Question:
simplify
(a) (32/5) + (23/11) × (22/15)
(b) (3/7) × (28/15) ÷ (14/5)
(c) (3/7) + (-2/21) × (-5/6)
(d) (7/8) + (1/6) – (1/12)
Solution:
(a) (32/5) + (23/11) × (22/15)
= (32/5) + (23/1) × (2/15)
= (32/5) + (46/15)
= (96 + 46)/15
= 142/15
(b) (3/7) × (28/15) ÷ (14/5)
= (3/7) × (28/15) ÷ (14/5)
= (1/1) × (4/5) ÷ (14/5)
= (4/5) ÷ (14/5)
= (4/5) × (5/14)
= (2/1) × (1/7)
= 2/7
(c) (3/7) + (-2/21) × (-5/6)
= (3/7) – (2/21) × (-5/6)
= (3/7) – (1/21) × (-5/3)
= (3/7) – (-5/63)
= (3/7) + (5/63)
= (27 + 5)/63
= 32/63
(d) (7/8) + (1/6) – (1/12)
= (7/8) + (1/6) – (1/12)
= ((14 + 1)/16) – (1/12)
= (15/16) – (1/12)
= (45-4)/48
= 41/48