Transcript Document
Welcome to MM204! Unit 3 Seminar To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here MM204 Unit 3 Seminar Agenda • Write repeated multiplication in exponential form • Evaluate numerical expressions containing exponents • Simplify numerical expressions containing addition, subtraction, multiplication, division, and exponents by correctly using the order of operations • Simplify numerical expressions using the distributive property Variables • A variable is a letter that represents an unknown amount. • Example: t would represent time a, b, c, d, x, y, etc. could all be variables. Exponents • Used to express repeated multiplication. • Example: The long notation would look like this: 2 * 2 * 2 * 2 which equals 16; our special shorthand would be 2^4 and is read as two to the power of four. • In this expression: 2^4 two to the power of four ‘2’ is the base ‘4’ is the actual exponent or power • Note: On the discussion board and in the chat dialogue we must use the caret symbol, which is ‘shift 6’ to stand for ‘to the power of’. For our Word project we will use the superscript formatting. • We will also deal with exponents that contain variables for the base. Example: Write x * x * x * x in exponential notation. Since we are multiplying x by itself 4 times, we would express this expression as x^4 This would be our final answer since we don’t know the value of x. What do we do if the base is negative? • When evaluating an exponent with a negative non-variable base the following statements are true as long as the negative sign is within parentheses: -if the exponent is even, the term will be positive - if the exponent is odd the term will be negative. Example • Example: Evaluate (-2)^6 = (-2)(-2)(-2)(-2)(-2)(-2) = 64 Even power; positive results. You try one: Everyone: Evaluate (-4)^3 One more note • Be careful where the negative sign is (-2)^4 is very different from -2^4. (-2)^4 = (-2)(-2)(-2)(-2) = 16 But -2^4 = - (2)(2)(2)(2) = -16 Order of Operations 1) Parentheses: Perform all operations on any terms within parentheses. 2) Exponents: Evaluate all exponents. 3) Multiplication/Division performed in order from left to right as they appear in the expression. 4) Addition/Subtraction performed in order from left to right as they appear in the expression. Examples • Evaluate 6 – 3^2 * 6 + 4 • Evaluate (1/4) / (2/3) + 11 * (1/6) Distributive Property • 2 ( x + 3) = 2*x + 2*3 = 2x + 6 • (9 – x)*11 = 11*9 – 11*x = 99 – 11x Be sure to “distribute” the number outside the parenthesis to all of the terms inside the parenthesis. Think of the numbers in the parenthesis like siblings, could you give one sibling something without giving the other one the same exact thing (without one getting upset)? Example • Multiply 4(x + 3y) Since we don’t know the values for either x or y then we cannot add those terms together so we must apply the distributive property. = 4(x) + 4(3y) = 4x + 12y This is our final answer as again, we don’t know the values for x or y so we cannot further simplify nor combine those terms. More examples • Example: Multiply - 2(3x^2 – 4x + 3) • We will still apply the distributive property, but this time we apply it to all three terms within the parentheses. = (-2)(3x^2) + (-2)(-4x) + (-2)(3) = -6x^2 + 8x – 6 • • • • Example: Evaluate -5(a – 2b) Evaluate (y/3)(3y – 4x – 6) Evaluate -3(2x + 3y – 5) • Questions?