A. Sifat-Sifat Pengerjaan Hitung pada Bilangan
Bulat
1. Sifat Komutatif (Pertukaran)
a. Sifat komutatif pada penjumlahan
A + B = B+ A
Ex. 3+ 5 = 5 + 3
Soal
1. 4 + 5 = 5 + . . .
2. –2 + 3 = 3 + . . . . .
3. –9 + . . . = 3 + . . .
4. . . . + (–2) = . . . + 12
5. –70 + . . . = –30 + . . .
b. Sifat komutatif pada perkalian
A x B = B x A
Ex. 4
x 2 = 2 x 4
Soal
1.
10 × 5 = 5 × .
. .
2.
4 × (–10) = .
. . × 4
3.
40 × . . . =
–5 × . . .
4.
–29 × . . . =
3 × . . .
5.
. . . × (–4) =
. . . × 50
2. Sifat Asosiatif (Pengelompokan)
a. Sifat asosiatif pada penjumlahan
(A + B) + A = A+ (B+ C)
Ex. (3+2)
+ 4 = 3 + (2 + 4)
Soal
1. (2 + (–1)) + 3 = . . . + (–1 + 3)
2. (1 + 2) + (–5) = 1 + (2 + . . . . .)
3. (. . . + (–3)) + 6 = 30 + (. . . + 6)
4. (39 + . .
.) + (–10) = 39 + (–5 + (–10))
5. (–45 + 4)
+ . . . = –45 + (4 + 7)
c. Sifat asosiatif pada perkalian
(A X B) X C = A X ( B X C)
Ex. ( 2 X 3)
X 4 = 2 X ( 3 X 4)
Soal
1. (2
× 4) × 3 = 8 × . . .
2. (4
× 5) × 8 = . . . × 8 = . . .
3. (5
× (–2)) × 4 = 5 × (–2 × . . .)
4. (–3
× 2) × 8 = . . . × (2 × . . .)
5. (–4
× (–6)) × 10 = . . . × (–6 × . . .)
3. Sifat Distributif (Penyebaran)
A X ( B+ C) = (A X B) + (A X C)
A X (
B - C) = (A X B) - (A X C)
Soal
1. (4
× 17) + (4 × 3) = 4 × (17 + . . .)
2.
(–3 × 9) + (–3 × 11) = . . . . × (9 + 11)
3. (–6
× 53) – (–6 × 28) = . . . × (. . . – 28)
4. 5
× (30 – 12) = (5 × . . .) – (5 × . . .)
5. 8
× (50 – 5) = (. . . × 50) – (8 × . . .)
6. 8
× (25 + 11) = (. . . × 25) + (8 × . . .)
7.
(4 × 17) – (4 × 7) = 4 × (17 – . . .)
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Post Test 1
1.
–10 + 2 =
___ + ___
2.
29 + (–11) =
___ + ___
3.
–20 + 50 =
___ + ___
4.
24 + (–40) =
___ + ___
5.
–15 + (–25) =
___ + ___
6.
10 × 6 =
___ + ___
7.
–5 × 9
= ___ + ___
8.
15 × (–3) =
___ + ___
9.
–50 × 2 =
___ + ___
10.
–30 × (–3)
= ___ + ___
11.
(50 + (–5)) + (–3) = ___ + (–5 + ___)
12.
(___ + (–60) + ___ = 65 + (–60 + (–3))
13.
(55 + (–30)) + 6 = ___ + (___ + 6)
14.
(–39 + ___) + ___ = ___ + (32 + (–4))
15.
(45 + ___) + (–9) = ___ + (27 + ___)
16.
(2 × 6) × 4 =
___ × (6 × 4)
17.
(–3 × 2) × 5
= ___ × (2 × 5)
18.
(4 × (–5)) × 2 = ___ × (___ × ___)
19.
(–3 × (–2)) × 6 = ___ × (___ × ___)
20.
(5 × (–4)) × (–3) = ___ × (___ × ___)
21.
(3 × 63) + (3 × 17) = ___ × (___ + ___)
22.
(–5 × 21) + (–5 × 19) = ___ × (___ + ___)
23.
(–4 × 46) + (–4 × 14) = ___ × (___ + ___)
24.
5 × (20 + 12) = (___ × ___) + (___ × ___)
25.
–6 × (30 + 5) = (___ × ___) + (___ × ___)
26.
(7 × 85) – (7 × 15) = ___ × (___ – ___)
27.
(–9 × 59) – (–9 × 19) = ___ × (___ – ___)
28.
(–11 × 29) – (–11 × 18) = ___ × (___ – ___)
29.
15 × (40 – 4) = (___ × ___) – (___ × ___)
30.
–12 × (50 – 5) = (___ × ___) – (___ × ___)
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Post Test 1
1.
–10 + 2 =
___ + ___
2.
29 + (–11) =
___ + ___
3.
–20 + 50 =
___ + ___
4.
24 + (–40) =
___ + ___
5.
–15 + (–25) =
___ + ___
6.
10 × 6 =
___ + ___
7.
–5 × 9
= ___ + ___
8.
15 × (–3) =
___ + ___
9.
–50 × 2 =
___ + ___
10.
–30 × (–3)
= ___ + ___
11.
(50 + (–5)) + (–3) = ___ + (–5 + ___)
12.
(___ + (–60) + ___ = 65 + (–60 + (–3))
13.
(55 + (–30)) + 6 = ___ + (___ + 6)
14.
(–39 + ___) + ___ = ___ + (32 + (–4))
15.
(45 + ___) + (–9) = ___ + (27 + ___)
16.
(2 × 6) × 4 =
___ × (6 × 4)
17.
(–3 × 2) × 5
= ___ × (2 × 5)
18.
(4 × (–5)) × 2 = ___ × (___ × ___)
19.
(–3 × (–2)) × 6 = ___ × (___ × ___)
20.
(5 × (–4)) × (–3) = ___ × (___ × ___)
21.
(3 × 63) + (3 × 17) = ___ × (___ + ___)
22.
(–5 × 21) + (–5 × 19) = ___ × (___ + ___)
23.
(–4 × 46) + (–4 × 14) = ___ × (___ + ___)
24.
5 × (20 + 12) = (___ × ___) + (___ × ___)
25.
–6 × (30 + 5) = (___ × ___) + (___ × ___)
26.
(7 × 85) – (7 × 15) = ___ × (___ – ___)
27.
(–9 × 59) – (–9 × 19) = ___ × (___ – ___)
28.
(–11 × 29) – (–11 × 18) = ___ × (___ – ___)
29.
15 × (40 – 4) = (___ × ___) – (___ × ___)
30.
–12 × (50 – 5) = (___ × ___) – (___ × ___)
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