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A - Unit Notes U1 - Algebra-1.rtf

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Ryerson University
BUS 100
David Schlanger

Math Skills for Business- Full Chapters 1 U1- FullChapter-Algebra Introduction to Algebra (Chapter 3) to understand the meanings of like terms and unlike terms. Algebra is generalized arithmetic operations that use letters of the alphabet to represent known or unknown quantities. We can use y to represent a companys profit or the costs of labour. The letters used to hold the places for unknown quantities are called variables, while known quantities are called constants. Variables denote a number or quantity that may vary in some circumstances.ics, because it could be used to solve a variety of complex problems much faster than using arithmetic methods. Many problems that mathematicians could not solve previously with arithmetic methods can now be solved with algebraic methods. As well, algebra has made it possible to apply mathematics in other areas of human endeavour such as economic planning, pharmacology, medicine, and public quantity that can take the place of b is 8, because 12 + 8 =20. So 8 is the true replacement value for b. What about y + y = 15? The replacement value for the first y could be any number not more than 15. However, the replacement value we pick for the first y will determine the value for the second y. If we say, for example, that the first y is 10, then the second y must be 5. As well, if the first y is 12, the second y must be 3. The reverse is also true. Try it for yourself by picking a replacement value for the second, and Consider another example, 4x + 8 = 40. In this example, we are looking for a number when multiplied by 4 and added 8 to it will give example is very important for understanding the solution tond checking. Eventually we will find that 8 is the replacement for x. equations involving two similar variables. However, with a systematic procedure of solving equations, we can easily solve that problem without going through the throes of guessing and 4. 2t t = = 2, because the two t cancel themselves out. 3. 2 Like Terms and = = 2x, because 7 goes into 14 Unlike Terms Consider again, 12 + b = 20. A number or letter separated by theut the multiplication sign between 20 and x or x and y. 2. y y y x x = yxa term. So 12 is a term; b too is a term. Letters of the same kind in an algebraic statement or expression are called like terms. For example, b + b + c = 2b + c. The two bs are like terms, so we can carry out the operations of addition on them. 4a3 , first multiply the numbers 4)ether to get 12 from (3 Look at more examples below. eg2 2b + 3b = 5b, whatever the a 2+ 3 5 . That is, keep the base a and add the exponents. We now have 12a a a a a a = a 2a. Divide the numbers, 12 2 = 6. Then subtract the exponents when dividing, so = a a = ayThisequalsace 6t + 6t = 12t) This is now fully simplified, since the two remaining ter. Thee not . final like terms. eg 5 3t -2t = t. Note: traditionally, mathematicians do not Thisisthe answ writsame. They just wrinote: We multiplied the top numbers to get 4, thingas a xa ( 2 x 2) and 6a for adding and subtracting like terms does not apply to the number letters to mult= aiget t.or division. In fact, multiplication and division are done as is shown in the following examples.ponent 3 tells us the number of times Multiplication/Division eg 1 y y y =uld be multiplied. We multiplied the top numbers to get 1 (1 x 1 x 1) and then the bottom numbers to get 27 (3 x 3 x 3). y2 x x = x x x x = 13. 5 = 5 x 5 x 5 eg 3 t t = t eg 4 4t 6t = 125 = (4 6) (t x t) = 24t. Not 1. 26t is the same as 26 t.z = 30 3.4z8x = 48 x x
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