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МатематикаВопрос:
105. Найдите значение выражения: а) 3 3/7 + 1 3/14 * (8 3/5 - 1 3/5); б) 2 5/9 * 2 1/4 - 6 2/9 * 3/8; в) (6 2/5 * 2 11/12 - 16) * 2 1/4; г) (1/2)^3 * (3 1/3 - 2 8/9)^2; д) (3 2/3 - 2 1/2) * 2 1/7 - 1 1/2; е) 12 * (11/12 - 9/10) * (3 - 1 1/3).
Ответ:
а) 3 3/7 + 1 3/14 * (8 3/5 - 1 3/5) = 24/7 + 17/14 * (43/5 - 8/5) = 24/7 + 17/14 * 35/5 = 24/7 + 17/14 * 7 = 24/7 + 17/2 = 48/14 + 119/14 = 167/14 = 11 13/14.
б) 2 5/9 * 2 1/4 - 6 2/9 * 3/8 = 23/9 * 9/4 - 56/9 * 3/8 = 23/4 - (56*3)/(9*8) = 23/4 - (7*3)/(9*1) = 23/4 - 21/9 = 23/4 - 7/3 = (69-28)/12 = 41/12 = 3 5/12.
в) (6 2/5 * 2 11/12 - 16) * 2 1/4 = (32/5 * 35/12 - 16) * 9/4 = (32*35)/(5*12) - 16) * 9/4 = (8*7)/3 - 16) * 9/4 = (56/3 - 48/3) * 9/4 = (8/3) * 9/4 = (8*9)/(3*4) = 2*3 = 6.
г) (1/2)^3 * (3 1/3 - 2 8/9)^2 = 1/8 * (10/3 - 26/9)^2 = 1/8 * (30/9 - 26/9)^2 = 1/8 * (4/9)^2 = 1/8 * 16/81 = 16/(8*81) = 2/81.
д) (3 2/3 - 2 1/2) * 2 1/7 - 1 1/2 = (11/3 - 5/2) * 15/7 - 3/2 = (22/6 - 15/6) * 15/7 - 3/2 = 7/6 * 15/7 - 3/2 = 15/6 - 3/2 = 5/2 - 3/2 = 2/2 = 1.
е) 12 * (11/12 - 9/10) * (3 - 1 1/3) = 12 * (55/60 - 54/60) * (9/3 - 4/3) = 12 * (1/60) * (5/3) = (12*1*5)/(60*3) = 60/180 = 1/3.
б) 2 5/9 * 2 1/4 - 6 2/9 * 3/8 = 23/9 * 9/4 - 56/9 * 3/8 = 23/4 - (56*3)/(9*8) = 23/4 - (7*3)/(9*1) = 23/4 - 21/9 = 23/4 - 7/3 = (69-28)/12 = 41/12 = 3 5/12.
в) (6 2/5 * 2 11/12 - 16) * 2 1/4 = (32/5 * 35/12 - 16) * 9/4 = (32*35)/(5*12) - 16) * 9/4 = (8*7)/3 - 16) * 9/4 = (56/3 - 48/3) * 9/4 = (8/3) * 9/4 = (8*9)/(3*4) = 2*3 = 6.
г) (1/2)^3 * (3 1/3 - 2 8/9)^2 = 1/8 * (10/3 - 26/9)^2 = 1/8 * (30/9 - 26/9)^2 = 1/8 * (4/9)^2 = 1/8 * 16/81 = 16/(8*81) = 2/81.
д) (3 2/3 - 2 1/2) * 2 1/7 - 1 1/2 = (11/3 - 5/2) * 15/7 - 3/2 = (22/6 - 15/6) * 15/7 - 3/2 = 7/6 * 15/7 - 3/2 = 15/6 - 3/2 = 5/2 - 3/2 = 2/2 = 1.
е) 12 * (11/12 - 9/10) * (3 - 1 1/3) = 12 * (55/60 - 54/60) * (9/3 - 4/3) = 12 * (1/60) * (5/3) = (12*1*5)/(60*3) = 60/180 = 1/3.
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