Simplification of Algebraic Expressions

Transcript

Simplification of Algebraic ExpressionsThink of simplifying as tidying up your toys. You put all the same kinds of toys together in the same box. In algebra, we do the same thing. We can only add or subtract things that are the same kind. We call these "like terms." Terms are "like terms" if they have the exact same letter. Example 1: Adding the Same Thing Imagine you run a shop that sells pencils. The letter p stands for the price of one pencil. On Monday, you sell 5 pencils, so you earn 5p. On Tuesday, you sell 3 more pencils, earning 3p. On Wednesday, you sell 10 more pencils, earning 10p. To find your total earnings, you add them up: 5p + 3p + 10p Since they all have the same letter (p), they are the same kind of thing. So, you just add the numbers: 5 + 3 + 10 = 18 Your total earnings are 18p. That's much simpler to write! Example 2: Grouping Different Things Now, let's find the perimeter (the distance around the outside) of a rectangle. Let l be for length and b be for breadth. The perimeter is: l + b + l + b Think of l as "lemons" and b as "bananas." Sort them out: Put the same fruits together. Lemons: l + l Bananas: b + b Count each group: You have 2 lemons, so you write 2l. You have 2 bananas, so you write 2b. So, the tidy, simplified expression is 2l + 2b. You can't add lemons and bananas together to get "4 lemon-bananas," so you keep them separate. In the same way, you can't add 2l and 2b because their letters are different. The Main Idea Simplifying just means: Find the terms that have the same letter ("like terms"). Group them together. Add or subtract their numbers. Keep the letter the same!