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ICSE-VIII-Mathematics

01: Rational Numbers Class 8 Maths

with Solutions - page 2

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  • #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
  • #3-i
    3/7 + (-4/9) + (-11/7) + 7/9
    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
  • #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
  • Qstn #4
    For each pair of rational numbers, verify commutative property of addition of rational numbers:
  • #4-i
    -8/7 and 5/14
    Ans : (-8)/7 and 5/14
    To show that : - (-8)/7 + 5/14 = 5/14 + (-8)/7
    ∵ (-8)/7 + 5/14
    ∴ LCM of 2 and 7 = 14
    = (-8 × 2)/(7 × 2) + (5 × 1)/(14 × 1)
    = (- 16 + 5)/14 = -(11)/14
    And, 5/14 + (-8)/7
    = {(5 × 1)/(14 × 1) + (-8 × 2)/(7 × 2)}
    = (5 - 16)/14 = (-11)/14
    ∴ (-8)/7 + 5/14 = 5/14 + (-8)/7
    This verifies the commutative property for the addition of rational numbers.
  • #4-ii
    5/9 and 5/-12
    Ans : 5/9 and 5/(-12)
    To show that : 5/9 + 5/(-12) = 5/(-12) + 5/9
    ∵ 5/9 + 5/(-12)
    ∴ LCM of 9 and 12 = 2 × 2 × 3 × 3 = 36
    = (5 × 4)/(9 × 4) - (5 × 3)/(12 × 3)
    = (20 - 15)/36 = 5/36
    And, 5/(-12) + 5/9
    = {(5 × 3)/(-12 × 3) + (5 × 4)/(12 × 3)}
    = (-15 + 20)/36 = 5/36
    ∴ 5/9 + 5/(-12) = 5/(-12) + 5/9
    This verifies the commutative property for the addition of rational numbers.
  • #4-iii
    -4/5 and -13/-15
    Ans : (-4/5) and (-13/-15)
    To show that :
    (-4/5) and (-13/-15) = (-13/-15) + (-4)/5
    ∵ (-4)/5 + 13/15
    ∴ LCM of 5 and 15 = 5 × 3 = 15
    = (-4 × 3)/(5 × 3) + (13 × 1)/(15 × 1)
    = (-12 + 13)/15 = 1/15
    And, 13/15 + (-4)/5
    = {(13 × 1)/(15 × 1) + (-4 × 3)/(5 × 3)}
    = (13 - 12)/15 = 1/15
    ∴ (-4)/5 + (-13/-15) = (-13/-15) + (-4)/5
    This verifies the commutative property for the addition of rational numbers.
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