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McGill University
Mathematics & Statistics (Sci)
MATH 111
Nabil Kahouadji

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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