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
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)
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
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