Topic 1 - Basic Algebra - 2.0 BASIC ALGEBRA 2.1 Basic...

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1 2.0 BASIC ALGEBRA 2.1 Basic Algebraic Terminology, Notations & Laws Addition Like terms can be added. E.g. a + a + a = 3 x a = 3a Unlike terms cannot be added. E.g. a + b + c = a + b + c Subtraction Like terms can be subtracted. E.g. 3a - a = 2a Unlike terms cannot be subtracted. E.g. a - b - c = a - b – c Multiplication Terms which are multiplied are being written next to each other, the signs of multiplication being omitted. E.g. i). 3 x a =3a ii). a x b = ab iii). 3 x a x b = 3ab Brackets The use of brackets has the same meaning as in arithmetic. E.g. i). 3(a +b) = 3 x (a + b) = (3 x a) + (3 x b) = 3a + 3b ii). c (a +b) = c x (a + b) = c x a + c x b = ca + cb Division E.g. i). 3a 3 ÷ = 3 3 a = 3 3 a × = a
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2 ii). 2 2 2 2 b 2a b a + = = a + 2 b iii). 2 ) ( 2 2 2b 2a b a = = a + b Eg. i). 3(b +c) + 2(c +b) = 3 x b +3 x c +2 x c+ 2 x b = 3b + 3c + 2c + 2b = 5b +5c = 5(b + c) ii). 7(a +b + c) – 3a + 2(b –c) = 7a +7b +7c – 3a +2b – 2c = 7a – 3a +7b +2b +7c -2c = 4a + 9b +5c iii). 8a (b + c) + 3b (a – c) = 8ab + 8ac + 3ab – 3bc = 11ab + 8ac – 3bc Note b x a = a x b ba = ab Fractions: Addition & Subtraction E.g. i). Add together a/3 and 2a/5 15 6 15 5 5 2 3 a a a a + = + = 15 6 5 a a = 15 11 a ii). Add together a/3b and 2c/5b b c b a b c b a 15 6 15 5 5 2 3 + = + = b c a 15 6 5
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3 iii). From 3d/4 subtract 5d/7 28 20 28 21 7 5 4 3 d d d d - = - = 28 20 21 d d - = 28 d iv). b a b a b a b a b a b a 10 10 10 5 10 8 2 5 4 - + = - + = b a a a 10 10 5 8 - = b a 10 3 v). 5 ) 2 ( 4 ) ( 5 2 4 d c d c d c d c - + = - + = 20 ) 2 ( 4 20 ) ( 5 d c d c - + = 20 4 8 5 5 d c d c - = 20 13 d c Fractions: Multiplication & Division E.g. i). Multiply 2a/3 and 4b/5. 5 3 4 2 5 4 3 2 × × = × b a b a = 15 4 2 b a × × × = 15 4 2 b a × × × = 15 8 ab ii). Multiply together 3a/5, 35b/48 and 4c/9 9 4 48 35 5 3 9 4 48 35 5 3 c b a c b a × × = × × = 36 7 abc iii). Divide 24ab/25 by 16bc/35
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4 bc ab bc ab 16 35 25 24 35 16 25 24 × = ÷ = bc ab 16 35 25 24 × = c a 10 21 iv).
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