Question

1) (1/4+1/6)*(2/5-1/2) 2) (4/7-3/2)*(1/13-1/4) 3) 4 2/3+1/4*(1 7/9-1/9) 4) 5 1/7-1/7*(1 3/4+1/4)​

Answer 1

№ 1.   (1/4 + 1/6) · (2/5 - 1/2) = (-1/24)

1) 1/4 + 1/6 = 3/12 + 2/12 = 5/12

2) 2/5 - 1/2 = 4/10 - 5/10 = -1/10

3) 5/12 · (-1/10) = -(1·1)/(12·2) = -1/24

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№ 2.   (4/7 - 3/2) · (1/13 - 1/4) = 9/56

1) 4/7 - 3/2 = 8/14 - 21/14 = -13/14

2) 1/13 - 1/4 = 4/52 - 13/52 = -9/52

3) -13/14 · (-9/52) = (1·9)/(14·4) = 9/56

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№ 3.   4 2/3 + 1/4 · (1 7/9 - 1/9) = 5 1/12

1) 1 7/9 - 1/9 = 1 6/9 = 1 2/3 = 5/3

2) 1/4 · 5/3 = 5/12

3) 4 2/3 + 5/12 = 4 8/12 + 5/12 = 4 13/12 = 5 1/12

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№ 4.  5 1/7 - 1/7 · (1 3/4 + 1/4) = 4 6/7

1) 1 3/4 + 1/4 = 1 4/4 = 2

2) 1/7 · 2 = 2/7

3) 5 1/7 - 2/7 = 4 8/7 - 2/7 = 4 6/7

Answer 2

Давайте рассмотрим данное выражение по частям:

1) (1/4+1/6) = (3/12+2/12) = 5/12 2) (2/5-1/2) = (4/10-6/12) = (8/20-10/20) = -2/20 = -1/10 3) (4/7-3/2) = (8/14-21/14) = -13/14 4) (1/13-1/4) = (4/52-13/52) = -9/52 5) (1+7/9-1/9) = (9/9+7/9-1/9) = 15/9 = 5/3 6) (1+3/4+1/4) = (4/4+3/4+1/4) = 8/4 = 2

Теперь подставим значения обратно в исходное выражение:

1) (5/12)*(-1/10) = -5/120 = -1/24 2) (-13/14)*(-9/52) = 117/728 3) 4+2/3+1/4*(5/3) = 4+2/3+5/12 = 12/3+2/3+5/12 = 19/3+5/12 = 57/12+5/12 = 62/12 = 31/6 4) 5+1/7-1/7*(2) = 5+1/7-2/7 = 35/7+1/7-2/7 = 34/7

Теперь сложим все полученные значения:

-1/24 + 117/728 + 31/6 + 34/7 = (-7+152+728+1248)/168 = 2121/168 = 353/28

Ответ: 353/28