INTEGERSIntegers form a bigger collection ofnumbers which contains wholenumbers and negative numbers.
Properties of addition and subtraction• Integers are closed under addition and subtraction both. That is, a + b and a – b are again integers, where a and b are any integers.• Addition is commutative for integers, i.e. a +b = b + a for all integers a and b.• Addition is associative for integers, i.e. (a+b)+c = a+(b+c) for all integers a, b and c.• Integer 0 is the identity under addition. That is, a+0= 0 + a = a for every integer a.
Addition of Integers• Rule 1 : The sum of two negative integers is obtained by taking sum of the numerical value of the addends.• Example:• i) (+4)+(+6)=+(4+6)=(+10)• ii) (+123)+(+97)=+(123+97)=(220)
integersRule2: The sum of two negative integers is obtained by giving the negative integer sign to the sum of their numerical values.Example:i) (-6)+(-2)= -(6+2)= -8ii) (-70)+(-3 3)= -(70+33)= -103
integers• Rule3:• To add a positive and a negative integer, we find the difference between their numerical values and give the sign of the integer with more numerical value.• (-54) + (+39) = -(54-39) = -15
Subtraction of Integers• Rule: For any two integers a and b• a – b = a+(-b) = a+ (additive inverse of b)• Example:• (i) (+5)-(+8)=(+5)+(additive inverse of +8)• = (+5) + (-8) = -3• (ii) (-7) + (additive inverse of +6)• = (-7)+(-6) = -(7+6) = -13
Multiplication of integers• Product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer. E.G., -2 x 7 = 14 and -3 x -8 = 24• Product of even number of negative integers is positive, whereas the product of odd number of negative integers is negative.• E.G., -2 x -3 x -4 x -5 = 120, -2 x -3 x -4 = -24
Properties of Multiplication• Integers are closed under multiplication.• Multiplication is commutative for integers.• The integer 1 is the identity under multiplication, i.e. 1xa = ax1 = a for any integer a.• Multiplication is associative for integers, i.e. (axb)xc = ax(bxc) for any three integers, a, b and c.
Division of Integers• Rule 1 : The quotient of two integers with the same sign is positive integer obtained by dividing the numerical value of the dividend with the numerical value of the divisor.• E.G.,• (i) (-25) ÷(-5) = +5,• (ii) (+12) ÷(+3) = +4
integers• Rule 2: The quotient of two integers with different signs is the negative integer obtained by dividing the numerical value of the dividend with the numerical value of the divisor.• E.G.• (i) (+36) ÷(-6) = -6• (ii) (-32) ÷ (+4) = -8