# Selina Concise Solutions for Chapter 2 Rational Numbers Class 7 ICSE Mathematics

## ### Exercise  2(A)

1. Write down a rational number whose numerator is the largest number of two digits and denominator is the smallest number of four digits.

Largest two digit = 99
Smallest number of four digit = 1000
Now,
numerator = 99 and denominator = 1000
∴ Rational number = 99/100

2. Write the numerator of each of the following rational numbers:

(i) -125/127

(ii) 37/-137

(iii) -85/93

(iv) 2

(v) 0

(i) -125/127
Numerator = -125

(ii) 37/-137
Numerator = 37

(iii) -85/93
Numerator = -85

(iv) 2 = 2/1
Numerator = 2

(v) 0 = 0/1
Numerator = 0

3. Write the denominator of each of the following rational numbers:

(i) 7/-15

(ii) -18/29

(iii) -3/4

(iv) - 7

(v) 0

(i) 7/-15
Denominator = -15

(ii) -18/29
Denominator =  29

(iii) -3/4
Denominator = 4

(iv) -7 = -7/1
Denominator = 1

(v) 0 = 0/1
Denominator = 1

4. Write down a rational number numerator (-5)×(-4) and denominator (28 – 27)×(8 – 5).

Numerator = (-5) × (-4) = 20
Denominator = (28 - 27) × (8 -5)
= 1 × 3 = 3
∴ Rational number = 20/5 = 4/1 = 4

5. (i) -15/1 in integer form is .....

(ii) 23/-1 in integer form is  .....

(iii) If 18 = 18/a then a = ......

(iv) If  -57 = 57/a then a = ......

(i) -15/1 in integer form is = -15

(ii) 23/-1 in integer form is = -23

(iii) If 18 = 18/a then a = 18/18 = 1

(iv) If  -57 = 57/a then a = 57/-57 = -1

6. Separate positive and negative rational numbers from the following :

-3/5, 3/-5, -3/-5, 3/5, 0, -13/-3, 15/-8, -15/8

Positive rational numbers are -3/-5 = 3/5 (as both are negative)
-13/-3 = 13/3  (as both are negative)
Negative rational numbers = -3/5, 3/-5, 15/-8 and -15/8
0 is neither positive nor negative integer.

7. Find three rational numbers equivalent to

(i) 3/5

(ii) 4/-7

(iii) -5/9

(iv) 8/-15

8. Which of the following are not rational numbers :

(i) -3

(ii) 0

(iii) 0/4

(iv) 8/0

(v) 0/0

(i) -3 = -3/1 is a rational number.

(ii) 0 = 0/1 is a rational number.

(iii) 0/4  is a rational number.

(iv) 8/0 is not a rational number .

(v) 0/0 is not a rational number as numerator and denominator both are zero.

9. Express each of the following integers as a rational number with denominator 7 :

(i) 5

(ii) -8

(iii) 0

(iv) -16

(v) 7

10. Express 3/5 as a rational number with denominator:

11. Express 4/7 as a rational number with numerator

12. Find x, such that:

(i) -2/3 = 6/x

(ii) 7/-4 = x/8

(iii) 3/7 = x/-35

(iv) -48/x = 6

(v) 36/x = 3

(vi) -27/x = 9

13. Express each of the following rational numbers to the lowest terms :
(i) 12/15
(ii) -120/144
(iii) -48/-72
(iv)14/-56

(i) -7/-8
(ii) 5/-12
(iii) -7/-20
(iv) 4/-9
We know that, a rational number is said to be in standard form, if its denominator is positive in lowest term.

### Exercise 2 (B)

1. Mark the following pairs of rational numbers on the separate number lines :
(i) 3/4 and -1/4
(ii) 2/5 and -3/5
(iii) 5/6 and -2/3
(iv) 2/5 and -4/5
(v) 1/4 and -5/4

2.  Compare :
(i) 3/5 and 5/7
(ii) -7/2 and 5/2
(vi) 3 and -1

3. Compare:
(i) -1/4 and 0
(ii) 1/4 and 0
(iii) -3/8 and 2/5
(iv) -5/8 and 7/-12
(v) 5/-9 and -5/-9
(vi) -7/8 and 5/-6
(vii)  2/7 and -3/-8
(viii) -5/8 and 7/-12
(i) -1/4 and 0
Since, -1/4 is a negative rational number and always less than 0.
∴ -1/4 < 0

(ii) 1/4 and 0
Since, 1/4 is a positive rational number and always greater than  0
∴ 1/4 > 0

(iii) -3/8 and 2/5
-3×5 and 2×8
[∵ a/b and c/d ⇒ a × d and b × c]

4. Arrange the given rational numbers in ascending order :
(i) 7/10 , -11/-30 and 5/-15
(ii) 4/-9, -5/12 and 2/-3

5. Arrange the given rational numbers in descending order :
(i) 5/8, 13/-16 and -7/12
(ii) 3/-10 , -13/30 and 8/-20

6. Fill in the blanks :
(i) 5/8 and 3/10 are on the  ...... side of zero.
(ii) -5/8 and 3/10 are on the ..... sides of zero.
(iii) -5/8 and -3/10 are on the ..... side of zero.
(iv) 5/8 and -3/10 are on the  .....  sides of zero.
(i) right
(ii) opposite
(iii) same/left
(iv) opposite

### Exercise 2 (C)

(i) 7/5 and 2/5
(ii) -4/9 and 2/9
(iii) 5/-12 and 1/12
(iv) 4/-15 and -7/-15
(v) -7/25 and 9/-25
(vi) -7/26 and 7/-26

