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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation4.13 Properties of Multiplication in Integers

 Property I: For any two integers a,b their product axb is also a integer. Examples: 2x(-3) = -6 (-3)x(-2) = 6 Property II: For any three integers a, b, and c, ax(bxc) = (axb)xc. Example: (-4)x[(-3)x5] = [(-4)x(-3)]x5 = 60 Property III: For any two integers a and b, axb = bxa. Example: 2x(-3) =3(-2) = -6 Property IV: For any integer a; ax0 = 0xa = 0. Examples: 6x0 = 0 (-7)x0 = 0 Property V: For any integer a; ax1 = 1xa = a. Examples: 1x7 = 7 1x(-8) = -8 Property VI: For any three integers a, b, and c; ax(b+c) = (axb)+(axc). Example: 2x[3+(-2)] = (2x3)+[2x(-2)] = 2 Directions: Solve the following multiplication problems. Also write at least five examples of your own for each property.
 Q 1: For any integer a; ax0 = 0xa = ________?0a1 Q 2: 5x(8+2) = _____?-5050 Q 3: 5x(-20)=____?-100100 Q 4: 50x0=______?500 Q 5: For any two integers a and b, their product axb will always be ___________.a positive integeran integera negative integer Q 6: For any integer a; ax1 = 1xa = _____?a+11a Q 7: 5x[(-6)x5] = ?-150150 Q 8: 5x[(-8)+2)=_________?-3050 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!