrational numbers, on the other hand, cannot be expressed in this form. Irrational numbers cannot be expressed as a ratio of two integers and have an infinite number of non-repeating decimal places.
4. How do we perform addition and subtraction of rational numbers?
Ans. To perform addition and subtraction of rational numbers, we need to first find a common denominator. Once we have the common denominator, we can add or subtract the numerators and simplify the result. For example, to add 3/4 and 5/6, we first find the common denominator, which is 12. Then, we convert both fractions to have 12 as the denominator and add the numerators. The result is 19/12, which can be simplified to 1 7/12.
5. What are some real-life examples where we use rational numbers?
Ans. Rational numbers are used in everyday life in several ways. For example, when we divide a pizza among a group of people, we use fractions which are rational numbers. When we measure ingredients while cooking, we use rational numbers. When we calculate our grades or percentages, we use rational numbers. Rational numbers are also used in banking and finance, where we deal with interest rates, loans, and mortgages.
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