Transcript Document
Linear Relationships Vocabulary Multiplication Property of -1 Multiplying a number by -1 always gives you the opposite of that number -4 12 -1 -1 =4 = -12 Multiplication Property of 0 Multiplying a number by 0 always gives you ZERO 12 x 3 x -3 x 5 x 0 x 8 = 0 -4 12 0 0 =0 =0 Examples of Dimensions 1 foot 5 feet Length, Width and Height are dimensions These are examples of rectangular arrays for the product of 8. Area Model for Multiplication 4 x 3 can be represented by this rectangle because 4 x 3 = 12. See the 12 boxes? Commutative Property of Multiplication To “commute” to work means you go to work one way and you come home the other way. X Y= Y X 5x8=8x5 You will always get the same product, no matter which way you solve it. Area Model for a Right Triangle Area of a right triangle = half the area of the rectangle. 4 3 The area of this right triangle is half of the area of 4 x 3 which would be 6 square units. Associative Property of Multiplication The 3 numbers don’t switch places! Only the parentheses do! FUNNEL METHOD! ( 2 x 3) x 4 = 2 x (3 x 4) Use the 6 x 4 = 2 x 12 ORDER OF OPERATIONS! 24 = 24 Terms are numbers and/or variables which can stand alone or are separated by “+”, “-”, “x” or “ “ Examples of Terms X -y 0.5 12a Find the Terms Problem 12 a + 13 b -8 – 12b 7+8 2x – 3y Term 1 Term 2 Coefficients Coefficients are numbers which are directly in front of a variable. 3x The “3” is the coefficient! The “x” is the variable! Coefficients Problem: x 3a -y 4a + 6b List the coefficients here: Like terms – numbers and/or variables which can be combined due to their “likeness” Example 1 Example 2 Example 3 5 -4y 5.2x -3 y 4x 1.45 8.2y -3x -1 0.5y x Combining or Collecting Like terms – you can combine/collect like terms by adding them up. Example 1 Example 2 Example 3 5 -4y 5.2x -3 y 4x 1.45 8.2y -3x -1 0.5y X = 2.45 = 5.7y = 7.2x Unlike Terms – numbers and/or variables which can not be combined. Example 1 Example 2 Example 3 15z -4b 5.2x -4a y 4y 1.45 8.2 -3 -1c 4.9d 12c Repeated Addition Property of Multiplication: every multiplication problem can be written as an addition problem. Product What it means 2x5 4x 3a 2 sets of 5 4 sets of “x” 3 sets of “a” Addition Problem 5+5 x+x+x+x a+a+a Multiplicative Identity Property of 1 Any number multiplied by 1, gives you that same identical number. -4 12 1 1 = -4 = 12 Equations of the Form: x+a=b One variable, two numbers. To solve for x, add the opposite of “a” to both sides of the equation. Examples: X+2=9 B + -9 = -27 14 + c = -92 -100 = -42 – (-d) x+a=b Identify the “a” and “b” in each equation. Problem X+2=9 B + -9 = -27 14 + c = -92 -100 = -42 – (-d) a b Addition Property of Equality: Given an equation, to keep the equation balanced, if you add something to the left hand side of the equation, you must add that same thing to the right hand side of the equation. Example: LEFT RIGHT x+2=9 Add -2 to both sides of the equation. -2 -2 X = 7 These are two equivalent equations.