# Chapter 3

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McGill University

Mathematics & Statistics (Sci)

MATH 111

Nabil Kahouadji

Winter

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MATH 111 – Winter 2012
3: ALGEBRAIC THINKING
3.1 Variables
variable: a missing element or an unknown, as in x + 7 = 11; can represent something, as in h = height;
an element in a set, as in A U B = {x|x Є U and x Є F}; needed to solve algebra problems
ie/ At the grocery store, three purchases were made:
$7 for apple + banana
$8 for banana + kiwi
$9 for apple + kiwi
What is the cost of each fruit?
let a represent the price of an apple in $
let b represent the price of a banana in $
let k represent the price of a kiwi in $
a + b = 7 b + k = 8 a + k = 9
a + b + b + k = 15 a + 3 = 7 4 + k = 9
9 + 2b = 15 a = 4 k = 5
2b = 6
b = 3 Therefore, an apple is $4, a banana is $3 and a kiwi in $5.
3.2 Equations
addition and multiplication property of equality: for any numbers a, b and c, if a = b, then a + c = b + c;
for any numbers a, b and c, if a = b, then ac = bc; what you do to one side you must do to the other
cancellation properties of equality: for any numbers a, b and c, if a + c = b + c, then a = b; for any
numbers a, b and c with c ≠ 0, if ac = bc then a = b; what you take away from one side you must take
away from the other
addition and subtraction property of equations: for any numbers a, b, c and d, if a = b and c =d th

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