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)
 
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) ·
 
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)
 
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