Ads Blocker Image Powered by Code Help Pro

Ads Blocker Detected!!!

We have detected that you are using extensions to block ads. Please support us by disabling these ads blocker.

Mathematics – Class 7 – Chapter 9 – Rational Numbers – Exercise 9.2 – NCERT Exercise Solution

1. Find the sum:

(i) (5/4) + (-11/4)

Solution:

= (5/4) – (11/4)

= [(5 – 11)/4]

= (-6/4)

Dividing both numerator and denominator by 3

= -3/2

(ii) (5/3) + (3/5)

Solution:

First, we have to find the LCM of the denominators of the given rational numbers.

LCM of 3 and 5 = 15

Now, for common denominator:

(5/3) = [(5×5)/ (3×5)] = (25/15)

(3/5) = [(3×3)/ (5×3)] = (9/15)

Then,

= (25/15) + (9/15)

= (25 + 9)/15

= 34/15

(iii) (-9/10) + (22/15)

Solution:

First, we find the LCM of the denominators of the given rational numbers.

LCM of 10 and 15 = 30

Now, for common denominator:

(-9/10) = [(-9×3)/ (10×3)] = (-27/30)

(22/15) = [(22×2)/ (15×2)] = (44/30)

Then,

= (-27/30) + (44/30)

= (-27 + 44)/30

= (17/30)

(iv) (-3/-11) + (5/9)

Solution:

First, we have to find the LCM of the denominators of the given rational numbers.

LCM of 11 and 9 = 99

Now, for common denominator:

(3/11) = [(3×9)/ (11×9)] = (27/99)

(5/9) = [(5×11)/ (9×11)] = (55/99)

Then,

= (27/99) + (55/99)

= (27 + 55)/99

= (82/99)

(v) (-8/19) + (-2/57)

Solution:

First, we have to find the LCM of the denominators of the given rational numbers.

LCM of 19 and 57 = 57

Now, for common denominator:

(-8/19) = [(-8×3)/ (19×3)] = (-24/57)

(-2/57) = [(-2×1)/ (57×1)] = (-2/57)

Then,

= (-24/57) – (2/57)

= (-24 – 2)/57

= (-26/57)

(vi) -2/3 + 0

Solution:

We know that if we add any number or fraction to zero then the answer will be the same number or fraction.

Hence,

= -2/3 + 0

= -2/3

Mathematics - Class 7 - Chapter 9 - Rational Numbers - Exercise 9.2 - NCERT Exercise Solution

We have, -7/3 + 23/5

We have to find the LCM of the denominators of the given rational numbers.

LCM of 3 and 5 = 15

Now, for making common denominator:

(-7/3) = [(-7×5)/ (3×5)] = (-35/15)

(23/5) = [(23×3)/ (15×3)] = (69/15)

Then,

= (-35/15) + (69/15)

= (-35 + 69)/15

= (34/15)

2. Find

(i) 7/24 – 17/36

Solution:

First, we have to find the LCM of the denominators of the given rational numbers.

LCM of 24 and 36 = 72

Now, for express into common denominator

(7/24) = [(7×3)/ (24×3)] = (21/72)

(17/36) = [(17×2)/ (36×2)] = (34/72)

Then,

= (21/72) – (34/72)

= (21 – 34)/72

= (-13/72)

(ii) 5/63 – (-6/21)

Solution:

We can also write -6/21 = -2/7

Now, we have

5/63 – (-2/7)

 5/63 + 2/7

We have to find the LCM of the denominators of the given rational numbers.

LCM of 63 and 7 = 63

Now, express into common denominator

(5/63) = [(5×1)/ (63×1)] = (5/63)

(2/7) = [(2×9)/ (7×9)] = (18/63)

Then,

= (5/63) + (18/63)

= (5 + 18)/63

= 23/63

(iii) -6/13 – (-7/15)

Solution:

According to the question,

LCM of 13 and 15 = 195

Now,

(-6/13) = [(-6×15)/ (13×15)] = (-90/195)

(7/15) = [(7×13)/ (15×13)] = (91/195)

Then,

= (-90/195) + (91/195)

= (-90 + 91)/195

= (1/195)

(iv) -3/8 – 7/11

Solution:

According to the question,

LCM of 8 and 11 = 88

Now,

(-3/8) = [(-3×11)/ (8×11)] = (-33/88)

(7/11) = [(7×8)/ (11×8)] = (56/88)

Then,

= (-33/88) – (56/88)

= (-33 – 56)/88

= (-89/88)

Mathematics - Class 7 - Chapter 9 - Rational Numbers - Exercise 9.2 - NCERT Exercise Solution

We have, -19/9 – 6

We have to find the LCM of the denominators of the given rational numbers.

LCM of 9 and 1 = 9

Now,

(-19/9) = [(-19×1)/ (9×1)] = (-19/9)

(6/1) = [(6×9)/ (1×9)] = (54/9)

Then,

= (-19/9) – (54/9)

= (-19 – 54)/9

= (-73/9)

3. Find the product:

(i) (9/2) × (-7/4)

Solution:

We have, (9/2) × (-7/4)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (9×-7)/ (2×4)

= -63/8

(ii) (3/10) × (-9)

Solution:

The above question can be written as (3/10) × (-9/1)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (3×-9)/ (10×1)

= -27/10

(iii) (-6/5) × (9/11)

Solution:

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (-6×9)/ (5×11)

= -54/55

(iv) (3/7) × (-2/5)

Solution:

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (3×-2)/ (7×5)

= -6/35

(v) (3/11) × (2/5)

Solution:

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (3×2)/ (11×5)

= 6/55

(vi) (3/-5) × (-5/3)

Solution:

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (3×-5)/ (-5×3)

On simplifying,

= (-15)/ (-15)

= 1

4. Find the value of:

(i) (-4) ÷ (2/3)

Solution:

Reciprocal of (2/3) is (3/2)

Now,

= (-4/1) × (3/2)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (-4×3) / (1×2)

= (-2×3) / (1×1)

= -6

(ii) (-3/5) ÷ 2

Solution:

Reciprocal of (2/1) is (1/2)

Now,

= (-3/5) × (1/2)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (-3×1) / (5×2)

= -3/10

(iii) (-4/5) ÷ (-3)

Solution:

Reciprocal of (-3) is (1/-3)

Now,

= (-4/5) × (1/-3)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (-4× (1)) / (5× (-3))

= -4/-15

= 4/15

(iv) (-1/8) ÷ 3/4

Solution:

Reciprocal of (3/4) is (4/3)

Now,

= (-1/8) × (4/3)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (-1×4) / (8×3)

= (-1×1) / (2×3)

= -1/6

(v) (-2/13) ÷ 1/7

Solution:

Reciprocal of (1/7) is (7/1)

Now,

= (-2/13) × (7/1)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (-2×7) / (13×1)

= -14/13

(vi) (-7/12) ÷ (-2/13)

Solution:

Reciprocal of (-2/13) is (13/-2)

Now,

= (-7/12) × (13/-2)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (-7× 13) / (12× (-2))

= -91/-24

= 91/24

(vii) (3/13) ÷ (-4/65)

Solution:

Reciprocal of (-4/65) is (65/-4)

Now,

= (3/13) × (65/-4)

Multiplying numerator by the numerator and denominator by the denominator of both rational numbers.

= (3×65) / (13× (-4))

= 195/-52

= -15/4

👍👍👍

Leave a Comment

error: