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PROPERTIES:

PROPERTIES:. CO mmutative Property: Changing the order when ADDING or MULTIPYING does not change the SUM or PRODUCT . Examples:. 3 + 8 = 8 + 3 11 = 11 18 + a = a + 18 (9)(-4)= (-4)(9) -36 = -36 4. 15a = a ∙ 15. Picture Example:. + = +.

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PROPERTIES:

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  1. PROPERTIES: COmmutative Property: Changing the order when ADDING or MULTIPYING does not change the SUM or PRODUCT.

  2. Examples: • 3 + 8 = 8 + 3 11 = 11 • 18 + a = a + 18 • (9)(-4)= (-4)(9) -36 = -36 4. 15a = a ∙ 15

  3. Picture Example: + = +

  4. ASSOCIATIVE: • Moving the parenthesis or REGROUPING the ADDENDS/ FACTORS does not change the SUM / PRODUCT.

  5. Examples: • (3 + 6) + 10 = 3 + (6+ 10) 9 + 10 = 3 + 16 19 = 19 2. (b + 1) + 3 = b + (1+ 3) b + 4 = b + 4

  6. Examples: • 3. (9 * 2) * 5 = 9 * (2 * 5) 18 * 5 = 9 * 10 90 = 90 4. (a * 3) * 5 = a ( 3 * 5) 15 a = 15 a

  7. ( + ) + = + ( + )

  8. IDENTITY: Any number added to ZEROis still that NUMBER. + 0 = Any number multiplied by 1 is still that number. x 1 =

  9. Examples: 32 + 0 = 32 -999 + 0 = -999 abc + 0 = abc

  10. Examples: 5 x 1 = 5 -89 x 1 = -89 cd x 1 = cd

  11. INVERSES: (opposite) • When adding a number to its OPPOSITE or INVERSE the result isZERO. + (- ) = 0 • When multiplying a number by its OPPOSITE or RECIPROCAL the product is ONE. x ( 1/ ) = 1

  12. Examples: • (-a) + a = 0 • 55 + (-55) = 0 • 1/3 * 3 = 1 • Y * 1/y = 1

  13. Distributive Property: • Examples: 1. 3( a + b) = 3a + 3b • -7 (2 + a) -7 (2) + -7(a) -14 - 7a

  14. What symbols are needed to make this the distributive property?

  15. MULTIPLICATIVE PROPERTY OF ZERO: • Any number times ZERO is ZERO!! • x 0 = 0

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