Part 4 ,Chapter1, Algebra1

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Grandma's Place of Natural Learning was not sure if you could get the typing under the picture so easy, but Grandma decided you or can tell her and she will type another lesson for it. Therefore, going onto the next page, the book begins to say "We tried some examples to see what happened when two even numbers were added together:2+4=6(even),10+8=18(even), 12+24=36(even),100+48=148(even),2+62=64(even),12+12=24(even) " I see a pattern!" the professor said triumphantly. "It looks as though, whenever you add together two even numbers, the result is another even number!" "I wouldn't bet the kingdom on it, though," Recordis said. "We may have been lucky with these examples." The ferry loader agreed that, as far as he could remember, adding together two even numbers had always produced another even number. "If that rule really is true, then I'm sure that another rule is true," Recordis said. "If you add together two odd numbers, the result must be an odd number." We tried some examples: 3+5=8(even),7+11=18(even)15+31=46(even),1+9=10(even),13+13=26(even),1+3=4(even). "Your suggested rule clearly is wrong!" the professor told Recordis. "In fact, it looks as if the opposite rule is true: Whenever you add together two odd numbers, the result is an even number." "Can you ever get an odd number for the answer when you add together two numbers?" Recordis asked in puzzlement. "Try adding one odd number and one even number," the king suggested. 3+6=9(odd), 15+98=113(odd),36+5=41(odd),1,983+1,984=3,967(odd),1+2=3(odd),7+8=15(odd) Recordis entered these seemingly correct rules in his notebook: Rules for Adding Odd and Even Numbers -If you add together two even numbers, the result is an even number. -If you add together two odd numbers, the result is an even number. -If you add together one even number and one odd number, the result is an odd number. "These rules will help a lot!" the grateful ferry loader said when it was time to return to work. "I am still worried, though," the king said, "We have not been able to 'prove' that these rules work. Suppose that they work all the time except for one exception. And if that exceptional situation happens to occur one day, and the ferry loader follows the rules, then the ferry will be unbalanced, and it will tip over. That would be disastrous.""