Exercise 6 Page 488

Let's first look at three examples to see if we can spot any pattern. 4* 5=20 6* 3=18 10* 7=70 We notice that each product is an even integer. We will now show that this is true for all products of an even and an odd integer. An even integer can be written as 2n, where n is an integer. An odd integer we can wríte as 2m+1, where m is an integer. Thus, we can write the product as follows.

2n* (2m+1) If we distribute the n, we get the following. 2n* (2m+1)=2(2mn+n) The term (2mn+n) is an integer which we can call p. We can then write the product. 2p Note that this must be an an even integer. Therefore the product of any even and any odd integer is a even integer.