NCERT Exercise 9.1 Question 2

Rational Numbers 7th Math

NCERT Exercise 9.1 Question 2

In this section, we will learn to find four more similar rational numbers as per the given patterns of rational numbers. In question (2) of NCERT Exercise 9.1, we have to find similar rational numbers in the given pattern of rational numbers.

Solution of Question number (2)(i) to question (2)(iv)

Question number(2) Write four more rational numbers in each of the following patterns:

(i) – 3/5 , – 6/10 , – 9/15 , – 12/20, . . . . .

Solution :

Given, rational numbers are – 3/5 , – 6/10, – 9/15, – 12/20, . . . . .

Thus, four more rational numbers of the given pattern = ?

It can be observed that, the numerator of next rational number is obtained by adding –3 and denominator of next rational number is obtained by adding 5

Thus, four more rational numbers of the given pattern are

– 12 – 3/20 + 5 = – 15/25

And, – 15 – 3/25 + 5 = – 18/30

And, – 18 – 3/30 + 5 = – 21/35

And, – 21 – 3/35 + 5 = – 24/40

Thus, four more rational numbers of the given pattern are

– 15/25 , – 18/30 , – 21/35 and – 24/40 Answer

(ii) – 1/4 , – 2/8 , – 3/12 , . . . .

Solution :

Given rational number are – 1/4 , – 2/8 , – 3/12, . . . .

Thus, four more rational numbers of given pattern = ?

It can be observed that, the numerator of the given rational numbers is obtained by adding –1 and denominator is obtained by adding 4

Thus four more rational numbers of the given pattern of rational numbers are

– 3 – 1/12 + 4 = – 4/16

And, – 4 – 1/16 + 4 = – 5/20

And, – 5 – 1/20 + 4 = – 6/24

And, – 6 – 1/24 + 4 = – 7/28

Thus, four more rational numbers of the given pattern are

– 4/16, – 5/20, – 6/24 and – 7/28 Answer

(iii) – 1/6 , 2/– 12 , 3/– 18 , 4/– 24, . . . . .

Solution :

Given rational numbers are – 1/6, 2/– 12, 3/– 18, 4/– 24, . . . . .

Thus, four more rational number of given pattern = ?

It is clear that, the second rational number is obtained by multiplying by 2 in numerator and denominator, and third rational number is obtained by multiplying 3 in the numerator and denominator, and fourth one is obtained by multiplying with 4 in numerator and denominator.

That means,

(1st) – 1/6,

(2nd) – 2/12 = – 1 × 2/6 × 2,

(3rd) – 3/18 = – 1 × 3/6 × 3,

And (4th) – 4/24 = – 1 × 4/6 × 4 and so on.

Thus, next four rational numbers of the given same pattern are

1 × 5/ – 6 × 5 = 5/ – 30

And, 1 × 6/ – 6 × 6 = 6/ – 36

And, 1 × 7/ – 6 × 7 = 7/ – 42

And, 1 × 8/ – 6 × 8 = 8/ – 48

Thus, four more rational numbers of the given pattern are

5/ – 30 , 6/ – 36 , 7/ – 42 and 8/ – 48 Answer

(iv) – 2/3 , 2/ – 3 , 4/ – 6 , 6/ – 9 . . . . . .

Solution :

The given rational numbers are – 2/3 , 2/ – 3 , 4/ – 6 , 6/ – 9 . . . . . .

Thus, 4 more rational numbers of the given pattern = ?

It can be observed that pattern of given rational numbers is

– 2/3 , 2/ – 3 , 2 × 2/ – 3 × 2 , 2 × 3/ – 3 × 3

Thus, four more rational numbers of given pattern are

2 × 4/ – 3 × 4 = 8/ – 12

And, 2 × 5/ – 3 × 5 = 10/ – 15

And, 2 × 6/ – 3 × 6 = 12/ – 18

And, 2 × 7/ – 3 × 7 = 14/ – 21

Thus, four rational numbers of the given patter are

8/ – 12 , 10/ – 15 , 12/ – 18 and 14/ – 21 Answer

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