San$Francisco$Tree$Lights
Addi$on'of'Frac$ons,'Connec$on'Frac$ons'and'Ra$onal'Expressions
Engineering'Connec$on:!(electricity,!circuits,!resistance,!power!and!current).!Students!will!be!
exposed!to!basic!concepts!of!electricity.!The!total!resistance!of!a!circuit!can!be!found!using!the!
addi<on!of!frac<ons.
Reinforces'Lessons:'Connec<ng!!Frac<ons!and!Ra<onal!Expressions!
In!this!sec<on,!you!will!learn!to!add!and!subtract!
frac%ons.!Let’s!say!you!are!an!electrical!engineer!and!
you!are!working!on!designing-the-ligh%ng-for-the-SanFrancisco-Christmas-tree-at-Union-Square.-Your!task!
is!to!find!the-total-power-required-to-light-the-wholetree.-In-order-to-find-the-power,-you-must-calculatethe-resistance-of-the-wiring-and-lights-to-the-flow-ofelectricity.-As-shown-in-the-picture,-the-ligh%ngsystem-consists-of-the-yellow-lights,-electric-redornaments,-and-the-star.-Let’s!review!what!some!of!
these!words!mean!first.
Figure'1:'San'Francisco'Christmas'Tree'during'the'night
Frac$on:!a!frac<on!is!one!quan<ty!divided!by!another!
quan<ty.!The!frac<on!"four!divided!by!five"!or!"four!over!five"!or!"four!fiLhs"!can!be!wriMen!as!
4!÷!5,!4/5!,!or!
Circuit:!!An!electric!circuit!typically!consists!of!various!types!of!electric!devices!such!as!lights,!or!
any!other!electric!device!connected!to!an!electric!source!like!a!baMery!through!electric!wires.!!
Electricity!flows!in!the!wiring!(flow!of!electrons)!from!one!point!to!another!and!in!its!way,!lights!
are!turned!on!and!devices!that!are!pluggedTin!start!running!
Current!(I):!Electric!current!is!the!rate!of!flow!of!electricity!(flow!of!electrons)!in!an!electric!
circuit.!The!unit!to!measure!the!amount!of!current!is!Amperes.!Electric!current!is!similar!to!
water!current!in!a!water!pipe.!
Resistance'(R):!Electricity!does!not!flow!freely!through!an!electric!circuit!(wiring!plus!electric!
devices).!Wiring!and!electric!equipment!create!roadblocks!to!the!flow!of!electricity.!!These!
roadblocks!are!what!we!call!‘resistance’.!!Resistance!is!the!reason!that!light!bulbs!and!wirings!
heat!up!when!connected.!!The!unit!to!measure!the!amount!of!resistance!of!an!electric!circuit!
to!the!flow!of!electricity!is!called!Ohms!(Ω).!
©"Math"&"Science"Center"WCCUSD""02/01/14
There$are$two$types$of$electric$circuits:$parallel$
There$are$two$types$of$electric$circuits:$parallel$
There$are$two$types$of$electric$circuits:$parallel$
There!are!two!types!of!electric!circuits:!parallel!
and$inOseries.$$A$parallel$circuit$is$when$devices$
and$inOseries.$$A$parallel$circuit$is$when$devices$
There$are$two$types$of$electric$circuits:$parallel$
and$inOseries.$$A$parallel$circuit$is$when$devices$
and!inTseries.!!A!parallel!circuit!is!when!devices!
are$connected$parallel$to$each$other$and$the$inO
are$connected$parallel$to$each$other$and$the$inO
and$inOseries.$$A$parallel$circuit$is$when$devices$
are$connected$parallel$to$each$other$and$the$inO
are!connected!parallel!to!each!other!and!the!inT
series$circuit$is$when$devices$are$connected$in$
series$circuit$is$when$devices$are$connected$in$
are$connected$parallel$to$each$other$and$the$inO
series$circuit$is$when$devices$are$connected$in$
series!circuit!is!when!devices!are!connected!in!
