Qstnid -A-3- Evaluate : (I) 3/7 + (-4/9) + (-11/7) + 7/9 (Ii) 2/3 + -4/5 + 1/3 + 2/5 (Iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (Iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (I) 3/7 + (-4/9) + (-11/7) + 7/9 (Ii) 2/3 + -4/5 + 1/3 + 2/5 (Iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (Iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (Ii) 2/3 + -4/5 + 1/3 + 2/5 (Iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (Iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (I) 3/7 + (-4/9) + (-11/7) + 7/9 (Ii) 2/3 + -4/5 + 1/3 + 2/5 (Iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (Iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (Ii) 2/3 + -4/5 + 1/3 + 2/5 (Iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (Iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 - 01: Rational Numbers Class 8 Maths

Home Learn Fast select Course

Show Unit/Chapter Change Unit Change Subject Last Menu

ICSE-VIII-Mathematics

01: Rational Numbers Class 8 Maths

with Solutions -

Qstn# A-3 Prvs-Qstn Next-Qstn

#3
Evaluate : (i) 3/7 + (-4/9) + (-11/7) + 7/9 (ii) 2/3 + -4/5 + 1/3 + 2/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (i) 3/7 + (-4/9) + (-11/7) + 7/9 (ii) 2/3 + -4/5 + 1/3 + 2/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (ii) 2/3 + -4/5 + 1/3 + 2/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (i) 3/7 + (-4/9) + (-11/7) + 7/9 (ii) 2/3 + -4/5 + 1/3 + 2/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7 (ii) 2/3 + -4/5 + 1/3 + 2/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
Ans : (i) 3/7 + (-4)/9 + (-11)/7 + 7/9
= {3/7 + (-11)/7} + {(-4)/9 + 7/9)
= (3 - 11)/7 + (-4 + 7)/9
= (-8)/7 + 3/9
= (-8)/7 + 1/3
∴ LCM of 3 and 2 = 3 × 7 = 21
= {(-8 × 3)/(7 × 3) + (1 × 7)/(3 × 7)}
(∵ LCM of 7 and 3 = 21)
= (-24 + 7)/21 = (-17)/21 (ii) 2/3 + (-4)/5 + 1/3 + 2/5
(2/3 + 1/3) + (-4/5 + 2/5)
= (2 + 1)/3 + (-4 + 2)/5
= 3/3 + (-2/5)
∴ LCM of 3 and 5 = 3 × 5 = 15
= (3 × 5)/(3 × 5) + (-2 × 3)/(5 × 3)
(∵ LCM of 3 and 5 = 15)
= (15 - 6)/15
= 9/15 = 3/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
= 4/7 + (-8)/9 + (-13)/7 + 17/9
= [4/7 + (-13)/7] + [(-8)/9 + 17/9]
= (4/7) - 13/7 + (-8)/9 + 17/9
= (-9)/7 + 9/7 = (-9)/7 + 1
= (-9 × 1)/(7 × 1) + (1 × 7)(1 × 7)
(∵ LCM of 1 and 7 = 7)
= (-9)/7 + 7/7 = (-2)/7 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
= (3/8 - 5/8) + {(-5)/12 + 3/12} + (3/7 - 2/7)
= (-2)/8 - 2/12 + 1/7
= (-1)/4 - 1/6 + 1/7
∴ LCM of 4, 6 and 7 = 2 × 2 × 3 × 7 = 84
= (-1 × 21)/(1 × 14)/(6 × 14) + (1 × 12)/(7 × 12)
(∵ LCM of 4, 6 and 7 = 84)
= (-21 - 14 + 12)/84
= (-35 + 12)/84 = (-23)/84 (i) 3/7 + (-4)/9 + (-11)/7 + 7/9
= {3/7 + (-11)/7} + {(-4)/9 + 7/9)
= (3 - 11)/7 + (-4 + 7)/9
= (-8)/7 + 3/9
= (-8)/7 + 1/3
∴ LCM of 3 and 2 = 3 × 7 = 21
= {(-8 × 3)/(7 × 3) + (1 × 7)/(3 × 7)}
(∵ LCM of 7 and 3 = 21)
= (-24 + 7)/21 = (-17)/21 (ii) 2/3 + (-4)/5 + 1/3 + 2/5
(2/3 + 1/3) + (-4/5 + 2/5)
= (2 + 1)/3 + (-4 + 2)/5
= 3/3 + (-2/5)
∴ LCM of 3 and 5 = 3 × 5 = 15
= (3 × 5)/(3 × 5) + (-2 × 3)/(5 × 3)
(∵ LCM of 3 and 5 = 15)
= (15 - 6)/15
= 9/15 = 3/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
