Part 10, Chapter 1, Algebra 1

Service Description

"We spent the next week working on a list of properties that seemed to describe the behavior of numbers. I won't detail all of the arguing that occurred, but we finally came up withe following list: POSTULATES FOR THE NATURAL NUMBERS -Every natural number a has a successor a+1. (For example, the successor of 5 is 6, the successor f 10 is 11, and so on.) -Every natural number a(except 1) has a predecessor a=1.(The predecessor of 9 is 8, and so on.) -The natural numbers can be put in order. In other words, if a and b are two natural numbers, then either a is greater than b(written a>b), a is less than b(a<b), or a is equal to b(a=b). -The commutative (order-doesn't-make-a-difference) property of addition: a+b=b+a for any two numbers a and b. -the commutative (order-doesn't-make-a-difference) property of multiplication: axb=bxa for any two numbers a and b. -The associative (where-you-put-the-parentheses-doesn't-make-a-difference) property of addition: (a+b) +c=a+(b+c) for any three numbers a, b, and c. (This property is known as the 'associative' property of addition, because it says that it doesn't matter which numbers associate with each other.) For example, (5+4)+3=5+(4+3) (9)+3=5+(7) 12=12 -The associative (where-you-put-the-parentheses-doesn't-make-a-difference) property of multiplication: (axb)xc=ax(bxc) for any three numbers a b, and c. For example, (2x6)x4=2x(6x4) 12x4=2x24 48=48 The associative properties of addition and multiplication mean that you can leave out the parentheses in expressions such as(a+b)+c and ax(bxc) and just write a+c+c and a x b x c. " "The king realized there could be a problem if an arithmetic expression contained more than one type of operation, because we might be unsure of what order to perform the operations. To make sure everyone in the kingdom acted consistently, he issued" a proclamation explained in the last part (11) of Chapter 1. (Grandma must now move to another lesson because she has run out of room to keep going.)