NCERT Exercise 9.1 Question 8

Rational Numbers 7th Math

NCERT Exercise 9.1 Question 8

In this section, we will learn to compare two rational numbers. In question number 8 of the NCERT Exercise 9.1, class seven, math, seven questions have been given. In each of the questions, there are two rational numbers with a blank box in the middle. The boxes given in the middle of the two rational numbers have to be filled with an appropriate sign out of > (greater than), < (less than), and = (equal to).

Solution of the NCERT Exercise 9.1 Question (8)

Question (8) Fill the boxes with the correct symbol out of >, <, and =

(i) – 5/7 ☐ 2/3

Solution :

Given rational numbers are – 5/7 ☐ 2/3

In the given rational numbers, one is a negative rational number and another is a positive rational number. We know that a negative number is smaller than the positive one.

Clearly, the negative rational number, – 5/7 is smaller than the positive rational number 2/3

Thus, the box in the middle will be filled with a less than (<) sign.

[Because negative numbers are always smaller than positive numbers.]

Thus, – 5/7 [<] 2/3 Answer

Question (8) (ii) – 4/5 ☐ – 5/7

Solution:

Given rational numbers are – 4/5 ☐ – 5/7

Here, both of the given rational numbers are negative.

As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater and the rational number having a smaller numerator is smaller.

Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.

Thus, to make the denominators of the given rational number equal, we need to find their LCM first.

The LCM of the denominators of given rational number = 5 × 7 = 35

Thus, now to make denominators of given rational numbers equal, i.e. = 35; we have to multiply their numerators and denominators with suitable numbers.

Thus, given rational numbers

= – 4 × 7/5 × 7 and – 5 × 5/7 × 5

= – 28/35 and – 25/35

Here, the numberator of the first rational number = – 28 and the numerator of the second rationl number = – 25

Since, – 28 is smaller than the – 25, thus, a less than (<) sign will be put in the box given in the middle of the rational numbers.

Thus, – 28/35 [ < ] – 25/35

Thus, the first rational number is smaller than the second rational number.

Thus, – 4/5 [ < ] – 5/7 Answer

Question (8) (iii) – 7/8 ☐ 14/ – 16

Solution :

Given rational numbers are – 7/8 ☐ 14/ – 16

= – 7/8 ☐ – 14/16

Here, both of the given rational numbers are negative.

As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater and the rational number having a smaller numerator is smaller.

Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.

Thus, to make the denominators of the given rational number equal, we need to find their LCM first.

The LCM of denominators 8 and 16 of given rational numbers = 16

Thus, now to make denominators of given rational numbers equal, i.e. = 16; we have to multiply their numerators and denominators with suitable numbers.

Thus, given rational numbers

= – 7 × 2/8 × 2 and – 14 × 1/ 16 × 1

= – 14/16 and – 14/16

After observing, it becomes clear that both of the rational numbers are equal.

= – 14/16 [ = ] – 14/16

Thus, both of the given rational numbers are equal, hence an equal (=) sign will be given in the box middle of them.

Thus, – 7/8 [=] 14/ – 16 Answer

Question (8) (iv) – 8/5 ☐ – 7/4

Solution:

Given rational numbers are – 8/5 and – 7/4

Here, both of the given rational numbers are negative.

As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater, and the rational number having a smaller numerator is smaller.

Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.

Thus, to make the denominators of the given rational number equal, we need to find their LCM first.

The LCM of denominators of given rational numbers = 5 × 4 = 20

Thus, now to make denominators of given rational numbers equal, i.e. = 20; we have to multiply their numerators and denominators with suitable numbers.

Thus, – 8/5 and – 7/4

= – 8 × 4/5 × 4 and – 7 × 5/4 × 5

= – 32/20 and – 35/20

Here, since, – 32 is greater than – 35, thus, a greater than (>) sign will be assigned in the box given in the middle.

Thus, clearly, – 32/20 [ > ] – 35/20

Thus, between the given rational numbers, the first is greater while second is smaller.

Thus, – 8/5 [ > ] – 7/4 Answer

Question (8) (v) 1/ – 3 ☐ – 1/4

Solution :

Given rational numbers are 1/ – 3 and – 1/4

= – 1/3 and – 1/4

Here, both of the given rational numbers are negative.

As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater, and the rational number having a smaller numerator is smaller.

Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.

Thus, to make the denominators of the given rational number equal, we need to find their LCM first.

The LCM of denominators of given rational numbers = 3 × 4 = 12

Thus, now to make denominators of given rational numbers equal, i.e. = 12; we have to multiply their numerators and denominators with suitable numbers.

Thus, – 1/3 and – 1/4

= – 1 × 4/3 × 4 and – 1 × 3/4 × 3

= – 4/12 and – 3/12

Here, – 4 is smaller than – 3, as when we put these numbers on a number line, the – 4 comes left to the – 3.

Thus, a less than (<) sign will be assigned in the middle box given between given two rational numbers

Thus, – 4/12 [ < ] – 3/12

Thus, clearly, the given first rational number is smaller than the second rational number.

Thus, 1/ – 3 [<] – 1/4 Answer

Question (8) (vi) 5/ – 11 ☐ – 5/11

Solution :

Given rational numbers are 5/ – 11 and – 5/11

= – 5/11 and – 5/11

By observing, it becomes clear that both of the given rational numbers are equal.

Thus, an equal to (=) sign will be assigned in the box given in the middle between given two rational numbers.

= – 5/11 [ = ] – 5/11

Thus, it is clear that, 5/ – 11 [=] – 5/11 Answer

(vii) 0 ☐ – 7/6

Solution :

Given rational numbers are 0 and – 7/6

= 0/1 and – 7/6

We know that negative numbers are smaller than zero 0, thus a greater than (>) sign will be assigned in the box given in the middle between given two rational numbers.

Thus, 0 [ > ] – 7/6 Answer

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