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4.3 Commutative Property (Additeol commutat, now that 3 +5=5+3%3D8,that is, the whole numbers can be added in any order. In, ber words, addition is commutative for whole numbers., IS, an we say the same for integers also?, e have 5+ (-6) =-1 and (- 6) + 5 = -1, re the following equal?, ) (-8) + (-9) and (-9) + (- 8), - 23) + 32 and 32 + (- 23), -45) +0 and 0 + (- 45), Try this with five other pairs of integers. Do you find any pair of integers for which the, ums are different when the order is changed? Certainly not. We say that addition is, ommutative for integers., general, for any two integers a and b, we can say, a + b = b+a, We know that subtraction is not commutative for whole numbers. Is it commutative a 12 t, for integers?, Consider the integers 5 and (-3)., Is 5-(-3) the same as (-3)-5? No, because 5-(-3) = 5 +3 = 8, and (-3) - 5, =- 3 - 5 = - 8., Take atleast five different pairs of integers and check this., We conclude that subtraction is not commutative for integers., 3.4 Associative Property 61ny $9611 99 g, Observe the following examples:, Consider the integers -3,-2 and-5., ook at (-5) + [(-3) + (-2)] and [(-5)+(-3)]+(-2)., n the first sum (-3) and (-2) are grouped together and in the second (-5) and (-3), are grouped together. We will check whether we get different results., (-3) +(-2), (-2), (-5) +(-3), -10, -5, -10, -8, of, of, (-5)+[(-3) +(-2)], [(-5) + (-3)]+(-2)