INTEGER DIVISION

Definition :

Integers are the set of whole numbers and their opposites.

The sign of an integer is positive if the number is greater than zero,

and the sign is negative if the number is less than zero.

The set of all integes represented by the set {... -4, -3, -2, -1, 0, 1, 2, 3, 4...}

NEGATIVE INTEGERS:{. . . -4, -3, -2, -1}

POSITIVE INTEGERS: {1, 2, 3, 4 ...}

{0} IS NEITHER POSITIVE NOR NEGATIVE, NEUTRAL

DIVISION RULE

  1. The quotient of two integers with same sign is positive
  2. The quotient of two integers with opposite signs is negative

Division and multiplication are opposite operations.

LOOK FOR THE PATTERN ON THE NEXT EXAMPLE;

 

MULTIPLICATION
RELATED DIVISION EQUATIONS
(-6)(3) = -18 -18÷3=-6 -18÷(-6)=3
(6)(-3)=-18 -18÷(-3)=6 -18÷6=-3
(-6)(-3) = 18 18÷(-3) =-6 18÷(-6) =-3

EXAMPLE 1

INTEGERS THE QUOTIENT THE RULES
(40) ÷ 5 +8 RULE 1
-40) ÷ (-5) +8 RULE 1
(-40) ÷ 5 -8 RULE 2
40 ÷ (-5) -8 RULE 2
144 ÷ 12 12 RULE 1
(-144) ÷ (-12) 12 RULE 1
(-144) ÷ 12 -12 RULE 2
144 ÷ -12 -12 RULE 2
     

 

FROM THE ABOVE EXAMPLE, WE SAW THAT DIVIDING TWO SAME SIGN INTEGERS GIVES POSITIVE, AND TWO DIFFERENT SIGN INTEGERS GIVE NEGATIVE NO MATTER THE ORDERS ARE. AT THE SAME TIME, LIKE WE ARE DOING MULTIPLICATION, WE MULTIPLY TWO NUMBERS AT A TIME, WE WILL SHOW THIS ON EXAMPLE 2.

EXAMPLE 2

INTEGERS
THE QUOTIENT RULES
(100) ÷ 5 ÷ 2 (100 ÷ 5)÷ 2 RULE 1
(-100) ÷ (-5) ÷ (-2) (-100 ÷ -5) ÷ -2 RULE 1 AND RULE 2
(-100) ÷ 5 ÷ 2 (-100 ÷ 5) ÷ 2 RULE 2 AND RULE 2
(-100 ) ÷ (-5) ÷ 2 (-100 ÷ -5) ÷ 2 RULE 1 AND RULE 1
(-100) ÷ (-5) ÷ -2 (-100 ÷ -5) ÷ -2 RULE 1 AND RULE 2

TEST YOURSELF