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It may be noted that: MULTIPLICATION OF WHOLE NUMBERS
Rowwise sum= (9 + 2 + 7) = (4 + 6 + 8) = (5 + 10 + 3) = 18.
Columnwise sum= (9 + 4 + 5) = (2 + 6 + 10) = (7 + 8 + 3) = 18. Let us consider 4 bundles, each consisting of 3 sticks.
Diagonalwise sum= (9 + 6 + 3) = (7 + 6 + 5) = 18. Total number of sticks
=3 + 3 + 3 + 3 = 12.
SUBTRACTION IN WHOLE NUMBERS Also, we may write:
total number of sticks
The operation of subtraction ts an inverse process of addition. = 4 times 3, written as 4 x 3 .
(14+9=23) = {(23-9)=14 and (23-14)=9}. .’. 4 × 3 = 12.
Again, consider 6 packets of 5 balls each.
PROPERTIES OF SUBTRACTION Total number of balls
= 5 + 5 + 5 + 5 + 5 + 5 = 30.
(i) If a and b are two whole numbers such that a > b or a = b then a - b ts a whole number; Also, we may write:
otherwise, subtraction ts not possible in whole numbers. total number of balls
EXAMPLE: (i) If we subtract two equal whole numbers, we get the whole number 0; = 6 times 5, written as 6 × 5.
e.g., (8 - 8) = 0, (6 - 6) = 0, (25 -25) = 0, etc. Therefore, 6 × 5 = 30.
(ii) If we subtract a smaller whole number from a larger one, we always get a whole number;
e.g., (16 -9) = 7, (37 -8) = 29, (23 -16) = 7, etc. It follows that multiplication is repeated addition.
(iii) Clearly, we cannot subtract 18 from 13; If the numbers are small, we can perform the operation of multiplication mentally as above and find the product.
i.g., (13 -18) is not defined in whole numbers. If the numbers are large, we multiply them using the-multiplication tables about which you have learnt
earlier.
(iv) For any two whole numbers a and b, (a - b) = (b - a).
However, we now list the various properties of multiplication on whole numbers. These properties will help us
EXAMPLE: (i) (8-5) = 3 but (5 - 8) is not defined in whole numbers. in finding easily the products of numbers, however large they may be.
(ii) (26 - 9) = 17 but (9 -26) is not defined in whole numbers.
(iii) For any whole number a, we have: (a -0) = a but (0 -a) PROPERTIES OF MULTIPLICATION OF WHOLE NUMBERS
is not defined in whole numbers.
(i) CLOSURE PROPERTY if a and b are whole numbers, then (a × b) is also a whole number.
EXAMPLE: (i) (9 - 0) = 9 but (0 -9) is not defined in whole numbers.
(ii) (24 -0) = 24 but (0 -24) is not defined in whole numbers. EXAMPLE: Let us take a few pairs of whole numbers and check in each case whether their product is a
whole number.
(iv) If a, b, c are any three whole numbers, then in general (a- b} - c -:t:- a One Another Product Is the product
Whole Number Whole Number a whole number?
EXAMPLE: Consider the numbers 8, 4 and 2. 9 8 9 × 8 = 72 Yes
(8 -4) -2 = ( 4 -2} = 2.
8 - ( 4 - 2) = ( 8 - 2) = 6. 12 7 12 × 7 = 84 Yes
(8 - 4)- 2 -:t:- 8 - (4 - 2). 16 10 16 × 10 = 160 Yes
Thus. we see that if we multiply two whole numbers, the product is also a whole number .
(v) If a, b, c are whole numbers such that a - b = c, then b + c = a.
(ii) COMMUTATIVE LAW if a and b are any two whole numbers then (a × b) = (b × a).
EXAMPLE: (i) 16 - 9 = 7 => 9 + 7 = 16.
(ii) 23 -8 = 15 => 8 + 15 = 23. (i) 7 × 5 = 35 and 5 × 7 = 35.
Is (7 × 5) = (5 × 7)? Yes.
OBSERVING PATTERNS (ii) 19 × 12 = 228 and 12 ×19 = 228.

Is (19 × 12) = (12 × 19)? Yes .
Study the following:
(i) 456-99 = 456-100 +l = (457-100) = 357. In general, commutative law of multi plication holds in whole numbers
(ii) 4962 -999 = 4962 -1000 + 1 = (4963-1000) = 3963.