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Linear Relationships Vocabulary

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Multiplying a number by -1 always gives you the opposite of that number -4 = 4 12 = -12 Multiplication Property of -1

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Multiplying a number by 0 always gives you ZERO -4 = 0 0 12 = 0 Multiplication Property of 0 0 12 x 3 x -3 x 5 x 0 x 8 = 0

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Examples of Dimensions 1 foot 5 feet Length, Width and Height are dimensions

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These are examples of rectangular arrays for the product of 8.

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Area Model for Multiplication 4 x 3 can be represented by this rectangle because 4 x 3 = 12. See the 12 boxes?

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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 5 x 8 = 8 x 5 You will always get the same product, no matter which way you solve it.

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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.

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Associative Property of Multiplication The 3 numbers don’t switch places! Only the parentheses do! ( 2 x 3) x 4 = 2 x (3 x 4) 6 x 4 = 2 x 12 24 = 24 FUNNEL METHOD! Use the ORDER OF OPERATIONS!

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Terms are numbers and/or variables which can stand alone or are separated by “+”, “-”, “x” or “ “ Examples of Terms X -y 0.5 12a

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Find the Terms ProblemTerm 1Term 2 12 a + 13 b -8 – 12b 7 + 8 2x – 3y

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Coefficients Coefficients are numbers which are directly in front of a variable. 3x The “3” is the coefficient! The “x” is the variable!

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Coefficients Problem:List the coefficients here: x 3a -y 4a + 6b

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Like terms – numbers and/or variables which can be combined due to their “likeness” -3 1.45 Example 1 5 Example 2 -4y y 8.2y 0.5y Example 3 5.2x 4x -3x x

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Combining or Collecting Like terms – you can combine/collect like terms by adding them up. -3 1.45 = 2.45 Example 1 5 Example 2 -4y y 8.2y 0.5y = 5.7y Example 3 5.2x 4x -3x X = 7.2x

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Unlike Terms – numbers and/or variables which can not be combined. -4a 1.45 -1c Example 1 15z Example 2 -4b y 8.2 4.9d Example 3 5.2x 4y -3 12c

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Repeated Addition Property of Multiplication: every multiplication problem can be written as an addition problem. ProductWhat it meansAddition Problem 2 x 52 sets of 55 + 5 4x4 sets of “x”x + x + x + x 3a3 sets of “a”a + a + a

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Any number multiplied by 1, gives you that same identical number. -4 = -4 1 12 = 12 1 Multiplicative Identity Property of 1

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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)

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Problemab X + 2 = 9 B + -9 = -27 14 + c = -92 -100 = -42 – (-d) x + a = b Identify the “a” and “b” in each equation.

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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: x + 2 = 9 LEFTRIGHT -2 Add -2 to both sides of the equation. X = 7 These are two equivalent equations.

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Properties of Equality

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