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ICSE-VIII-Mathematics

01: Rational Numbers Class 8 Maths

with Solutions -
Qstn# A-2 Prvs-QstnNext-Qstn
  • #2
    Evaluate: (i) 5/9 + -7/6 (ii) 4 + 3/-5 (iii) 1/-15 + 5/-12 (iv) 5/9 + 3/-4 (ix) 4/-9 + 1 (v) -8/9 + -5/12 (vi) 0 + -2/7 (vii) 5/-11 + 0 (viii) 2 + -3/5
    Ans : (i) 5/9 + (-7)/6
    ∴ LCM of 9 and 6 = 2 × 3 × 3 = 18
    = (5 × 2)/(9 × 2) - (7 × 3)/(6 × 3)
    (∵ LCM of 9 and 6 = 18)
    = (10 - 21)/18 = -11/8 (ii) 4 + 3/(-5)
    = 4/1 + 3/(-5)
    = 4/1 - 3/5
    = (4 × 5)/(1 × 5) - (3 × 1)/(5 × 1)
    (∵ LCM 1 and 5 = 5)
    = (20 - 3)/5 = 17/5 = 3.2/5 (iii) 1/(-15) + 5/(-12)
    = (-1)/15 + (5/-12)
    = (-1)/15 - 5/12
    ∴ LCM of 15 and 12 = 2 × 2 × 3 × 5 = 60
    = (-1 × 4)/(15 × 4) - (5 × 5)/(12 × 5)
    (∵ LCM of 15 and 12 = 60)
    = (-1 × 4)/(15 × 4) - (5 × 5)/(12 × 5)
    (∵ LCM of 15 and 12 = 60)
    = (-4 - 25)/60 = -29/60 (iv) 5/9 + 3/(-4)
    = 5/9 - ¾
    (∴ LCM of 9 and 4 = 2 × 2 × 3 × 3 = 36)
    = (5 × 4)/(9 × 4) - (3 × 9)/(4 × 9)
    = (20 - 27)/36 = (-7)/36
    (∵ LCM of 9 and 4 = 36) (ix) 4/(-9) + 1
    = (-4)/9 + 1/1 (∵ LCM of 9 and 1 = 9)
    = (-4 × 1)/(9 × 1) + (1 × 9)/(1 × 9)
    = (-4 + 9)/9 = 5/9 (v) (-8)/9 + (-5)/12
    ∴ LCM = 9, 12 = 2 × 2 × 3 × 3 = 36
    = (-8 × 4)/(9 × 4) - (5 × 3)/(12 × 3)
    = (-32 - 15)/36 (∵ LCM of 9 and 12 = 36)
    = (-47)/36 (vi) 0 + (-2)/7
    = (0 × 7)/(1 × 7) - (2 × 1)/(7 × 1) (∵ LCM of 0 and 7 = 7)
    = (0 - 2)/7 = -2/7 (vii) 5/-11 + 0
    = (-5 × 1)/(11 × 1) + (0 × 11)/(1 × 11)
    (∵ LCM of 0 and 11 = 11)
    = (-5 + 0)/11 = (-5)/11 (viii) 2 + (-3)/5
    = 2/1 - 3/5 (∵ LCM of 1 and 5 = 5)
    = (2 × 5)/(1 × 5) - (3 × 1)/(5 × 1)
    = (10 - 3)/5 = 7/5 = 1 2/5
  • #2-i
    5/9 + -7/6
    Ans : 5/9 + (-7)/6
    ∴ LCM of 9 and 6 = 2 × 3 × 3 = 18
    = (5 × 2)/(9 × 2) - (7 × 3)/(6 × 3)
    (∵ LCM of 9 and 6 = 18)
    = (10 - 21)/18 = -11/8
  • #2-ii
    4 + 3/-5
    Ans : 4 + 3/(-5)
    = 4/1 + 3/(-5)
    = 4/1 - 3/5
    = (4 × 5)/(1 × 5) - (3 × 1)/(5 × 1)
    (∵ LCM 1 and 5 = 5)
    = (20 - 3)/5 = 17/5 = 3.2/5
  • #2-iii
    1/-15 + 5/-12
    Ans : 1/(-15) + 5/(-12)
    = (-1)/15 + (5/-12)
    = (-1)/15 - 5/12
    ∴ LCM of 15 and 12 = 2 × 2 × 3 × 5 = 60
    = (-1 × 4)/(15 × 4) - (5 × 5)/(12 × 5)
    (∵ LCM of 15 and 12 = 60)
    = (-1 × 4)/(15 × 4) - (5 × 5)/(12 × 5)
    (∵ LCM of 15 and 12 = 60)
    = (-4 - 25)/60 = -29/60
  • #2-iv
    5/9 + 3/-4
    Ans : 5/9 + 3/(-4)
    = 5/9 - ¾
    (∴ LCM of 9 and 4 = 2 × 2 × 3 × 3 = 36)
    = (5 × 4)/(9 × 4) - (3 × 9)/(4 × 9)
    = (20 - 27)/36 = (-7)/36
    (∵ LCM of 9 and 4 = 36)
  • #2-ix
    4/-9 + 1
    Ans : 4/(-9) + 1
    = (-4)/9 + 1/1 (∵ LCM of 9 and 1 = 9)
    = (-4 × 1)/(9 × 1) + (1 × 9)/(1 × 9)
    = (-4 + 9)/9 = 5/9
  • #2-v
    -8/9 + -5/12
    Ans : (-8)/9 + (-5)/12
    ∴ LCM = 9, 12 = 2 × 2 × 3 × 3 = 36
    = (-8 × 4)/(9 × 4) - (5 × 3)/(12 × 3)
    = (-32 - 15)/36 (∵ LCM of 9 and 12 = 36)
    = (-47)/36
  • #2-vi
    0 + -2/7
    Ans : 0 + (-2)/7
    = (0 × 7)/(1 × 7) - (2 × 1)/(7 × 1) (∵ LCM of 0 and 7 = 7)
    = (0 - 2)/7 = -2/7
  • #2-vii
    5/-11 + 0
    Ans : 5/-11 + 0
    = (-5 × 1)/(11 × 1) + (0 × 11)/(1 × 11)
    (∵ LCM of 0 and 11 = 11)
    = (-5 + 0)/11 = (-5)/11
  • #2-viii
    2 + -3/5
    Ans : 2 + (-3)/5
    = 2/1 - 3/5 (∵ LCM of 1 and 5 = 5)
    = (2 × 5)/(1 × 5) - (3 × 1)/(5 × 1)
    = (10 - 3)/5 = 7/5 = 1 2/5