CHAPTER 1 KNOWING OUR NUMBERS PART 2 Multiplication

CHAPTER: 1 KNOWING OUR NUMBERS - PART 2 Multiplication of Integers

We have learnt in the previous classes that multiplication is simply a process of repeated addition. Illustrations: a) 5 x 4= 5+5+5+5 =20 b) (-3)x 3 = (-3)+(-3)= -9 c) (-4) x 2= (-4) + (-4) = -8

IMPORTANT POINTS TO REMEMBER I. The product of two positive (+ve) integers is always a positive(+ve) integer. i. e. positive integer x positive integer = positive integer e. g. 2 x 2 = 4 always and it will never be -4. ii. The product of one positive (+ve) integer and one negative(-ve) integer is always a negative(-ve) integer. i. e. Negative integer x positive integer = Negative integer Positive integer x Negative integer = Negative integer e. g. -2 x 4 = -8 or 2 x (-4) = 8 iii. The product of two negative (-ve) integers is a positive integer. i. e Negative integer x Negative integer = positive integer e. g (-2) x (-2) = 4

PROPERTIES OF MULTIPLICATION OF INTEGERS 1. Closure property of Multiplication: Multiplication of integers obeys the closure property. If a and b are integers , then a x b is also an integer. Illustration: If a=4 and b = -3 , (both are integers). then a x b = 4 x (-3) = -12 which is also an integer. 2. Commutative Property of Multiplication: The product of two integers remains the same if their positions are interchanged. If a and b are integers then axb=bxa Illustration: (-4) x 3 = -12, 3 x (-4) = -12 Therefore, (-4) x 3 = 3 x (-4) Therefore a x b = b x a

3. Associative property of Multiplication: The product of three or more integers remains the same irrespective of the order In which they are multiplied. If a , b and c are three integers then (a x b) x c = a x (b x c) Illustration: (-3 x 4 ) x 5 = -12 x 5 = -60 (-3) x (4 x 5) = (-3) x 20 = -60 Therefore (-3 x 4) x 5 = (-3) x (4 x 5) Therefore ( a x b ) x c = a x (b x c) 4. Multiplicative Identity : The product of any integer with 1 is the integer itself. If a is any integer then a x 1 = a = 1 x a. Illustration: (-4) x 1 = -4 = 1 x (-4)

5. Zero property of Multiplication: The product of any integer with zero is always zero i. e if a is any integer than a x 0= a Illustration (-4) x 0 = 0 and 0 x (-4) = 0 6. Distributive property of multiplication: Product of an integer with the sum of two other integers is equal to sum of the products of the first integer with the other two integers. i. e if a, b and c are integers than a x (b x c) = a x b + a x c Illustration 3 x(4 +6) ( 3 x 4 ) +(3 x 6) =3 x 10 = 12 + 18 = 30 =30 Therefore 3 x (4 + 6) = (3 x 4) + (3 x 6) Therefore a x (b + c) = a x b + a x c

TRY IT YOURSELF: a)Multiply: i) (-5) x (-7)=35 ii) 9 x(-4) = - 36 b)Find the value using properties of multiplication of integers 4394 x 99 - ( - 4394) Solution: = 4394 x 99 + 4394 =4394 x 99 + 4394 x 1 ( Identity property) = 4394 x (99 + 1) (Distributive property ) = 4394 x( 100) = 439400

TRY IT YOURSELF: 1) Multiply: a) (-63) x (-7) b) (-7) x (15) 2) Find , using properties of multiplication: a) 1398 x 99 - (-1398) b) 7084 x 99 +7084