part 5, Chapter 1, Algebra 1

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""I had thought that we already knew everything that it was possible ever to know about numbers," Recordis said. "After all, we do know our multiplication tables. But I can see how it will help if we can come up with behavior rules for numbers." After lunch Ms. O'Reilly gave us a very easy problem. She showed us a list of the number of hours that each hotel employee had worked that week, and we had to calculate the payroll. Since each employee was paid $10 per hour (and none of them worked overtime) it was a simple matter of multiplication to calculate the total pay. For example, John Jones ad worked 25 hours, and therefore earned 10X25=250 dollars, an Sue Smith had worked 29 hours, earning 10X29=290 dollars. "Our method of operation in this case is very clear," the professor said. She wrote out a simple rule for how to calculate pay: Look at the number of hours on the list. Then multiply by 10. "That is a very good easy-to-follow rule," Recordis agreed. "However, there must be a shorter way to write the rule." Since Recordis' job involved a lot of writing, he often suffered from writer's cramp and was always looking for ways to reduce the amount of writing he needed to do. The king suggested that we could write the expression for pay as follows: 10 times (number of hours worked) "We can shorten that further by using the multiplication sign," the professor suggested. 10X(number of hours worked) "We can just write (hours) instead of (number of hours worked)," the professor added. 10X(hours) "Good idea," Recordis agreed. "Why didn't we think of that?" "To make it even shorter, we can just use the letter "h" to stand for hours," the king suggested. 10Xh "Hold it!" Recordis objected violently. "You can't use a letter to stand for a number! Letters and numbers are fundamentally different entities. They can't be mixed, or we will end up in real trouble." "But the expression 10Xh is much shorter than 10X(number of hours worked), even though the two expressions mean exactly the same thing," the king said. "We made the expression shorter just to make things easier for you." "I have always liked things to be shorter," Recordis agreed, "but not at the expense of utter confusion!" (We have 12 more pages to cover in the next 7 days with a couple as a test. That leaves 2 pages per day which Grandma will type and enter early so she has time to start some more things. 19 Chapters with one a week will leave it finished in spring. Keep looking for things the weekend.)