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Properties of Real Numbers

Properties of Real Numbers. Relationships that are always true for real numbers are called _____________, which are rules used to rewrite and compare expressions. properties. 1 + 2 = 2 + 1 a + b = b + a. C hanging O rder does not change the outcome. 1 ● 2 = 2 ● 1 a b = b a.

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Properties of Real Numbers

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  1. Properties of Real Numbers

  2. Relationships that are always true for real numbers are called _____________, which are rules used to rewrite and compare expressions. properties

  3. 1 + 2 = 2 + 1 a + b = b + a Changing Order does not change the outcome 1 ● 2 = 2 ● 1 a b = b a (8 + 6) + 7 = 8 + (6 + 7) (a + b) + c = a + (b + c) Regrouping Order stays the same only ( ) move 4● (5 ●9) = (4 ●5) ● 9 (ab) ● c = a ● (bc ) (Change who you associate [hang out] with) a(b + c) = ab + ac a(b - c) = ab - ac 10 (1 + 7) = 10 ● 1 + 10 ●7 15(x - 4) = 15 ● x – 15 ●4

  4. Adding “0” = no change -17 + 0 = -17 Multiply by 1= no change 1● 99y = 99y a + (-a) = 0 14 + (-14) = 0

  5. Multiply by 0, you get 0 (7003)(0) = 0 -1(a) = -a -1(2) = -2 -1(-5) = 5 Multiply by -1, you change the sign

  6. Identifying Properties(What property is shown in each example?) Zero Property of Multiplication Associative Prop. of Addition Identity of Addition (Additive Identity) Identity of Multiplication (Multiplicative Identity) Commutative Prop. (Addition) The “z” and the √ y have been switched.

  7. Using Properties for Mental Calculations F. A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. What is the total cost for a ticket, a drink, and popcorn? Use mental math. G. A can hold 3 tennis balls. A box holds 4 cans. A case holds 6 boxes. How many tennis balls are in 10 cases? Use mental math. $7.75 + $2.40 + $1.25 = (7.75 +1.25 + 2.40) = 9.00 + 2.40 = 11.40 3●4 ●6 ●10 = 720

  8. Writing Equivalent Expressions (5 ● 3)n 15n 7b + 12 7b + ( 4 + 8) (7b + 4) + 8 1 6x (2.1 ● 4.5)x 9.45x 6 + (3 + 4h) (6 + 3) + 4h 9+ 4h

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