Part 2, Chapter 1, Algebra 1

Service Description

Grandma's Place of Natural Learning is continuing Chapter 1 of Algebra 1 Quoting, "We had learned all of this n arithmetic, so we had no trouble managing the hotel's brisk business. However, occasionally Recordis would become confused. One weekend he got the cards for Saturday and Sunday mixed up. "I know that six guests checked in one day, and two checked in the other day, but I can't remember whether it was six on Saturday and two on Sunday or two on Saturday and six on Sunday. So, I don't know if the total number of guests that checked in was 2+6 or 6+2. We'll have to call them all to find out when they checked in." "What difference does it make?" the professor said, looking up from her work with her latest special research project. "When you add two numbers, it doesn't make any difference which order you add them in (That is the rule to make a notation of). We know that 2+6=8, and we also know that 6+2=8, so we're sure that 8 guests checked in over the weekend." "That worked out lucky for us this time," Recordis sighed in relief. "It wasn't luck!" the professor insisted. "If you add 'any' two numbers together, the order doesn't matter." She tried some examples: 3+5=8 5+3=8 16+10=26 10+16=26 9+12=21 12+9=21 1+9=10 9+1=10 Recordis could see that this rule would save a little bit of work, so he wrote it in the notebook in which he recorded significant things. He called this rule the "order-doesn't-make-a-difference property of addition." ("The formal name is the 'commutative' property"). The king joined the discussion with a cautionary note. "How do we know that this property is true for every pair of numbers?" he asked. "We 've already checked it for five pairs of numbers," Recordis said. "Isn't that enough to satisfy you?" Although Recordis had been skeptical of this new property at first, it only took a few examples to convince him that the property was absolutely true. "We could check to make sure that it is true for every possible pair of numbers," the professor said. "Then we'd be absolutely sure." Recordis grumbled that this sounded like a lot of work, but he began to list all of the numbers. 1,2,3,4,5,6,7,8,9,10,11,12,... "By the way ,how many numbers are there?" he asked." (We will do more of this chapter in another lesson.)