This is the full solutions for the problems and exercises about operations on integers, order of operations, and PEMDAS rules.

Practice Exercises 1

a.) 12 + (-4) = 8
b.) (-9) + 3 = – 6
c.) (-7) + (- 5) = -12
d.) 8 + 3 + (-11) = (8+3) + (-11) = (11) + (-11) = 0
e.) 6 + (-10) + (-2) = 6 + (-10 + -2) = 6 + (-12) = -6

Practice Exercises 2

a.) 3 – 5 = (3) + (-5) = -2
b.) -9 – 4 = (-9) + (-4) = -13
c.) (-7) – (- 8) = (-7) + (8) = 1
d.) – 2 – 6 = (-2) + (-6) = -8
e.) 1 – (-10) = (1) + (10) = 11

Practice Exercises 3

a.) 4 × (- 5) = -20
b.) (-2) × (- 4) = 8
c.) 6 × (- 3) = -18
d.) 8 × 2 × (-1) = -16
e.) (-3) × (2) × (-7) = 42

Practice Exercises 4
a.)-20 ÷ 4 = -5
b.) 18 ÷ (- 6) = -3
c.) (-16) ÷ (- 2) = 8
d.) 0 ÷ 8 = 0
e.) 9 ÷ 3 = 3

1.) 2 + 3 × 5

2 + 3 × 5
= 2 + 15
= 17

2.) (2 + 3) × 5

(2 + 3) × 5 = (5) × 5
= 25

3.) 3 × (-3) + 4 × (-2)

= 3× (-3) + 4× (-2)
= (-9) + (-8)
= -17

4.) 3(5^2 – 8)

3(5 × 5 – 8)
= 3(25 – 8)
= 3(17)
= 51

5.)  2(5 – 8)^2
= 2(-3)^2
= 2(-3 × -3)
= 2(9)
= 18

6.) 16 + (-4) + 12 + (-8 x 3)

= 16 + (-4) + 12 + (-24)
= (16 + 12) + (-4 + -24)
= (28) + (-28)
= 0

7.) (3^2 + 2^2)^2 = ?

= (3 × 3 +2× 2)^2
= (9 + 4)^2
= (13)^2
= 13 × 13
= 169

8.) 6 + 3 × 2 – 5 = ?

= 6 + (3 × 2) – 5
= 6 + 6 – 5
= 12 – 5
= 7

9.) 8 – 12(3 – 4) + (-5 × 2)

= 8 – 12(3 – 4) + (-5 × 2)
= 8 – 12(-1) + (-10)
= 8 – (-12) + (-10)
= 20 + (-10)
= 10

10.) 7 + 3 × (-5) – 9 / 3 = ?

= 7 + 3 × (-5) – 9/3
= 7 + (-15) – 3
= 7 + (-18)
= -11