Odpowiedź:
(3/4 - 1/2) * 3 i 1/2 = (3/4 - 2/4) * 3 i 1/2 = 1/4 * 7/2 = 7/8
7/8 * 4/5 - 2/3 * 6/14 = 7/10 - 2/7 = 49/70 - 20/70 = 29/70
2 i 1/3 * (1 i 3/4 - 7/8) = 2 i 1/3 * (1 i 6/8 - 7/8) = 2 i 1/3 * (14/8 - 7/8) = 7/3 * 7/8 = 49/24 = 2 i 1/24
3 i 1/5 * 1/2 - 5/7 * 1 i 2/5 = 16/5 * 1/2 - 5/7 * 7/5 = 8/5 - 1 = 1 i 3/5 - 1 = 3/5
1/5 * (3 i 3/7 - 2/7 * 5 i 1/2) = 1/5 * (3 i 3/7 - 2/7 * 11/2) = 1/5 * (3 i 3/7 - 11/7) = 1/5 * (3 i 3/7 - 1 i 4/7) = 1/5 * (2 i 10/7 - 1 i 4/7) = 1/5 * 1 i 6/7 = 1/5 * 13/7 = 13/35
(3 i 3/4 + 2 i 1/8) : 5 = (3 i 6/8 + 2 i 1/8) : 5 = 5 i 7/8 : 5 = 47/8 * 1/5 = 47/40 = 1 i 7/40
6 i 1/8 : 4 + 2 i 3/4 = 49/8 * 1/4 + 2 i 3/4 = 49/32 + 2 i 3/4 = 1 i 17/32 + 2 i 24/32 = 3 i 41/32 = 4 i 9/32
3 i 1/6 + 2 i 1/3 : 3 = 3 i 1/6 + 7/3 * 1/3 = 3 i 1/6 + 7/9 = 3 i 3/18 + 14/18 = 3 i 17/18
(4 i 3/5 - 2 i 1/2) : 2 = 4 i 6/10 - 2 i 5/10) : 2 = 2 i 1/10 : 2 = 21/10 * 1/2 = 21/20 = 1 i 1/20
1.
a)
(3/4 - 1/2) * 3 1/2 = (3/4 - 2/4) * 7/2 = 1/4 * 7/2 = 7/8
b)
7/8 * 4/5 - 2/3 * 6/14 = 7/2 * 1/5 - 1 * 2/7 = 7/10 - 2/7 = 49/70 - 20/70 =
= 29/70
c)
2 1/3 * (1 3/4 - 7/8) = 7/3 * (1 6/8 - 7/8) = 7/3 * (14/8 - 7/8) = 7/3 * 7/8 =
= 49/24 = 2 1/24
d)
3 1/5 * 1/2 - 5/7 * 1 2/5 = 16/5 * 1/2 - 5/7 * 7/5 = 16/10 - 1 = 16/10 - 10/10 =
= 6/10 = 3/5
e)
1/5 * (3 3/7 - 2/7 * 5 1/2) = 1/5 * (3 3/7 - 2/7 * 11/2) = 1/5 * (3 3/7 - 22/14) =
= 1/5 * (3 6/14 - 1 8/14) = 1/5 * ( 2 20/14 - 1 8/14) = 1/5 * 1 12/14 =
= 1/5 * 1 6/7 = 1/5 * 13/7 = 13/35
2.