= 4/7 + (-8)/9 + (-13)/7 + 17/9
= [4/7 + (-13)/7] + [(-8)/9 + 17/9]
= (4/7) - 13/7 + (-8)/9 + 17/9
= (-9)/7 + 9/7 = (-9)/7 + 1
= (-9 × 1)/(7 × 1) + (1 × 7)(1 × 7)
(∵ LCM of 1 and 7 = 7)
= (-9)/7 + 7/7 = (-2)/7 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
= (3/8 - 5/8) + {(-5)/12 + 3/12} + (3/7 - 2/7)
= (-2)/8 - 2/12 + 1/7
= (-1)/4 - 1/6 + 1/7
∴ LCM of 4, 6 and 7 = 2 × 2 × 3 × 7 = 84
= (-1 × 21)/(1 × 14)/(6 × 14) + (1 × 12)/(7 × 12)
(∵ LCM of 4, 6 and 7 = 84)
= (-21 - 14 + 12)/84
= (-35 + 12)/84 = (-23)/84 (ii) 2/3 + (-4)/5 + 1/3 + 2/5
(2/3 + 1/3) + (-4/5 + 2/5)
= (2 + 1)/3 + (-4 + 2)/5
= 3/3 + (-2/5)
∴ LCM of 3 and 5 = 3 × 5 = 15
= (3 × 5)/(3 × 5) + (-2 × 3)/(5 × 3)
(∵ LCM of 3 and 5 = 15)
= (15 - 6)/15
= 9/15 = 3/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
= 4/7 + (-8)/9 + (-13)/7 + 17/9
= [4/7 + (-13)/7] + [(-8)/9 + 17/9]
= (4/7) - 13/7 + (-8)/9 + 17/9
= (-9)/7 + 9/7 = (-9)/7 + 1
= (-9 × 1)/(7 × 1) + (1 × 7)(1 × 7)
(∵ LCM of 1 and 7 = 7)
= (-9)/7 + 7/7 = (-2)/7 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
= (3/8 - 5/8) + {(-5)/12 + 3/12} + (3/7 - 2/7)
= (-2)/8 - 2/12 + 1/7
= (-1)/4 - 1/6 + 1/7
∴ LCM of 4, 6 and 7 = 2 × 2 × 3 × 7 = 84
= (-1 × 21)/(1 × 14)/(6 × 14) + (1 × 12)/(7 × 12)
(∵ LCM of 4, 6 and 7 = 84)
= (-21 - 14 + 12)/84
= (-35 + 12)/84 = (-23)/84 (i) 3/7 + (-4)/9 + (-11)/7 + 7/9
= {3/7 + (-11)/7} + {(-4)/9 + 7/9)
= (3 - 11)/7 + (-4 + 7)/9
= (-8)/7 + 3/9
= (-8)/7 + 1/3
∴ LCM of 3 and 2 = 3 × 7 = 21
= {(-8 × 3)/(7 × 3) + (1 × 7)/(3 × 7)}
(∵ LCM of 7 and 3 = 21)
= (-24 + 7)/21 = (-17)/21 (ii) 2/3 + (-4)/5 + 1/3 + 2/5
(2/3 + 1/3) + (-4/5 + 2/5)
= (2 + 1)/3 + (-4 + 2)/5
= 3/3 + (-2/5)
∴ LCM of 3 and 5 = 3 × 5 = 15
= (3 × 5)/(3 × 5) + (-2 × 3)/(5 × 3)
(∵ LCM of 3 and 5 = 15)
= (15 - 6)/15
= 9/15 = 3/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
= 4/7 + (-8)/9 + (-13)/7 + 17/9
= [4/7 + (-13)/7] + [(-8)/9 + 17/9]
= (4/7) - 13/7 + (-8)/9 + 17/9
= (-9)/7 + 9/7 = (-9)/7 + 1
= (-9 × 1)/(7 × 1) + (1 × 7)(1 × 7)
(∵ LCM of 1 and 7 = 7)
= (-9)/7 + 7/7 = (-2)/7 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
= (3/8 - 5/8) + {(-5)/12 + 3/12} + (3/7 - 2/7)
= (-2)/8 - 2/12 + 1/7
= (-1)/4 - 1/6 + 1/7
∴ LCM of 4, 6 and 7 = 2 × 2 × 3 × 7 = 84
= (-1 × 21)/(1 × 14)/(6 × 14) + (1 × 12)/(7 × 12)
(∵ LCM of 4, 6 and 7 = 84)
= (-21 - 14 + 12)/84
= (-35 + 12)/84 = (-23)/84 (ii) 2/3 + (-4)/5 + 1/3 + 2/5
(2/3 + 1/3) + (-4/5 + 2/5)
= (2 + 1)/3 + (-4 + 2)/5
= 3/3 + (-2/5)
∴ LCM of 3 and 5 = 3 × 5 = 15
= (3 × 5)/(3 × 5) + (-2 × 3)/(5 × 3)
(∵ LCM of 3 and 5 = 15)
= (15 - 6)/15
= 9/15 = 3/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
= 4/7 + (-8)/9 + (-13)/7 + 17/9
= [4/7 + (-13)/7] + [(-8)/9 + 17/9]
= (4/7) - 13/7 + (-8)/9 + 17/9
= (-9)/7 + 9/7 = (-9)/7 + 1
= (-9 × 1)/(7 × 1) + (1 × 7)(1 × 7)
(∵ LCM of 1 and 7 = 7)
= (-9)/7 + 7/7 = (-2)/7 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
= (3/8 - 5/8) + {(-5)/12 + 3/12} + (3/7 - 2/7)
= (-2)/8 - 2/12 + 1/7
= (-1)/4 - 1/6 + 1/7
∴ LCM of 4, 6 and 7 = 2 × 2 × 3 × 7 = 84
= (-1 × 21)/(1 × 14)/(6 × 14) + (1 × 12)/(7 × 12)
(∵ LCM of 4, 6 and 7 = 84)
= (-21 - 14 + 12)/84
= (-35 + 12)/84 = (-23)/84

