Åk 6–9

English/فارسی
 8.8 Exercises – Mathematical Rules
1. Calculate
 Ex. 5 + 12 ÷ 4 Answer: 5 + 3 = 8 a) 5 · 3 + 7 b) 6 + 2 · 9 c) 7 + 2 · 32 d) 15 - 24 ÷ 23 e) 45 + 53 ÷ 52

2. Use the communicative law for the following calculations.
 Ex. 10 · 3 · 4 Answer: 10 · 12 = 120 a) 4 · 3 · 5 b) 4 + 7 + 6 c) 9 · 2 · 8 d) 5 + 4 + 5 + 8 e) 8 + 3 + 2 + 5 f) 5 + 3 + 4 + 7 g) 32 + 26 + 18 + 34 h) 5 · 4 · 8 i) 132 + 126 + 118 + 134 j) 4 · 7 · 25

3. Use the distributive law for the following calculations.
 Ex. 6 · 38 = 6(30 + 8) Answer: 180 + 48 = 228 a) 9 · 8 = 9(5 + 3) b) 7 · 12 = 7(10 + 2) c) 9(10 - 2) d) 5 · 43 = 5(40 + 3) e) 6 · 15 = 6(20 - 5) f) 4 · 75 = 4(100 - 25) g) 5 · 39 = 5(40 - 1) h) 5 · 39 = 5(30 + 9) i) 3 · 147 = 3(100 + 40 + 7) j) 8 · 396 = 8(300 + 90 + 6)

4. Use the rules for square roots in order to calculate the square roots.
 Ex. 82 = (6 + 2)2 Answer: 36 + 24 + 4 = 64 a) 72 = (2 + 5)2 b) 72 = (10 - 3)2 c) 92 = (7 + 2)2 d) 92 = (10 - 1)2 e) 92 = (4 + 5)2 f) 82 = (10 - 2)2 g) 122 = (10 + 2)2 h) 152 = (10 + 5)2 i) 322 = (30 + 2)2 j) 482 = (40 + 8)2

5. Use the difference of squares to calculate the following products.
 Ex. 6 · 2 = (4 + 2)(4 - 2) = 42 - 22 Answer: 16 - 4 = 12 a) 10 · 2 = (6 + 4)(6 - 4) = 62 - 42 b) 13 · 3 = (8 + 5)(8 - 5) = 82 - 52 c) 7 · 13 = (10 - 3)(10 + 3) = 102 - 32 d) 6 · 16 = (11 - 5)(11 + 5) = 112 - 52 e) 32 · 28 = (30 + 2)(30 - 2) = 302 - 22 f) 43 · 57 = (50 - 7)(50 + 7) = 502 - 72 g) 34 · 46 = (40 - 6)(40 + 6) = 402 - 62 h) 82 · 78 = (80 + 2)(80 - 2) = 802 - 22 i) 512 · 488 = (500 + 12)(500 - 12) = 5002 - 122 j) 315 · 285 = (300 - 15)(300 + 15) = 3002 - 152