series.$The$picture$on$the$left$shows$two$bulbs$
series.$The$picture$on$the$left$shows$two$bulbs$
series$circuit$is$when$devices$are$connected$in$
series.$The$picture$on$the$left$shows$two$bulbs$
series.!The!picture!on!the!leL!shows!two!bulbs!
connected$to$a$battery$in$series$and$the$second$
connected$to$a$battery$in$series$and$the$second$
series.$The$picture$on$the$left$shows$two$bulbs$
connected$to$a$battery$in$series$and$the$second$
connected!to!a!baMery!in!series!and!the!second!
shows$the$same$lights$connected$in$parallel.$InO
shows$the$same$lights$connected$in$parallel.$InO
connected$to$a$battery$in$series$and$the$second$
shows$the$same$lights$connected$in$parallel.$InO
shows!the!same!lights!connected!in!parallel.!InT
series$circuits$the$resistance$to$the$flow$of$
series$circuits$the$resistance$to$the$flow$of$
shows$the$same$lights$connected$in$parallel.$InO
series$circuits$the$resistance$to$the$flow$of$
series!circuits!the!resistance!to!the!flow!of!
electricity$is$equal$to$the$resistance$created$by$
electricity$is$equal$to$the$resistance$created$by$
series$circuits$the$resistance$to$the$flow$of$
electricity$is$equal$to$the$resistance$created$by$
electricity!is!equal!to!the!resistance!created!by!
wiring$and$all$the$lights$and$other$devices$
wiring$and$all$the$lights$and$other$devices$
electricity$is$equal$to$the$resistance$created$by$
wiring$and$all$the$lights$and$other$devices$
wiring!and!all!the!lights!and!other!devices!
wiring$and$all$the$lights$and$other$devices$
connected!to!it.!
ure'2:'Left9In9Series'Circuit.'Right9Parallel'Circuit
!
Figure'2:'Left9In9Series'Circuit.'Right9Parallel'Circuit
! connected$to$it.$$
connected$to$it.$$
ure'2:'Left9In9Series'Circuit.'Right9Parallel'Circuit!
connected$to$it.$$
Figure'2:'Left9In9Series'Circuit.'Right9Parallel'Circuit
Figure'2:'Left9In9Series'Circuit.'Right9Parallel'Circuit!
connected$to$it.$$
$
$When!devices!are!connected!inTseries!the!formula!for!total!resistance!is!as!follows
When$devices$are$connected$inOseries$the$formula$for$total$resistance$is$as$follows$
n$devices$are$connected$inOseries$the$formula$for$total$resistance$is$as$follows$
n$devices$are$connected$inOseries$the$formula$for$total$resistance$is$as$follows$
When$devices$are$connected$inOseries$the$formula$for$total$resistance$is$as$follows$
= !1
+ !2
+ !3 + ⋯.$
!"#"$% =!"#"$%
!1 + !2
+ !3
+ ⋯.$
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !"#"$% = !1 + !2 + !3 + ⋯.$
!"#"$% = !1 + !2 + !3 + ⋯.$
When$devices$are$connected$in$parallel$the$formula$for$total$resistance$is$as$follows$
n$devices$are$connected$in$parallel$the$formula$for$total$resistance$is$as$follows$
When!devices!are!connected!in!parallel!the!formula!for!total!resistance!is!as!follows
n$devices$are$connected$in$parallel$the$formula$for$total$resistance$is$as$follows$
When$devices$are$connected$in$parallel$the$formula$for$total$resistance$is$as$follows$
1
1
11 1 1 1 1
= + 1+ + ⋯$
+
+ ⋯$
1 = 1 + 1
1 !2
1 !3 1
!"#"$% =!"#"$%
!1 +1!2 !1
+ !3
+ ⋯$
!2 = !3 +
+
+ ⋯$
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !"#"$% !1!"#"$%
!1 !2 !3
$
$The!San!Francisco!Christmas!tree!ligh<ng!is!an!
