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Which is greater in each of the following:
(i) 2/3, 5/2
(ii) −5/6, −4/3
(iii) −3/4, 2/(−3)
(iv) −1/4, 1/4
(v) − \(3{\Large\frac{2}{7}}\) , − \(3{\Large\frac{4}{5}}\)

Solution:

To solve this question we will take the L.C.M of the denominator of the rational numbers or convert them into like fractions.

After converting them into like fractions, arrangement can easily be done by comparing the numerators.

(i) 2/3, 5/2

L.C.M of 3 and 2 is 6

2/3 = (2 × 2)/(3 × 2) = 4/6

5/2 = (5 × 3)/(2 × 3) = 15/6

Since, 4/6 < 15/6

So, 2/3 < 5/2

(ii) −5/6 , −4/3

L.C.M of 6 and 3 is 6

- 5/6 = (−5 × 1)/(6 × 1) = −5/6

- 4/3 = (−4 × 2)/(3 × 2) = −8/6

Since,−5/6 > −8/6

So,−5/6 > −4/3

(iii) −3/4 , 2/−3

L.C.M of 4 and 3 is 12

−3/4 = (−3 × 3)/(4× 3) = −9/12

2/(−3) = (2 × 4)/(−3 × 4) = −8/12

Since, −9/12 < −8/12

So, −3/4 < 2/(−3)

(iv) −1/4 , 1/4

−1/4 < 1/4

(Negative number is always smaller than the positive number)

(v) − \(3{\Large\frac{2}{7}}\) , − \(3{\Large\frac{4}{5}}\)

− \(3{\Large\frac{2}{7}}\) = −23/7 and − \(3{\Large\frac{4}{5}}\) = −19/5

L.C.M of 7 and 5 is 35

−23/7 = (−23 × 5)/(7 × 5) = −115/35

−19/7 = (−19 × 7)/(7 × 5) = −133/35

Since, −115/35 > −133/35

So, − \(3{\Large\frac{2}{7}}\) > − \(3{\Large\frac{4}{5}}\)

☛ Check: NCERT Solutions for Class 7 Maths Chapter 9

Video Solution:

Which is greater in each of the following: (i) 2/3, 5/2 (ii) −5/6, −4/3 (iii) −3/4, 2/(−3) (iv) −1/4, 1/4 (v) − \(3{\Large\frac{2}{7}}\) , − \(3{\Large\frac{4}{5}}\)

Class 7 Maths NCERT Solutions Chapter 9 Exercise 9.1 Question 9

Summary:

In each of the following: (i) 2/3, 5/2 (ii) −5/6, −4/3 (iii) −3/4, 2/(−3) (iv) −1/4, 1/4 (v) − \(3{\Large\frac{2}{7}}\) , − \(3{\Large\frac{4}{5}}\) we see that, (i) 2/3 < 5/2 (ii) −5/6 > −4/3 (iii) −3/4 < 2/(−3) (iv) −1/4 < 1/4 (v) − \(3{\Large\frac{2}{7}}\) > − \(3{\Large\frac{4}{5}}\)

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