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# A - Unit Notes U1 - Algebra-1.rtf

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Ryerson University

Business

BUS 100

David Schlanger

Fall

Description

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 health.ly
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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