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(iii) MULTIPLICATIVE PROPERTY OF ZERO For every whole number a, we have SOLVED EXAMPLES
(a × 0) = (0 × a) = 0.
EXAMPLE 1. Multiply 197 by 54.
EXAMPLE: (i) 9 × 0 = 0 × 9 = 0 (ii) 37 × 0 = 0 × 37 = 0 SOLUTION. We have:
(iii) 2386 × 0 = 0 × 2386 = 0 197 × 54 = 197 × (50 + 4)
= 197 × 50 + 197 × 4 (by distributi ve law )
(iv) MULTIPLICATIVE PROPERTY OF 1 For any whole number a we have: (a × 1) = (1 × a) = a. = 9850 + 788 = 10638.
= (1000 × 2995) = 2995000.

EXAMPLE: (i) 8 × 1 = 1 × 8 = 8 (ii) 76 × 1 = 1 × 76 = 76
(iii) 2345 × 1 = 1 × 2345 = 2345 EXAMPLE: Find the product 37256 ×25 × 40.
SOLUTION: We have
(v) ASSOCIATIVE LAW if a, b, care any whole numbers, then (ax b) x c =ax (bx c). 37256 × 25 × 40 = 37256 × (25 × 40)
= 37256 × 1000 = 37256000.
EXAMPLE: Take the whole numbers 9, 7 and 10.
(9 × 7) × 10 = 63× 10 = 630. EXAMPLE 10. Find each of the following products:
9 × (7 ×10) = 9 × 70 = 630. (i) 30674 × 9 (ii) 4578 × 99 (iii) 23756 × 999
(9 × 7) × 10 = 9 × (7 × 10). SOLUTION We have:
(i) 30674 × 9 = 30674 × (10 - 1)

(vi) DISTRIBUTIVE LAW OF MULTIPLICATION OVER ADDITION For any whole numbers a. b, c we = (30674 ×10) - (30674 × 1)
have: a × (b + c) = (a × b) + (a × c). = (306740 - 30674) = 276066.
(ii) 4578 × 99 = 4578 × (100 -1)
EXAMPLE: Consider the whole numbers 16, 9 and 8. = (4578 × 100) - (4578 × 1)
16 × (9 + 8) = (16 ×17) = 272. = (457800 - 4578) = 453222
(16 × 9) + (16 × 8) = (144 + 128) = 272. (iii) 23756 × 999 = 23756 × (1000 - 1)
16 × (9 + 8) = (16 × 9) + (16 × 8). = (23756 × 1000) - (23756 × 1)
(vii) DISTRIBUTIVE LAW OF MULTIPLICATION OVER SUBTRACTION For any whole numbers a, b, c = (23756000 -23756) = 23732244.
we have: a × (b - c) =(a × b)- (a × c).
DIVISION IN WHOLE NUMBERS

EXAMPLE: Consider the whole numbers 11, 6 and 4.
11 × (6 - 4) = (11 × 2) = 22. Division is the inverse operation of multiplication.
(11 × 6) - (11 × 4) = (66 - 44) = 22. Let a and b be two whole numbers. Dividing a by b means finding a whole number c such that b × c = a and we
11 × (6 - 4) = (11 × 6) - (11 × 4). write, a + b = c.
Thus, a + b = c => b = c => a = b × c.

EXAMPLE: Dividing 48 by 8 is the same as finding a whole number which when multiplied by 8 gives 48.
Clearly, such a number is 6, as 8 x 6 = 48.
Similarly, we have:
63 + 9 = 7, 84 + 14 = 6, etc.