Odpowiedź:
1. Oblicz
a)
(7/10)^2 = 49/100
b)
(1 3/8)^2 = (11/8)² = 121/64 = 1 57/64
c)
(3/4)^3 = 27/64
d)
(1 2/3)^3 = (5/3)³ = 125/27 = 4 17/27
2.
Oblicz
a)
(7/8 - 3/4) x 2 2/3 = (7/8 - 6/8) * 8/3 = 1/8 * 8/3 = 1/3
b)
4x³ + 3/4 - (2 1/2) = 4x³ + 3/4 - 2 2/4 = 4x³ + 3/4 - 1 6/4 = 4x³ - 1 3/4
4x³ - 1 3/4 = 0
4x³ = 7/4 /:4
x³ = 7/16
x = ∛7/16
c)
1 1/2 x (2 1/4 - 1 5/8) + (3/4)^2 = 3/2 * (1 5/4 - 1 5/8) + 9/16 = 3/2 * (1 10/8 - 1 5/8) + 9/16 = 3/2 * 5/8 + 9/16 = 15/16 + 9/16 = 24/16 = 1 8/16 = 1 1/2
3. Oblicz
a)
4/5 : 3 = 4/5 * 1/3 = 4/15
b)
15/16 : 6 = 15/16 * 1/6 = 15/96
c)
1 2/9 : 11 = 11/9 * 1/11 = 1/9
d)
2 4/5 : 7 = 14/5 * 1/7 = 2/5
4.
Oblicz
a)
5 + 2 2/5 x 3/4 = 5 + 12/5 * 3/4 = 5 + 9/5 = 6 4/5
b)
1/14 : 1 1/7 = 1/14 : 8/7 = 1/14 * 7/8 = 1/16
5.
Oblicz
(3/7 - 1/3) : (1 + 1/3) = (9/21 - 7/21) : 1 1/3 = 2/21 : 4/3 = 2/21 * 3/4 = 1/14
6. Wykonaj dzielenie
a)
1 1/7 : 1/14 = 8/7 * 14 = 16
b)
1/14 : 1 1/7 = 1/14 : 8/7 = 1/14 * 7/8 = 1/16
7.
Oblicz
a)
18 x 4 2/3 = 18 * 14/3 = 6 * 14 = 84
b)
1 1/2 x 2 2/3 = 3/2 * 8/3 = 4
c)
2 1/7 : 12 = 15/7 * 1/12 = 5/7 * 1/4 = 5/28
d)
7 1/3 : 1 2/9 = 22/3 : 11/9 = 22/3 * 9/11 = 6
8.
Wskaż wynik działania
3 1/9 x 2 1/3 = 28/9 * 7/3 = 196/27 odp.D
A. 3/4 B.27/196 C.4/3 D. 196/27
9. Oblicz. Wynik przestaw w najprostszej postaci.
a)
5/9 + 1/6 = 10/18 + 3/18 = 13/18
b)
3 3/8 + 1 7/12 = 3 9/24 + 1 14/24 = 4 23/24
c)
7/10 - 3/8 = 28/40 - 15/40 = 13/40
d)
4 1/10 - 2 3/4 = 3 11/10 - 2 3/4 = 3 22/20 - 2 15/20 = 1 7/20
e)
1 1/7 x 5 = 8/7 * 5 = 40/7 = 5 5/7
f)
4/5 : 3 = 4/5 * 1/3 = 4/15
c) 1 1/2x(2 1/4-1 5/8)+(3/4)^2
3. Oblicz
a) 4/5:3
b) 15/16:6
c) 1 2/9:11
d) 2 4/5:7
4. Oblicz
a) 5+2 2/5x3/4
b) 1/14:1 1/7
5. Oblicz
(3/7-1/3):(1+1/3)
6. Wykonaj dzielenie
a) 1 1/7: 1/14
b) 1/14:1 1/7
7. Oblicz
a) 18x4 2/3
b) 1 1/2x 2 2/3
c) 2 1/7: 12
d) 7 1/3:1 2/9
8. Wskaż wynik działania 3 1/9x2 1/3
A. 3/4 B.27/196 C.4/3 D. 196/27
9. Oblicz. Wynik przestaw w najprostszej postaci.
a) 5/9+1/6
b) 3 3/8+1 7/12
c) 7/10-3/8
d) 4 1/10-2 3/4
e) 1 1/7x5
f) 4/5:3
Szczegółowe wyjaśnienie:
