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ICSE-VIII-Mathematics

01: Rational Numbers Class 8 Maths

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  • #1
    Add, each pair of rational numbers, given below, and show that their addition (sum) is also a rational number: (i) -5/8 and 3/8 (ii) -8/13 and -4/13 (iii) 6/11 and -9/11 (iv) 5/-26 and 8/39 (v) 5/-6 and 2/3 (vi) -2 and 2/5 (vii) 9/-4 and -3/8 (viii) 7/-18 and 8/27 (i) -5/8 and 3/8 (ii) -8/13 and -4/13 (iii) 6/11 and -9/11 (iv) 5/-26 and 8/39 (v) 5/-6 and 2/3 (vi) -2 and 2/5 (vii) 9/-4 and -3/8 (viii) 7/-18 and 8/27
    Ans : (i) (-5)/8 and 3/8
    = (-5)/8 + 3/8
    (∵ Denominators are same, ∴ LCM = 8)
    = (-5 + 3)/8
    = (-2)/8 = (-1)/4
    Which is a rational number. (ii) (-8)/13 and (-4)/13
    = (-8)/13 + (-4)/13
    (∵ LCM of 13 and 13 = 13)
    = (- 8 - 4)/13 = (-12)/13
    Which is a rational number. (iii) 6/11 and (-9)/11
    = 6/11 + (-9)/11
    (∵ Denominator are same, ∴ LCM = 11)
    = (6 - 9)/11 = (-3)/11
    Which is a rational number. (iv) 5/(-26) and 8/39
    = 5/(-26) + 8/39
    = (-5 × 3)/(26 × 3) + (8 × 2)/(39 × 2)
    ∴ LCM of 26 and 39 = 2 × 3 × 13 = 78
    = (-15 + 16)/78 (∵ LCM of 26 and 39 = 78)
    = 1/78
    Which is a rational number. (v) 5/(-6) and 2/3
    = (-5)/6 + 2/3
    ∴ LCM of 6, 3 = 2 × 3 = 6
    = (-5 × 1)/(6×1) + (2 × 2)/(3 × 2)
    (∵ LCM of 6 and 3 = 6)
    = (-5 + 4)/6 = (-1)/6
    Which is a rational number. (vi) (-2) and 2/5
    = (-2)/1 + 2/5 (∵ LCM of 1 and 5 = 5)
    = (-2 × 5)/(1 × 5) + (2 × 1)/(5 × 1)
    = (-10 + 2)/5 = (-8)/5
    Which is a rational number. (vii) 9/-(4) and (-3)/8
    = (-9)/4 + (-3)/8
    ∴ LCM of 4 and 8 = 2 × 2 × 2 = 8
    = (-9 × 2)/(4 × 2) - (3 × 1)/(8 × 1)
    (∵ LCM of 4 and 8 = 8)
    = (- 18 - 3)/8 = (-21)/8
    Which is a rational number. (viii) 7/(-18) and 8/27
    = 7/(-18) + 8/27
    = (-7 × 3)/(18 × 3) + (8 × 2)/(27 × 2)
    ∴ LCM of 18 and 27 = 2 × 3 × 3 × 3 = 54
    = (-21 + 16)/54 = (-5/54)
    Which is rational number. (i) (-5)/8 and 3/8
    = (-5)/8 + 3/8
    (∵ Denominators are same, ∴ LCM = 8)
    = (-5 + 3)/8
    = (-2)/8 = (-1)/4
    Which is a rational number. (ii) (-8)/13 and (-4)/13
    = (-8)/13 + (-4)/13
    (∵ LCM of 13 and 13 = 13)
    = (- 8 - 4)/13 = (-12)/13
    Which is a rational number. (iii) 6/11 and (-9)/11
    = 6/11 + (-9)/11
    (∵ Denominator are same, ∴ LCM = 11)
    = (6 - 9)/11 = (-3)/11
    Which is a rational number. (iv) 5/(-26) and 8/39
    = 5/(-26) + 8/39
    = (-5 × 3)/(26 × 3) + (8 × 2)/(39 × 2)
