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Number Theory

Number Theory. B3 Translations. Translating Operations. Addition. 2. +. x. Addition. 2. +. x. Add Backwards. x. +. 2. Subtraction. 5. –. y. Subtract in ( ). 2. ( – ). 5. y. Subtraction. 5. –. y. y. –. 5. Subtract Backwards. Multiplication. 3. •. a.

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Number Theory

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  1. Number Theory B3 Translations

  2. Translating Operations Addition 2 + x Addition 2 + x Add Backwards x + 2 Subtraction 5 – y Subtract in ( ) 2 ( – ) 5 y Subtraction 5 – y y – 5 Subtract Backwards Multiplication 3 • a 3a Multiplication 3 Should write as • a 3a 4 b Division 4 ÷ b 4 b Division 4 ÷ b Should write as Parentheses ( ) 2 • ( ) x + 5

  3. Examples: Subtract – but where do I put the sign? Start in the middle because we don’t know which way we are going to go Translate the following into algebraic expressions A. 6 less than 2 times a ______________________________ B. 3 more than the product of 5 and y ____________________________ C. The difference of x and 9 more than 3 ______________________________ D. 5 more than the quantity of x minus 4 ______________________________ E. one-third the difference of x and 8 ______________________________ 2 a – 6 Multiply 5y • + 3 Subtract in ( ) 3 + ( – ) x 9 () x – 4 + 5 Subtract in ( ) 1 3 ( – ) x 8

  4. Translating Signs Is x + 2 = 10 Is greater than x + 2 > 10 x + 2 ≥ 10 x + 2 < 10 Is less than x + 2 ≤ 10

  5. Examples: ? What do we want to call it? • Ten less than a number is seven ___________________________ B. The difference of a number and 4 is greater than 9 __________________________ C. The difference of the product of 3 and x and the product of 6 and y is less than 23 ________________________________ x – 10 = 7 ( – ) x 4 > 9 multiply ( – ) 3x 6y < 23

  6. Practice Problems Now try the practice problems on your own

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