Jeanie cjc
of 8
Transcript of Jeanie cjc
-
8/19/2019 Jeanie cjc
1/19
Operations onReal Numbers
-
8/19/2019 Jeanie cjc
2/19
Operations on Real Numbers
Real Numbers can be combined using the familiar operations:
AdditionSubtractionMultiplicationDivision
-
8/19/2019 Jeanie cjc
3/19
Order of Operations on Real Numbers
When evaluation arithmetic expressions that contain
several of these operations, e use the folloingconvention to determine the order in hich
operations are performed!
-
8/19/2019 Jeanie cjc
4/19
Order of Operations on Real Numbers
"! #erform operations inside parenthesis first
beginning ith the innermost pair!
$n dividing to expressions, the numerator and
denominator of the %uotient are treated as if
the& are ithin parentheses!
-
8/19/2019 Jeanie cjc
5/19
Order of Operations on Real Numbers
'! #erform all multiplication and division
Wor(ing from left to right!
)! #erform all addition and subtraction
Wor(ing from left to right!
-
8/19/2019 Jeanie cjc
6/19
*ind the value of the expression
+valuating an Arithmetic +xpression
-
8/19/2019 Jeanie cjc
7/19
*irst e evaluate the numerator and denominator of the %uotient
Recall, these are treated as if the& are inside parentheses
+valuating an Arithmetic +xpression
-
8/19/2019 Jeanie cjc
8/19
#roperties of Real Numbers
-
8/19/2019 Jeanie cjc
9/19
ommutative #ropert&
a - b . b - a
ab . ba
/hen e add or multipl& to numbers, the orderof addition or multiplication doesn0t matter!1
-
8/19/2019 Jeanie cjc
10/19
Associative #ropert&
2a - b3 - c . a - 2b - c3
2ab3c . a2bc3
/hen e add or multipl& three numbers, it doesn0tmatter hich to e add or multipl& first!1
-
8/19/2019 Jeanie cjc
11/19
Distributive #ropert&
/Whenever e multipl&
a number b& a sum!1
-
8/19/2019 Jeanie cjc
12/19
' 2) - 43
' x ) ' x 4
-
8/19/2019 Jeanie cjc
13/19
5sing the properties6 +xample 2a3
' - 2) - 73
. ' - 27 - )3
. 2' - 73 - )
2ommutative #ropert& of Addition3
2Associative #ropert& of Addition3
-
8/19/2019 Jeanie cjc
14/19
5sing the properties6 +xample 2b3
'2x - )3
. '2x3 - '2)3
. 'x - 8
2Distributive #ropert&3
2Simplif&3
-
8/19/2019 Jeanie cjc
15/19
5sing the properties6 +xample 2c3
2a - b32x - &3
. x2a - b3 - &2a - b3
. 2ax - bx3 - 2a& - b&3
. ax - bx - a& - b&
2Distributive #ropert&3
2Distributive #ropert&3
2Associative #ropert&3
-
8/19/2019 Jeanie cjc
16/19
Addition andSubtraction
-
8/19/2019 Jeanie cjc
17/19
Additive $dentit&
9he number is special for addition!
$t is called the ADD$9$;+ $D+N9$9
-
8/19/2019 Jeanie cjc
18/19
Subtraction
+ver& real number a has a negative,
-a, that satisfies a + (-a) = !
Subtraction undoes addition.
-
8/19/2019 Jeanie cjc
19/19
