Lesson 1.1b Notesheet: Evaluate and Simplify Expressions Translate an English Phrase to an Algebraic Expression (Ref: OpenStax Elementary Algebra: Page 34) The result of the four Math Operation: sum: result of an addition Sum of a plus b a + b difference: result of a subtraction Difference of a minus b a - b product: result of a multiplication Product of a times b a ∙ b quotient: result of a division Quotient of a divided by b a / b Translate English phrases into algebraic expressions: (Ref: OpenStax page 39) ⓐ four t∗∗∗∗imes the sum of p and q. _ _ ⓑ the sum of four times p and q. _ _ 163. the difference of 14 and 9 164. __ _ 165. the product of 9 and 7 _ _ 167. the quotient of 36 and 9 _ _ 169. the sum of 8x and 3x _ _ 171. the quotient of y and 3 _ _ 173. eight times the difference of y and nine _ _ 174. seven times the difference of y and one _ _ 175. Eric has rock and classical CDs in his car. The number of rock CDs is 3 more than the two times the number of classical CDs. Let c represent the number of classical CDs. Write an expression for the number of rock CDs. _ _ 176. The number of girls in a second-grade class is 4 less than the two times the number of boys. Let b represent the number of boys. Write an expression for the number of girls. _ _ 177. Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies. _ _ 178. Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives. _ _ Algebraic Properties Notes: Notes: Simplify the following 1. 2(x + 3) 2. -(x - 3) 3. -6(4 - y) _ _ _ _ _ _ 4. 3x(x + 2) 5. -2x(y - 4) 6. (4 - x)(-y) _ _ _ _ _ _ 7. (x)(x + 3) 8. -(-x - 9) -y 9. 2(3 - y) -x _ _ _ _ _ _ Like-Terms – terms in an expression that have the same variables and exponents and therefore can be added or subtracted to yield a different coefficient. Examples: 1x+2x = 3x, x+x = 2x, 2axy2+3axy2 = 5axy2 In the following exercises, identify the like terms. 145. x3, 8x, 14, 8y, 5, 8x3 _ _ _ _ _ _ 146. 3w2, 6z, 1, 4z, 9, w2 _ _ _ _ _ _ Notes: Simplify the following expressions by combining like terms.(Ref: OpenStax page 39) _ 11y _ _ 10u+3 _ _ 10d+11 _ _ 22a+-2 _ _ _ _ _ _ _