(3 3/4 + 2 1/8) : 5 = (3 6/8 + 2 1/8) * 1/5 = 5 7/8 * 1/5 = 47/8 * 1/5 =
= 47/40 = 1 7/40
6 1/8 : 4 + 2 3/4 = 49/8 * 1/4 + 2 3/4 = 49/32 + 2 24/32 =
= 1 16/32 + 2 24/32 = 3 40/32 = 4 8/32 = 4 1/4
3 1/6 + 2 1/3 : 3 = 3 1/6 + 7/3 * 1/3 = 3 1/6 + 7/9 = 3 3/18 + 14/18 =
= 3 17/18
(4 3/5 - 2 1/2) : 2 = (4 6/10 - 2 5/10) * 1/2 = 2 1/10 * 1/2 = 21/10 * 1/2 =
= 21/20 = 1 1/20
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Odpowiedź:
(3/4 - 1/2) * 3 i 1/2 = (3/4 - 2/4) * 3 i 1/2 = 1/4 * 7/2 = 7/8
7/8 * 4/5 - 2/3 * 6/14 = 7/10 - 2/7 = 49/70 - 20/70 = 29/70
2 i 1/3 * (1 i 3/4 - 7/8) = 2 i 1/3 * (1 i 6/8 - 7/8) = 2 i 1/3 * (14/8 - 7/8) = 7/3 * 7/8 = 49/24 = 2 i 1/24
3 i 1/5 * 1/2 - 5/7 * 1 i 2/5 = 16/5 * 1/2 - 5/7 * 7/5 = 8/5 - 1 = 1 i 3/5 - 1 = 3/5
1/5 * (3 i 3/7 - 2/7 * 5 i 1/2) = 1/5 * (3 i 3/7 - 2/7 * 11/2) = 1/5 * (3 i 3/7 - 11/7) = 1/5 * (3 i 3/7 - 1 i 4/7) = 1/5 * (2 i 10/7 - 1 i 4/7) = 1/5 * 1 i 6/7 = 1/5 * 13/7 = 13/35
(3 i 3/4 + 2 i 1/8) : 5 = (3 i 6/8 + 2 i 1/8) : 5 = 5 i 7/8 : 5 = 47/8 * 1/5 = 47/40 = 1 i 7/40
6 i 1/8 : 4 + 2 i 3/4 = 49/8 * 1/4 + 2 i 3/4 = 49/32 + 2 i 3/4 = 1 i 17/32 + 2 i 24/32 = 3 i 41/32 = 4 i 9/32
3 i 1/6 + 2 i 1/3 : 3 = 3 i 1/6 + 7/3 * 1/3 = 3 i 1/6 + 7/9 = 3 i 3/18 + 14/18 = 3 i 17/18
(4 i 3/5 - 2 i 1/2) : 2 = 4 i 6/10 - 2 i 5/10) : 2 = 2 i 1/10 : 2 = 21/10 * 1/2 = 21/20 = 1 i 1/20
Odpowiedź:
1.
a)
(3/4 - 1/2) * 3 1/2 = (3/4 - 2/4) * 7/2 = 1/4 * 7/2 = 7/8
b)
7/8 * 4/5 - 2/3 * 6/14 = 7/2 * 1/5 - 1 * 2/7 = 7/10 - 2/7 = 49/70 - 20/70 =
= 29/70
c)
2 1/3 * (1 3/4 - 7/8) = 7/3 * (1 6/8 - 7/8) = 7/3 * (14/8 - 7/8) = 7/3 * 7/8 =
= 49/24 = 2 1/24
d)
3 1/5 * 1/2 - 5/7 * 1 2/5 = 16/5 * 1/2 - 5/7 * 7/5 = 16/10 - 1 = 16/10 - 10/10 =
= 6/10 = 3/5
e)
1/5 * (3 3/7 - 2/7 * 5 1/2) = 1/5 * (3 3/7 - 2/7 * 11/2) = 1/5 * (3 3/7 - 22/14) =
= 1/5 * (3 6/14 - 1 8/14) = 1/5 * ( 2 20/14 - 1 8/14) = 1/5 * 1 12/14 =
= 1/5 * 1 6/7 = 1/5 * 13/7 = 13/35
2.
(3 3/4 + 2 1/8) : 5 = (3 6/8 + 2 1/8) * 1/5 = 5 7/8 * 1/5 = 47/8 * 1/5 =
= 47/40 = 1 7/40
6 1/8 : 4 + 2 3/4 = 49/8 * 1/4 + 2 3/4 = 49/32 + 2 24/32 =
= 1 16/32 + 2 24/32 = 3 40/32 = 4 8/32 = 4 1/4
3 1/6 + 2 1/3 : 3 = 3 1/6 + 7/3 * 1/3 = 3 1/6 + 7/9 = 3 3/18 + 14/18 =
= 3 17/18
(4 3/5 - 2 1/2) : 2 = (4 6/10 - 2 5/10) * 1/2 = 2 1/10 * 1/2 = 21/10 * 1/2 =
= 21/20 = 1 1/20