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Faster Arithmetic Methods

Faster Arithmetic Methods. Arranging arithmetic problems in a different order can allow them to be solved more readily. Properties of addition and multiplication:. Commutative Property: a + b = b + a a  b = b  a. Associative Property: ( a + b ) + c = a + ( b + c )

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Faster Arithmetic Methods

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  1. Faster Arithmetic Methods Arranging arithmetic problems in a different order can allow them to be solved more readily. Properties of addition and multiplication: Commutative Property: a + b = b + a a b = b  a Associative Property: (a + b) + c = a + (b + c) (a b)  c = a  (b  c) Distributive Property: a (b + c) = a  b + a  c Factoring

  2. Faster Arithmetic Methods What is the value of the sum ? Rearrange || 1 || 1 || 1 || 1

  3. Faster Arithmetic Methods What is the value of 1  9 + 2  99 + 3  999 + 4  9999 + 5  99999? 1  (10  1) + 2  (100  1) + 3  (1000  1) + 4  (10000  1) + 5  (100000  1) 10  1 + 200  2 + 3000  3 + 40000  4 + 500000  5 10 + 200 + 3000 + 40000 + 500000  1  2  3  4  5 543210  15 543195

  4. Faster Arithmetic Methods What is the value of 55  33  15? 55  33  15 11 11 3 5 15(11  11  1) 15(11  1)(11 + 1) = 15(10)(12) = 1800 15(121  1) 15(120) 10(120) + 5(120) 1200 + 600 = 1800

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