    ∴ LCM of 26 and 39 = 2 × 3 × 13 = 78
    = (-15 + 16)/78 (∵ LCM of 26 and 39 = 78)
    = 1/78
    Which is a rational number. (v) 5/(-6) and 2/3
    = (-5)/6 + 2/3
    ∴ LCM of 6, 3 = 2 × 3 = 6
    = (-5 × 1)/(6×1) + (2 × 2)/(3 × 2)
    (∵ LCM of 6 and 3 = 6)
    = (-5 + 4)/6 = (-1)/6
    Which is a rational number. (vi) (-2) and 2/5
    = (-2)/1 + 2/5 (∵ LCM of 1 and 5 = 5)
    = (-2 × 5)/(1 × 5) + (2 × 1)/(5 × 1)
    = (-10 + 2)/5 = (-8)/5
    Which is a rational number. (vii) 9/-(4) and (-3)/8
    = (-9)/4 + (-3)/8
    ∴ LCM of 4 and 8 = 2 × 2 × 2 = 8
    = (-9 × 2)/(4 × 2) - (3 × 1)/(8 × 1)
    (∵ LCM of 4 and 8 = 8)
    = (- 18 - 3)/8 = (-21)/8
    Which is a rational number. (viii) 7/(-18) and 8/27
    = 7/(-18) + 8/27
    = (-7 × 3)/(18 × 3) + (8 × 2)/(27 × 2)
    ∴ LCM of 18 and 27 = 2 × 3 × 3 × 3 = 54
    = (-21 + 16)/54 = (-5/54)
    Which is rational number.
  • #1-i
    -5/8 and 3/8
    Ans : (-5)/8 and 3/8
    = (-5)/8 + 3/8
    (∵ Denominators are same, ∴ LCM = 8)
    = (-5 + 3)/8
    = (-2)/8 = (-1)/4
    Which is a rational number.
  • #1-ii
    -8/13 and -4/13
    Ans : (-8)/13 and (-4)/13
    = (-8)/13 + (-4)/13
    (∵ LCM of 13 and 13 = 13)
    = (- 8 - 4)/13 = (-12)/13
    Which is a rational number.
  • #1-iii
    6/11 and -9/11
    Ans : 6/11 and (-9)/11
    = 6/11 + (-9)/11
    (∵ Denominator are same, ∴ LCM = 11)
    = (6 - 9)/11 = (-3)/11
    Which is a rational number.
  • #1-iv
    5/-26 and 8/39
    Ans : 5/(-26) and 8/39
    = 5/(-26) + 8/39
    = (-5 × 3)/(26 × 3) + (8 × 2)/(39 × 2)
    ∴ LCM of 26 and 39 = 2 × 3 × 13 = 78
    = (-15 + 16)/78 (∵ LCM of 26 and 39 = 78)
    = 1/78
    Which is a rational number.
  • #1-v
    5/-6 and 2/3
    Ans : 5/(-6) and 2/3
    = (-5)/6 + 2/3
    ∴ LCM of 6, 3 = 2 × 3 = 6
    = (-5 × 1)/(6×1) + (2 × 2)/(3 × 2)
    (∵ LCM of 6 and 3 = 6)
    = (-5 + 4)/6 = (-1)/6
    Which is a rational number.
  • #1-vi
    -2 and 2/5
    Ans : (-2) and 2/5
    = (-2)/1 + 2/5 (∵ LCM of 1 and 5 = 5)
    = (-2 × 5)/(1 × 5) + (2 × 1)/(5 × 1)
    = (-10 + 2)/5 = (-8)/5
    Which is a rational number.
  • #1-vii
    9/-4 and -3/8
    Ans : 9/-(4) and (-3)/8
    = (-9)/4 + (-3)/8
    ∴ LCM of 4 and 8 = 2 × 2 × 2 = 8
    = (-9 × 2)/(4 × 2) - (3 × 1)/(8 × 1)
    (∵ LCM of 4 and 8 = 8)
    = (- 18 - 3)/8 = (-21)/8
    Which is a rational number.
  • #1-viii
    7/-18 and 8/27
    Ans : 7/(-18) and 8/27
    = 7/(-18) + 8/27
    = (-7 × 3)/(18 × 3) + (8 × 2)/(27 × 2)
    ∴ LCM of 18 and 27 = 2 × 3 × 3 × 3 = 54
    = (-21 + 16)/54 = (-5/54)
    Which is rational number.