TOPICS

Exercise - 1.2

Rational Numbers

**Question-1 :-** Represent these numbers on the number line.

(i) 7/4, (ii) -5/6.

(i) 7/4 on the number line. Divide line between two natural number in 4 parts. Thus, the rational number 7/4 lies at a distance of 7 points from 0 towards positive number line. (ii) -5/6 on the number line. Divide line between two natural number in 6 parts. Thus, the rational number -5/6 lies at a distance of 5 points from 0 towards negative number line.

**Question-2 :-** Represent -2/11, -5/11, -9/11 on the number line.

-2/11, -5/11, -9/11 on the number line. Divide line between two natural number in 11 parts. Thus, the rational number -2/11, -5/11, -9/11 lie at a distance of 2, 5, 9 points from 0 towards negative number line respectively.

**Question-3 :-** Write five rational numbers which are smaller than 2.

2 can be written as 10/5. Thus, 5 natural numbers smaller than 2 are: 9/5, 8/5, 7/5, 6/5 and 5/5.

**Question-4 :-** Find ten rational numbers between -2/5 and 1/2.

-2/5 and 1/2 Here, L.C.M. of 5 and 2 is 10. Since, -2/5 x 2/2 = -4/10 and 1/2 x 5/5 = 5/10. Again, -4/10 x 2/2 = -8/20 and 5/10 x 2/2 = 10/20. Rational numbers are -7/20, -6/20, -5/20,.........9/20. Now, we can take any ten rational numbers in between -2/5 and 1/2.

**Question-5 :-** Find five rational numbers between.

(i) 2/3 and 4/5

(ii) -3/2 and 5/3

(iii) 1/4 and 1/2

(i) 2/3 and 4/5 Here, L.C.M. of 3 and 5 is 15. Since, 2/3 x 5/5 = 10/15 and 4/5 x 3/3 = 12/15. Again, 10/15 x 4/4 = 40/60 and 12/15 x 4/4 = 48/60. Rational numbers are 41/60, 42/60, 43/60, 44/60, 45/60, 46/60, 47/60. Now, we can take any five rational numbers in between 2/3 and 4/5. (ii) -3/2 and 5/3 Here, L.C.M. of 2 and 3 is 6. Since, -3/2 x 3/3 = -9/6 and 5/3 x 2/2 = 10/6. Rational numbers are -8/6, -7/6, -6/6,.........10/6. Now, we can take any five rational numbers in between -3/2 and 5/3. (iii) 1/4 and 1/2 Here, L.C.M. of 4 and 2 is 4. Since, 1/4 x 1/1 = 1/4 and 1/2 x 2/2 = 2/4. Again, 1/4 x 6/6 = 6/24 and 2/4 x 6/6 = 12/24. Rational numbers are 7/24, 8/24, 9/24, 10/24, 11/24. Now, five rational numbers in between 1/4 and 1/2 are 7/24, 8/24, 9/24, 10/24, 11/24.

**Question-6 :-** Write five rational numbers greater than -2.

-2 can be written as -16/8. Five rational numbers greater than -2 are: -15/8, -14/8, -13/8, -12/8 and -11/8

**Question-7 :-** Find ten rational numbers between 3/5 and 3/4.

3/5 and 3/4 Here, L.C.M. of 5 and 4 is 20. Since, 3/5 x 4/4 = 12/20 and 3/4 x 5/5 = 15/20. Again, 12/20 x 4/4 = 48/80 and 15/20 x 4/4 = 60/80. Rational numbers are 47/80, 48/80, 49/80,.......60/80 Now, we can take any ten rational numbers in between 3/5 and 3/4.

CLASSES