Post on 17-Jan-2016
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Simplifying Expressions
Simplifying Expressions in Algebraic ExpressionsApplications in Atomic Sciences
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Simplifying Expressions
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!
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Simplifying Expressions
The Objective of this presentation is show how:
to simplify algebraic expressions by using the rules for order operations to evaluate algebraic expressions.
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Simplifying Expressions
Simplifying Expressions
Perform operations within parentheses first.
Multiply (divide) in order from left to right.
Add (subtract) in order from left to right.
Two Examples
14 -30+10 =
=)( - 91
41
101
=
)( - 0.110.25101
)( 0.14101 = )( 0.140.1 = 0.014
-16 +10
= -414- +10
10 3
(a)
(b)
Rules
=
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Simplifying Expressions
Simplifying Expressions
Perform operations within parenthesis first.
Add (subtract) in order from left to right.
Two Simple Examples
(10 3)14- +10
=
14 -30+10 =-16 +10
= -4
14 - +10
=(10 3) (a) ?
=
=
=
Multiply (divide) in order from left to right.
Perform operations within parentheses first.
Add (subtract) in order from left to right.
Rules
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Simplifying Expressions
=)( -91
41
101
=
)( - 0.110.25101
)(0.14101
= )(0.140.1 = 0.014
Another way that technicians, scientists and engineers often simplify this type of algebraic expression.
=)( - 91
41
101 )(10
1 (9-4)
(4 9)= )( 5
36101 =
0.014)(0.14101 =
Rules used?
Perform operations within parentheses first.
Multiply (divide) in order from left to right.
(b)
=
0.014
Rule to use first?Perform operations within parenthesis
0.014
Multiply (divide) in order from left to right.
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Simplifying Expressions
Two Generalization Examples
=)( -d1
b1
101 )(
10
1 (d – b)(b d)
Simplifying Expressions
Perform operations within parentheses first.
Multiply (divide) in order from left to right.
Add (subtract) in order from left to right.
Rules
(a)
)( - 91
41
101
For the previous problem, b was equal to 4 andd was equal to 9
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Simplifying Expressions
=)( -n2
1 n1
1101 )( (n2–
n1)10
1
(n1 n2)
This time the symbol n1 replaces the letter b and the symbol n2 replaces the letter d.
(b)
=)( -d1
b1
101 )( (d – b)
101
(b d)
Technical workers often use different symbol combinations for the letters b and d.
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Simplifying Expressions
Evaluation of a new expression
)( -n2
1 n1
1
10
12 2
This time let n1 equal 2 and n2 equal 3
= ? 0.014)(0.14101 =
=)( -3
1 2
1101
)( (9 -4)
101
(4 9)2 2
= ?
NOTE: The calculations inside the parentheses were completed before multiplying by one tenth.
)( 5 3610
1 =
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Simplifying Expressions
Perform operations within parenthesis first.
Reciprocal Expressions
10[ ]1
=-1
10[ ] = 0.10
-1
10[ ] =0.10
Three easy examples of reciprocal expression manipulationsa)
b)
2 + 6 +2[ ]1
=
10[ ]1
=
There is nothing to do inside this parentheses
There is something to do inside this parentheses
Multiply (divide) in order from left to right.
2 + 3(2) +2[ ]1
=
RulesPerform operations within parentheses first.
Add (subtract) in order from left to right.
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Simplifying Expressions
These two expressions are same.
)( -n2
1 n1
112 210[ ]
1=
-1
)( -n2
1 n1
112 210[ ]
c)
)( - 41
4320[ ]1
= =
[ ]1
)( 4220
-1
10[ ]
A typical reciprocal (inverse) expression used in technology
10[ ]1
=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.
RulesPerform operations within parentheses first.
Reciprocal Expressions
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Simplifying Expressions
What is the value of this expression when n1 equals 2 and n2 equals 3?
)( -n2
1 n1
112 210[ ]
1=
-1
)( -n2
1 n1
112 210[ ]
Practice Problem
RulesPerform operations within parentheses first.
Reciprocal Expressions
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Simplifying Expressions
NOTE:
22
= 2 times 2 = 4
32= 3 times 3 = 9
= =
Perform operations within all parentheses first!
=)( -3
1 2
1
101
2 2[ ]-1
)(101 (9 -
4)(4 9)
[ ]-1
== )( 5 3610
1[ ]-1
)(0.14101[ ]
-1
0.014[ ]-1
71.4
n1 equals 2 and n2 equals 3
The calculation of the inverse is the last thing done.
)( -n2
1 n1
112 210[ ]
-1
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Simplifying Expressions
= =
Perform operations within parentheses first
=)( -3
1 2
1
101
2 2[ ]-1
)(101 (9 -
4)(4 9)
[ ]-1
== )( 5 3610
1[ ]-1
)(0.14101[ ]
-1
0.014[ ]-1
71.4The calculation of the inverse is the last thing done.
1
0.014( )0.014[ ]-1NOTE:
=
1
0.014( ) is the inverse of the number 71.4
1)
2)
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Simplifying Expressions
3 quick review questions to see what we remember
1)What are, in the correct order of use, the rules for simplifyingalgebraic expressions?
2)What is another way to write the following algebraic expression?
71.43)
Perform operations within parentheses first.
Multiply (divide) in order from left to right.
Add (subtract) in order from left to right.
)( -n2
1 n1
1 )( (n2– n1)(n1 n2)
=
What is
(b)
(a) the inverse of ? 1
0.014( )1
0.014( )the reciprocal of the the number 71.4?
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Simplifying Expressions
What do you think?
1)
(a)
Is the inverse of a number always the same as the reciprocal of that number? Why/Why not?
Are the two algebraic expressions show below equal? Why/why not?
-2
)( -n2
1 n1
112 210[ ]
2)
(b)
)( -n2
1 n1
112 210[ ]
1
2
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Simplifying Expressions