(i) -2/5 and 3/7
(ii) -5/6 and 4/9
(iii) -3 and 2/3
(iv) -5/9 and 7/18
(v) -7/24 and -5/48
(vi) 1/-18 and 5/-27
(vii) -9/25 and 1/-75
(viii) 13/-16 and -11/24
(ix) -9/-16 and -11/8

3. Evaluate:
(i) -2/5 + 3/5 + -1/5
(ii) -8/9 + 4/9 + -2/9
(iii) 5/-24 + -1/8 + 3/16
(iv) -7/6 + 4/-15 + -4/-30
(v) -2 + 2/5 + -2/15
(vi) -11/12 + 5/16 + -3/8

4. Evaluate :
(i) -11/18 + -3/9 + 2/-3
(ii) -9/4 + 13/3 + 25/6
(iii) -5 + 5/-8 + -5/-12
(iv) -2/3 + 5/2 + 2
(v) 5 + -3/4 + -5/8

5. Subtract:
(i) 2/9 from 5/9
(ii) -6/11 from -3/-11
(iii) -2/15 from -8/15
(iv) 11/18 from -5/18
(v) -4/11 from  -2

6. Subtract:
(i) -3/10 from 1/5
(ii) -6/25 from -8/5
(iii) -7/4 from -2
(iv) -16/21 from 1
(v) -8/15 from 0
(vi) 0 from -3/8
(vii) -2 from -3/10
(viii) 5/8 from -5/16
(ix) 4 from -3/13

7. The sum of two rational numbers is 11/24. If one of them is 3/8, find the other.

8. The sum of two rational numbers is -7/11. If one of them is  13/24,  find the other.

9. The sum of two rational numbers is -4. If one of them is -13/12, find the other.
∵ Sum of two rational number = -4 and one of them = -13/12

10. What should be added to -3/6 to get -11/24 ?
Let the required rational number be x
Other number = -3/16
Sum of two number = 11/24
According to question,

11. What should be added to -3/5 to get 2 ?
Let the required rational number be x
Other number = -3/5
Sum of two number = 2
According to question,

12. What should be subtracted from -4/5 to get 1 ?
Let the required rational number = x
Other number = -4/5
Difference of two number = 1
According to question,

13. The sum of two numbers is -6/5. If one of them is -2, find the other.
∵ Sum of two rational number = -6/5  and one of them = -2

14.  What should be added to -7/12 to get 3/8 ?
Let the required rational number be = x  other number =  -7/12
Sum of two numbers = 3/8

15. What should be subtracted from 5/9 to get 9/5 ?
Let the first number be x  Other number  = 5/9
Difference of two number = 9/5
According to question,

### Exercise 2 (D)

1. Evaluate:
(i) 5/4 × 3/7
(ii) 2/3 × -6/7
(iii) (-12/5) × (10/-3)
(iv) -45/39 × -13/15
(vii) (-8/9) × (-3/16)
(viii) (5/-27) × (-9/20)

2. Multiply:

3. Evaluate :

6. Divide :
(i) 15/28 by 3/4
(ii) -20/9 by -5/9
(iii) 16/-5 by -8/7
(iv) -7 by -14/5
(v) -14 by 7/-2
(vi) -22/44 by 11/18
(vii) 35 by -7/9
(viii) 21/44 by -11/9

7. Evaluate :

8. The product of two numbers is  14. If one of the numbers is -8/7, find the other.
∵ Product of two numbers = 14  and one of these two numbers = -8/7

9. The cost of 11 pens is ₹ 11/3 . Find the cost of one pen.
The cost of  11 pens  = 11/3
The cost of one pen = 11/3 ÷11
= 11/3 × 1/11
= ₹ 1/3

10. If 6 identical articles can be bought for ₹ 40/17. Find the cost of each aticle.
Cost of 6 articles  = ₹ 40/17
Cost of each  article = 40/17 ÷6
= 40/17 × 1/6
= ₹ 20/51

11. By what number should -3/8 be multiplied so that the product is -9/16 ?

12. By what number should -5/7 be divided so -15 that the result is -15/28 ?

13. Evaluate
(32/15 + 8/5) ÷ (32/15 - 8/5).

14. Seven equal piece are made out of a rope 5 of 152/7 m. Find the length of each piece.
Length of 7 pieces of rope  = 152/7
Length of each piece = 152/7 ÷7

### Exercise 2 (E)

1. Evaluate :
(i) -2/3 + 3/4
(ii) 7/-27 + 11/18
(iii) -3/8 + -5/12
(iv) 9/-16 + -5/-12
(v) -5/9 + -7/12 + 11/8
(vi) 7/-26 + 16/39
(vii) -2/3 - (-5/7)
(viii) -5/7 - (-3/8)
(ix) 7/26 + 2 + -11/13
(x)  -1 + 2/-3 + 5/6

2. The sum of two rational numbers is -3/8. If one of them is 3/16, find the other,
Sum of two numbers = -3/8
One number = 3/16

3. The sun of two rational numbers is -5 . If one of them is -52/25 , find the other .
Sum of two numbers = -5
One number = -52/25

4. What rational number should be added to -3/16 to get 11/24
Sum of two number = 11/24
One number = -3/16

5.  what rational number  should be added to -3/5 to get 2 ?

6. What rational number should be subtracted from  -5/12 to get 5/24

7. What rational number should be subtracted from 5/8 to get 8/5 ?

8. Evaluate
(i) (7/8 × 24/21) + (-5/9 × 6/-25)
(ii) (8/15 × -25/16) + (-18/35 × 5/6)
(iii) (18/33 × -22/27) - (13/25 × -75/26)
(iv) (-13/7 × -35/39) - (-7/45 × 9/14)