Summary - ECONOMIC250math

-have different purposes: Ø { 3 * [ 5 - ( 6 : 2 ) ] + 10 ]= 16→Here they are needed for grouping items from each other and serves a clarity purpose. Ø ( 8 ) ( 3 ) ( 4 ) = 96→Here they are used to indicate multiplication. Ø 2 * ( 8 + 3 ) = 22 Here they indicate the order in which a series of operations should be carried out. Ø → Here they are used to indicate the independent variable. Independent variable is x. Powers -show how many times a number must be multiplied by each other ex. 33 = 27, which implies 3 x 3 x 3 Variables and letters -a given symbol (letter) for unknown quantity ex. (x) Square root (√) -the inverse of the square of a number ex. 32 = 9 → √9 =3 Note: but Addition -if all terms in equation have the same sign, the answer is the sum of the absolute values of terms with the appropriate sign ex. 6 + 4 + 5 + 11 = 26 - 2 - 15 - 5 - 10= - 32 Subtraction -if terms in equation have different signs, the answer is sum of positive terms minus absolute value of negative terms, and the sign of the answer is the sign of terms which absolute value is the largest ex. - 7 + 9 - 12 - 14 - 3 + 8 + 3 = ( 9 + 8 + 3 ) - ( 7 + 12 + 14 + 3 ) = 20 - 36 Ø Symbols ex. 2x + 3y + 4z + 4x - y - z = 6x + 2y + z ex. b a - y x = b y a y b x × × − × , where b and y can both be not equal to zero Ø Number and symbols ex. 1 + 2x - 4 - 5x = - 3 - 7x Essential Mathematics for Economics and Business b Multiplication/ Division→ outcome of sign is dependent on amount of negative signs of the quantities multiplied/ divided by each other (uneven number: negative outcome, even number: positive outcome) A x B, (A•B), (A*B), (AB) A times B (the product of A and B) B A , (A/B) A divided by B Ø Numbers ex. 4 x ( - 3 ) x 5 / ( - 6 ) = 10 (even negative terms cancel each other out) ex. - 8 x 6 / ( - 4 ) x ( - 2 ) = - 24 (uneven negative terms result in a negative answer) Ø Symbols Ex.(x + y)² = (x + y)(x + y) = x · x + yx + xy + yy = x ²+ 2xy + y² Ex. 2x/2 = x Ex. b y a x y x b a × × × = , where b and y cannot be equal to zero Ex. b x a y x y a b × × = / / , where b, x and y cannot be equal to zero Ø Other important identities Ø (x − y)² = x ²− 2xy + y² Ø (x + y)(x − y) = x ²− y² Ø Fractions • Please note that while dividing, the denominator cannot be equal to zero! 0 5 11 1 2 = + + − x x x x = 1 → because only zero divided by any number is zero → substitute x into the denominator to check that it does not equal zero Equations and inequalities Linear equations • An equation is defined as an x-dependent mathematical expression Example: 7x + 3 = 10 7x = 7 x = 1 • Often we compactly denote an equation in the form f(x) Example: f(x) = 7x + 3 The general form of equation is