In each of the following, find an equivalent form of the rational number having a common denominator: (i) (3/4) and (5/12) (ii) (2/3), (7/6) and (11/12) (iii) (5/7), (3/8), (9/14) and (20/21)
Answers
(i) Given (3/4) and (5/12) On multiplying both numerator and denominator by 3 (3/4) = (3 × 3)/ (4 × 3) = (9/12) Equivalent forms with same denominators are (9/12) and (5/12)
(ii) Given (2/3), (7/6) and (11/12) On multiplying both numerator and denominator by 4 (2/3) = (2 × 4)/ (3 × 4) = (8/12) And (7/6) = (7 × 2)/ (6 × 2) = (14/12) Equivalent forms are (8/12), (14/12) and (11/12) having same denominators
(iii) Given (5/7), (3/8), (9/14) and (20/21) (5/7) = (5 × 24)/ (7 × 24) = (120/168) [on multiplying both numerator and denominator by 24] (3/8) = (3 × 21)/ (8 × 21) = (63/168) [on multiplying both numerator and denominator by 21] (9/14) = (9 × 12)/ (14 × 12) = (108/168) [on multiplying both numerator and denominator by 12] (20/21) = (20 × 8)/ (21×8) = (160/168) [on multiplying both numerator and denominator by 8] Forms are (120/168), (63/168), (108/168) and (160/168) having same denominators.
i) Given (3/4) and (5/12) On multiplying both numerator and denominator by 3 (3/4) = (3 × 3)/ (4 × 3) = (9/12) Equivalent forms with same denominators are (9/12) and (5/12)
(ii) Given (2/3), (7/6) and (11/12) On multiplying both numerator and denominator by 4 (2/3) = (2 × 4)/ (3 × 4) = (8/12) And (7/6) = (7 × 2)/ (6 × 2) = (14/12) Equivalent forms are (8/12), (14/12) and (11/12) having same denominators
(iii) Given (5/7), (3/8), (9/14) and (20/21) (5/7) = (5 × 24)/ (7 × 24) = (120/168) [on multiplying both numerator and denominator by 24] (3/8) = (3 × 21)/ (8 × 21) = (63/168) [on multiplying both numerator and denominator by 21] (9/14) = (9 × 12)/ (14 × 12) = (108/168) [on multiplying both numerator and denominator by 12] (20/21) = (20 × 8)/ (21×8) = (160/168) [on multiplying both numerator and denominator by 8] Forms are (120/168), (63/168), (108/168) and (160/168) having same denominators.
Step-by-step explanation: