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Simplifying Expressions in Algebraic Expressions Applications in Atomic Sciences

Simplifying Expressions in Algebraic Expressions Applications in Atomic Sciences. Scientists, engineers and technicians need, develop, and use mathematics to explain, describe, and predict what nature, processes, and equipment do.

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Simplifying Expressions in Algebraic Expressions Applications in Atomic Sciences

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  1. Simplifying Expressions in Algebraic Expressions Applications in Atomic Sciences

  2. Scientists, engineers and technicians need, develop, and use mathematics to explain, describe, and predict what nature, processes, and equipment do. Many times the math they use is the math that is taught in ALGEBRA 1!

  3. The Objective of this presentation is show how: tosimplify algebraic expressions by using the rules for order operations to evaluate algebraic expressions.

  4. 10 3 -16 +10 = -4 ( ) 1 ( ) ( ) 1 1 1 1 0.14 = - - 0.25 0.11 10 10 4 9 10 ( ) 0.14 0.1 Simplifying Expressions Rules Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. Two Examples (a) 14- +10 = 14 -30+10 = (b) = 0.014 = =

  5. (10 3) 14 - +10 = 14- (10 3) +10 = -16 +10 = -4 Simplifying Expressions Rules Perform operations within parenthesis first. Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. Add (subtract) in order from left to right. Two Simple Examples (a) ? = = 14 -30+10 = =

  6. 1 1 1 1 - 0.25 0.11 = ( ) - ( ) 10 10 4 9 1 = ( 0.14 ) ( 0.14 ) = 0.014 = 0.1 10 (9-4) ( ) 1 1 1 1 - 10 4 9 10 (49) ( ) ( 5 ) 1 1 = = 0.014 0.14 10 10 36 (b) 0.014 Rules used? Perform operations within parentheses first. Multiply (divide) in order from left to right. Multiply (divide) in order from left to right. Another way that technicians, scientists and engineers often simplify this type of algebraic expression. ( ) = = Rule to use first? 0.014 = Perform operations within parenthesis

  7. ( ) 1 1 1 ( ) 1 (d – b) 1 1 1 - - = 10 4 9 (bd) 10 b d 10 Simplifying Expressions Rules Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. Two Generalization Examples ( ) (a) For the previous problem, bwas equal to4and dwas equal to9

  8. 1 1 1 1 (d – b) ( ) ( ) - = 10 b d 10 (bd) 1 ( ) ( (n2– n1) ) 1 1 1 - = (n1n2) 10 n1 n2 10 Technical workers often use different symbol combinations for the lettersbandd. (b) This time the symboln1replaces the letterband the symboln2replaces the letterd.

  9. 1 1 1 (9 -4) ( ) ( ) 1 - = 10 2 2 2 3 10 (49) ( ) 1 1 1 - ( ) ( 5 ) 1 1 = = 2 10 n1 2 n2 0.14 10 10 36 Evaluation of a new expression = ? This time let n1 equal2and n2 equal3 = ? 0.014 NOTE:The calculations inside the parentheses were completed before multiplying by one tenth.

  10. 1 -1 [ ] 10 ] [ 10 1 1 1 -1 [ ] = = 10 = 0.10 = ] ] ] [ [ [ 2 + 3(2) +2 2 + 6 +2 10 Reciprocal Expressions Rules Perform operations within parenthesis first. Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. Three easy examples of reciprocal expression manipulations a) = 0.10 = There is nothing to do inside this parentheses b) There is something to do inside this parentheses

  11. Rules Perform operations within parentheses first. 1 -1 [ ] 1 1 10 = ] ] ] [ [ [ ( ) 2 ( ) 3 1 10 20 20 - 4 4 4 1 -1 [ ] ( ) 1 1 1 - [ ] 2 ( ) 1 1 n1 2 n2 10 1 - 2 n1 2 n2 10 Reciprocal Expressions This version is popular in technical applications because it takes up less space on a piece of paper and is easier to type on a computer. c) = = A typical reciprocal (inverse) expression used in technology = These two expressions are same.

  12. Rules Perform operations within parentheses first. 1 -1 [ ] ( ) 1 1 1 = - [ ] 2 ( ) 1 1 n1 2 n2 10 1 - 2 n1 2 n2 10 Reciprocal Expressions Practice Problem What is the value of this expression whenn1equals 2andn2equals 3?

  13. -1 [ ] ( ) 1 1 1 - 2 n1 2 n2 10 n1 equals2andn2equals 3 -1 -1 ] [ ] 1 1 [ ( ) ( (9 -4) ) 1 1 - = 2 2 10 2 3 10 (49) -1 -1 ] [ ] [ ( ) ( 5 ) 1 1 = 0.14 2 10 36 10 2 The calculation of the inverse is the last thing done. 2 [ ] -1 3 0.014 Perform operations within all parentheses first! NOTE: = 2 times 2 = 4 = 3 times 3 = 9 = = 71.4 =

  14. 1 1 ( ( ) ) 0.014 0.014 -1 -1 ] [ ] 1 1 [ ( ) ( (9 -4) ) 1 1 - = 2 2 10 2 3 10 (49) -1 -1 ] [ ] [ ( ) ( 5 ) 1 1 = 0.14 10 36 10 The calculation of the inverse is the last thing done. [ [ ] ] -1 -1 0.014 0.014 Perform operations within parentheses first NOTE: = 1) is the inverse of the number 71.4 2) = = 71.4 =

  15. What are, in the correct order of use, the rules for simplifying algebraic expressions? 1 1 ( ( ) ) 0.014 0.014 ( ) ( (n2– n1) ) 1 1 - (n1n2) n1 n2 (a) the inverse of ? 3 quick review questions to see what we remember 1) Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. 2) What is another way to write the following algebraic expression? = 3) What is 71.4 (b) the reciprocal of the the number 71.4?

  16. 2 1 -2 [ ] ( ) 1 1 1 - [ ] 2 ( ) 1 1 n1 2 n2 10 1 - 2 n1 2 n2 10 What do you think? 1) Are the two algebraic expressions show below equal? Why/why not? (a) (b) 2) Is the inverse of a number always the same as the reciprocal of that number? Why/Why not?

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