Odpowiedź:
Poziom A
a) 3 ∙ 2/7 = 6/7
b) (4/15) ∙ 2 = 8/15
c) 2 ∙ 11/31 = 22/31
Poziom B
a) 3 ∙ 4/7 = 12/7 = 7/7 + 5/7 = 1 + 5/7 = 1i5/7 (jedna cała i 5/7).
b) (11/15) ∙ 2 = 22/15 = 15/15 + 7/15 = 1 + 7/15 = 1i7/15
(jedna cała i 7/15).
c) 7 ∙ 10/33 = 70/33 = 66/33 + 4/33 = 2 + 4/33 = 2i4/33
(2 całe i 4/33).
Poziom C
a) 3 ∙ 2/9 = 2/3.
b) (5/18) ∙ 3 = 5/6.
c) 15 ∙ 1/5 = 3 ∙ 1 = 3
Poziom D
a) 3 ∙ 1½ = 4 + 1/2 = 4i1/2 (4 całe i 1/2).
b) (2i2/3) ∙ 4 = 10 + 2/3 = 10i2/3 (10 całych i 2/3).
c) 5 ∙ 2i3/10 = 11 + 1/2 = 11i1/2 (11 całych i 1/2).
d) 6 ∙ 1i2/5 = 8 + 2/5 = 8i2/5 (8 całych i 2/5)
e) (4i1/7) ∙ 10 = 41 + 3/7 = 41i3/7 (41 całych i 3/7)
f) (1i9/10) ∙ 5 = 9 + 1/2 = 9i1/2 (9 całych i 1/2)
g) 3 ∙ (2i4/11) = 7 + 1/11 = 7i1/11 (7 całych i 1/11)
h) 7 ∙ (2i3/14) = 15 + 1/2 = 15i1/2 (15 całych i 1/2)
Szczegółowe wyjaśnienie:
Działania polegają tu głównie na zamianie liczb mieszanych (liczb całkowitych i ułamków) na ułamki o wspólnym mianowniku, tak by można było te ułamki dodać, uprościć i wykonać mnożenie.
Poziom A
a) 3 ∙ 2/7 = 6/7
b) (4/15) ∙ 2 = 8/15
c) 2 ∙ 11/31 = 22/31
Poziom B
a) 3 ∙ 4/7 = 12/7 = 7/7 + 5/7 = 1 + 5/7 = 1i5/7 (jedna cała i 5/7).
b) (11/15) ∙ 2 = 22/15 = 15/15 + 7/15 = 1 + 7/15 = 1i7/15
(jedna cała i 7/15).
c) 7 ∙ 10/33 = 70/33 = 66/33 + 4/33 = 2 + 4/33 = 2i4/33
(2 całe i 4/33).
Poziom C
a) 3 ∙ 2/9 = 2/3.
b) (5/18) ∙ 3 = 5/6.
c) 15 ∙ 1/5 = 3 ∙ 1 = 3
Poziom D
a) 3 ∙ 1½ = 3 ∙ (2/2 + 1/2) = 3 ∙ 3/2 = 9/2 = 8/2 + 1/2 = 4 + 1/2 =
= 4i1/2 (4 całe i 1/2).
b) (2i2/3) ∙ 4 = (2 + 2/3) ∙ 4 = (6/3 + 2/3) ∙ 4 =( 8/3) ∙ 4 = 32/3 =
= 30/3 + 2/3 = 10 + 2/3 = 10i2/3 (10 całych i 2/3).
c) 5 ∙ 2i3/10 = 5 ∙ (2 + 3/10) = 5 ∙ (20/10 + 3/10) = 5 ∙ 23/10 =
= 23/2 = 22/2 + 1/2 = 11 + 1/2 = 11i1/2 (11 całych i 1/2).
d) 6 ∙ 1i2/5 = 6 ∙ (1 + 2/5) = 6 ∙ (5/5 + 2/5) = 6 ∙ 7/5 = 42/5 =
= 40/5 + 2/5 = 8 + 2/5 = 8i2/5 (8 całych i 2/5)
e) (4i1/7) ∙ 10 = (4 + 1/7) ∙ 10 = (28/7 + 1/7) ∙ 10 = (29/7) ∙ 10 =
= 290/7 = 287/7 + 3/7 = 41 + 3/7 = 41i3/7 (41 całych i 3/7)
f) (1i9/10) ∙ 5 = (1 + 9/10) ∙ 5 = (10/10 + 9/10) ∙ 5 = (19/10) ∙ 5
= 19/2 = 18/2 + 1/2 = 9 + 1/2 = 9i1/2 (9 całych i 1/2)
g) 3 ∙ (2i4/11) = 3 ∙ (2 + 4/11) = 3 ∙ (22/11 + 4/11) = 3 ∙ 26/11 =
= 78/11 = 77/11 + 1/11 = 7 + 1/11 = 7i1/11 (7 całych i 1/11)
h) 7 ∙ (2i3/14) = 7 ∙ (2 + 3/14) = 7 ∙ (28/14 + 3/14) = 7 ∙ 31/14 =
= 31/2 = 30/2 + 1/2 = 15 + 1/2 = 15i1/2 (15 całych i 1/2)
