Solution of NCERT Exercise 9.1 Question 6

Rational Numbers 7th Math

Solution of NCERT Exercise 9.1 Question 6

In this section, we will learn to find the same or equivalent rational numbers in the given pairs of rational numbers. Question 6 of NCERT Exercise 9.1 has a total of seven similar questions in which pairs having the same or equivalent rational numbers are to be identified.

Question (6) Which of the following pairs represent the same rational number?

(i) – 7/21 and 3/9

Solution :

Given, – 7/21 and 3/9

= – 7 × 1/7 × 3 and 3 × 1/3 × 3

= – 1/3 and 1/3

But, – 1/3 ≠ 1/3

Since, in this pair, one rational number is negative and another is positive thus, this is not a pair of the same or equivalent rational numbers.

Thus, Answer = No

Question (6) (ii) – 16/20 and 20/– 25

This question is to identify whether this pair of rational numbers have the same (equivalent) rational numbers or not.

Solution :

Given rational numbers are – 16/20 and 20/ – 25

= – 4 × 4/4 × 5 and 4 × 5/ – 5 × 5

= – 4/5 and 4/– 5

= – 4/5 and – 4/5

Clearly, given pair have the same or equivalent rational numbers. Thus, Answer = Yes.

Question (6) (iii) – 2/– 3 and 2/3

This question is to identify whether this pair of rational numbers have the same (equivalent) rational numbers or not.

Solution :

Given rational numbers are – 2/– 3 and 2/3

= 2/3 and 2/3

Clearly, given pair have the same or equivalent rational numbers. Thus, Answer = Yes.

Question (6) (iv) – 3/5 and – 12/20

This question is to identify whether the given pair of rational numbers have the same (equivalent) rational numbers or not.

Solution :

Given rational numbers are – 3/5 and – 12/20

= – 3/5 and – 3 × 4/5 × 4

= – 3/5 and – 3/5

Clearly, given pair have the same or equivalent rational numbers. Thus, Answer = Yes.

Question (6) (v) 8/ – 5 and – 24/15

This question is to identify whether the given pair of rational numbers have the same (equivalent) rational numbers or not.

Solution :

Given rational numbers are 8/– 5 and – 24/15

= 8/ – 5 and – 8 × 3/5 × 3

= 8/ – 5 and – 8/5

= – 8/5 and – 8/5

Clearly, given pair have the same or equivalent rational numbers. Thus, Answer = Yes.

Question (6) (vi) 1/3 and – 1/9

This question is to identify whether the given pair of rational numbers have the same (equivalent) rational numbers or not.

Solution :

Given rational numbers are 1/3 and – 1/9

Clearly, the given pair of rational numbers do not have the same or equivalent rational numbers. Thus, Answer = No.

Question (6) (vii) – 5/ – 9 and 5/– 9

This question is to identify whether the given pair of rational numbers have the same (equivalent) rational numbers or not.

Solution:

Given rational numbers are – 5/ – 9 and 5/ – 9

= 5/9 and – 5/9

Clearly, the given pair of rational numbers do not have the same or equivalent rational numbers. Thus, Answer = No.

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