**Question 1. Subtract the first rational number from the second in each of the following**:

**(i) 3/8 and 5/8**

**Solution:**

= 5/8 – 3/8

As denominators are same

= (5 – 3) / 8

= 2/8

= 1/4

**(ii) -7/9 and 4/9**

**Solution:**

= 4/9 – (-7/9)

= 4/9 + 7/9

As denominators are same

= (4 + 7) / 9

= 11/9

**(iii) -2/11 and -9/11**

**Solution:**

= -9/11 – (-2/11)

= -9/11 + 2/11

As denominators are same

= (-9 + 2) / 11

= -7/11

**(iv)11/13 and -4/13**

**Solution:**

=-4/13-11/13

As denominators are same

=(-4-11) / 13

=(-15) / 13

**(v)1/4 and -3/8**

**Solution:**

=-3/8-1/4

LCM of 4 and 8 is 8

=(-3-1×2) / 8

=(-3-2) / 8

=(-5) / 8

=(-5) / 8

**(vi)-2/3 and 5/6**

**Solution:**

=5/6- (-2/3)

=5/6+2/3

LCM of 2 and 3 is 6

=(5+(2×2)) / 6

=(5+4) / 6

=9/6

=3/2

**(vii)-6/7 and -13/14**

**Solution:**

=-13/14- (-6/7)

=-13/14+6/7

LCM of 14 and 7 is 14

=(-13+6×2) / 14

=(-13+12) / 14

=-1/14

**(viii)-8/33 and -7/22**

**Solution:**

=-7/22- (-8/33)

=-7/22+8/33

LCM of 22 and 33

22=11×2

33=11×3

LCM is 66

=(-7×3+8×2) / 66

=(-21+16) / 66

=(-5) / 66

**Question 2.Evaluate each of the following:**

**(i) 2/3-3/5**

**Solution:**

LCM of 3 and 5 is 15

=(2×5-3×3) / 15

=(10-9) / 15

=1/15

**(ii) -4/7-2/-3**

**Solution:**

This can be written as

=-4/7- (-2)/3

=-4/7+2/3

LCM of 7 and 3 is 21

=(-4×3+2×7) / 21

=(-12+14) / 21

=2/21

**(iii) 4/7 – (-5/-7)**

**Solution:**

This can be written as

=4/7-(5)/7

As denominators are same

=(4-5) / 7

=(-1) / 7

**(iv) -2 – (5/9)**

**Solution:**

=-2/1-5/9

LCM of 1 and 9 is 9

=(-2×9-5×1) / 9

=(-18-5) / 9

=(-23) / 9

**(v) -3/-8 – (-2/7)**

**Solution:**

This can be written as

=3/8+2/7

LCM of 8 and 7 is 56

=(3×7+2×8) / 56

=(21+16) / 56

=37/16

**(vi) -4/13 – (-5/26)**

**Solution:**

This can be written as

=-4/13+5/26

LCM of 13 and 26 is 26

=(-4×2+5×1) / 26

=(-8+5) / 26

=(-3) / 26

**(vii)-5/14 – (-2/7)**

**Solution:**

This can be written as

=-5/14+2/7

LCM of 14 and 7 is 14

=(-5×1+2×2) / 14

=(-5+4) / 14

=(-1) / 14

**(viii)13/15 – 12/25**

**Solution:**

15=3×5

25=5×5

LCM is 5×5×3=75

=(13×5-12×3) / 75

=(65-36) / 75

=(29) / 75

**(ix) -6/13 – (-7/13)**

**Solution:**

This can be written as

=-6/13+7/13

As denominators are same

=(-6+7) / 13

=1/13

**(x) 7/24 – 19/36**

**Solution:**

24=2×2×2×3

36=2×2×3×3

LCM is 2×2×2×3×3 =72

=(7×3-19×2) / 72

=(21-38) / 72

=(-17) / 72

**(xi) 5/63 – (-8/21)**

**Solution:**

This can be written as

=5/63+8/21

LCM of 21 and 63 is 63

=(5×1+8×3) / 63

=(5+24) / 63

=29/63

**Question 3. Sum of two numbers is 5/9. If one of the numbers is 1/3,** **find the other.**

**Solution:**

Let the other number be x

1/3+x=5/9 (As sum is 5/9)

x=5/9-1/3 (On transposing 1/3)

LCM of 3 and 9 is 9

x=(5×1-1×3) / 9

x=(5-3) / 9

x=2/9

Therefore, other number is 2/9

**Question 4. The sum of two numbers is -1/3. If one of the numbers is -12/3,find the other.**

**Solution:**

Let the other number be x

-12/3+x=-1/3 (As -1/3 is the sum)

x=-1/3+12/3(Transposing -12/3)

x=(-1+12) / 3

x=11/3

Therefore, the other number is 11/3

**Question 5. The sum of the two numbers is -4/3. If one of the numbers is -5, find the other.**

**Solution:**

Sum of two numbers = -4/3

One of the number = -5/1

-5+x=-4/3

x=-4/3+5/1 (Transposing -5)

LCM of 3 and 1 is 3

x= (-4×1+5×3) / 3

= (-4 + 15)/3

= 11/3

The other number is 11/3

**Question 6. The sum of the two rational numbers is -8. If one of the numbers is -15/7, find the other.**

**Solution:**

Sum of two rational numbers = -8/1

One of the number = -15/7

Let the other rational number as x

x + -15/7 = -8

7 is the LCM

(7x -15) / 7 = -8

Transposing 7 to the right side

7x -15 = -8×7

7x — 15 = -56

7x = -56+15

x = -41/7

Other number is -41/7

**Question 7. What should be added to -7/8 to get 5/9?**

**Solution:**

Let the number to be added be x

-7/8+x=5/9

x=5/9+7/8 (Transposing -7/8)

LCM of 9 and 8 is 72

x=(5×8+7×9) / 72

x=(40+63) / 72

x=103/72

Therefore, 103/72 should be added

**Question 8. What number should be added to -5/11 to get 26/33?**

**Solution:**

Let the number to be added be x

-5/11+x=26/33

x=26/33+5/11 (Transposing 5/11)

LCM of 33 and 11 is 33

x=(26×1+5×3) / 33

x=(26+15) / 33

x=41/33

Therefore, 41/33 should be added

**Question 9. What number must be added to -5/7 to get -2/3?**

**Solution:**

Let the number be x

-5/7+x=-2/3

x=-2/3+5/7 (Transposing -5/7)

LCM of 3 and 7 is 21

x=(-2×7+5×3) / 21

x=(-14+15) / 21

x=1/21

Therefore, 1/21 should be added

**Question 10. What number should be subtracted from -5/3 to get 5/6?**

**Solution:**

Let the number be x

-5/3 – x = 5/6

-x = 5/6 + 5/3 (Transposing 5/3)

LCM of 3 and 6 is 6

-x = (5 × 1 + 5 × 2) / 6

-x=(5+10) / 6

-x=15/6

x=-15/6

x=-5/2

Therefore, -5/2 should be subtracted.