#3-i
3/7 + (-4/9) + (-11/7) + 7/9 (ii) 2/3 + -4/5 + 1/3 + 2/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
Ans : 3/7 + (-4)/9 + (-11)/7 + 7/9
= {3/7 + (-11)/7} + {(-4)/9 + 7/9)
= (3 - 11)/7 + (-4 + 7)/9
= (-8)/7 + 3/9
= (-8)/7 + 1/3
∴ LCM of 3 and 2 = 3 × 7 = 21
= {(-8 × 3)/(7 × 3) + (1 × 7)/(3 × 7)}
(∵ LCM of 7 and 3 = 21)
= (-24 + 7)/21 = (-17)/21 (ii) 2/3 + (-4)/5 + 1/3 + 2/5
(2/3 + 1/3) + (-4/5 + 2/5)
= (2 + 1)/3 + (-4 + 2)/5
= 3/3 + (-2/5)
∴ LCM of 3 and 5 = 3 × 5 = 15
= (3 × 5)/(3 × 5) + (-2 × 3)/(5 × 3)
(∵ LCM of 3 and 5 = 15)
= (15 - 6)/15
= 9/15 = 3/5 (iii) 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
= 4/7 + (-8)/9 + (-13)/7 + 17/9
= [4/7 + (-13)/7] + [(-8)/9 + 17/9]
= (4/7) - 13/7 + (-8)/9 + 17/9
= (-9)/7 + 9/7 = (-9)/7 + 1
= (-9 × 1)/(7 × 1) + (1 × 7)(1 × 7)
(∵ LCM of 1 and 7 = 7)
= (-9)/7 + 7/7 = (-2)/7 (iv) 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
= (3/8 - 5/8) + {(-5)/12 + 3/12} + (3/7 - 2/7)
= (-2)/8 - 2/12 + 1/7
= (-1)/4 - 1/6 + 1/7
∴ LCM of 4, 6 and 7 = 2 × 2 × 3 × 7 = 84
= (-1 × 21)/(1 × 14)/(6 × 14) + (1 × 12)/(7 × 12)
(∵ LCM of 4, 6 and 7 = 84)
= (-21 - 14 + 12)/84
= (-35 + 12)/84 = (-23)/84

#3-ii
2/3 + -4/5 + 1/3 + 2/5
Ans : 2/3 + (-4)/5 + 1/3 + 2/5
(2/3 + 1/3) + (-4/5 + 2/5)
= (2 + 1)/3 + (-4 + 2)/5
= 3/3 + (-2/5)
∴ LCM of 3 and 5 = 3 × 5 = 15
= (3 × 5)/(3 × 5) + (-2 × 3)/(5 × 3)
(∵ LCM of 3 and 5 = 15)
= (15 - 6)/15
= 9/15 = 3/5

#3-iii
4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
Ans : 4/7 + 0 + (-8)/9 + (-13)/7 + 17/9
= 4/7 + (-8)/9 + (-13)/7 + 17/9
= [4/7 + (-13)/7] + [(-8)/9 + 17/9]
= (4/7) - 13/7 + (-8)/9 + 17/9
= (-9)/7 + 9/7 = (-9)/7 + 1
= (-9 × 1)/(7 × 1) + (1 × 7)(1 × 7)
(∵ LCM of 1 and 7 = 7)
= (-9)/7 + 7/7 = (-2)/7

#3-iv
3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
Ans : 3/8 + (-5)/12 + 3/7 + 3/12 + (-5)/8 + (-2)/7
= (3/8 - 5/8) + {(-5)/12 + 3/12} + (3/7 - 2/7)
= (-2)/8 - 2/12 + 1/7
= (-1)/4 - 1/6 + 1/7
∴ LCM of 4, 6 and 7 = 2 × 2 × 3 × 7 = 84
= (-1 × 21)/(1 × 14)/(6 × 14) + (1 × 12)/(7 × 12)
(∵ LCM of 4, 6 and 7 = 84)
= (-21 - 14 + 12)/84
= (-35 + 12)/84 = (-23)/84