The$San$Francisco$Christmas$tree$lighting$is$an$
an$Francisco$Christmas$tree$lighting$is$an$
example!of!a!complex!circuit!that!combines!both!
an$Francisco$Christmas$tree$lighting$is$an$
example$of$a$complex$circuit$that$combines$both$
ple$of$a$complex$circuit$that$combines$both$
The$San$Francisco$Christmas$tree$lighting$is$an$
parallel!and!inTseries!circuits.!The!light!bulbs!in!each!
ple$of$a$complex$circuit$that$combines$both$
parallel$and$inOseries$circuits.$The$light$bulbs$in$
el$and$inOseries$circuits.$The$light$bulbs$in$
example$of$a$complex$circuit$that$combines$both$
sec<on!are!connected!in!series!and!then!the!
el$and$inOseries$circuits.$The$light$bulbs$in$
each$section$are$connected$in$series$and$then$the$
section$are$connected$in$series$and$then$the$
parallel$and$inOseries$circuits.$The$light$bulbs$in$
sec<ons!are!connected!in!parallel!similar!to!the!
section$are$connected$in$series$and$then$the$
sections$are$connected$in$parallel$similar$to$the$
ons$are$connected$in$parallel$similar$to$the$
each$section$are$connected$in$series$and$then$the$
picture!to!the!right.!Therefore!for!the!Christmas!
ons$are$connected$in$parallel$similar$to$the$
picture$to$the$right.$Therefore$for$the$Christmas$
re$to$the$right.$Therefore$for$the$Christmas$
sections$are$connected$in$parallel$similar$to$the$
tree!example,!assume!the!lights!in!each!color!are!
re$to$the$right.$Therefore$for$the$Christmas$
tree$example,$assume$the$lights$in$each$color$are$
example,$assume$the$lights$in$each$color$are$
picture$to$the$right.$Therefore$for$the$Christmas$
connect!in!series!and!various!color!lights!are!
example,$assume$the$lights$in$each$color$are$
connect$in$series$and$various$color$lights$are$
tree$example,$assume$the$lights$in$each$color$are$
ect$in$series$and$various$color$lights$are$
Figure'3:'Combination'circuit.'C'and'D'represent'the'yellow'
connected!in!parallel.!!The!total!resistance!would!be!
Figure'3:'Combination'circuit.'C'and'D'represent'the'yellow'
Figure'3:'Combination'circuit.'C'and'D'represent'the'yellow'
ect$in$series$and$various$color$lights$are$
light'bulbs,'while'B'represents'the'red'ornaments,'and'A'
connected$in$parallel.$$The$total$resistance$would$
Figure'3:'Combination'circuit.'C'and'D'represent'the'yellow'
light'bulbs,'while'B'represents'the'red'ornaments,'and'A'
light'bulbs,'while'B'represents'the'red'ornaments,'and'A'
connect$in$series$and$various$color$lights$are$
ected$in$parallel.$$The$total$resistance$would$
calculated!as:
Figure'3:'Combination'circuit.'C'and'D'represent'the'yellow'
represents'the'star
'
light'bulbs,'while'B'represents'the'red'ornaments,'and'A'
represents'the'star
'
ected$in$parallel.$$The$total$resistance$would$
represents'the'star
be$calculated$as:$
light'bulbs,'while'B'represents'the'red'ornaments,'and'A'
connected$in$parallel.$$The$total$resistance$would$
lculated$as:$
represents'the'star'
represents'the'star'
lculated$as:$
be$calculated$as:$
!
!
! !
!
!
!
!
+
+
'
! = ! ! != ! !
!
!
!
+
+
'
+!
+!
+
⋯
!
!
!
!
!
!
!"##
!"#$%!!
!"#$%!!
!"#$%!!
!"#$%!!"!
!"#!!"#$%&#'(
!"#$
!!"## = ! !!"#$%!! +!
+ !!"#$' +
!"#$%!! +!!"#$%!! + ⋯ !!"#$%!!"! + !!"#!!"#$%&#'(
= !!"#$%!!
+
'
!!"##
!!"#$%!!
+!
+!
+
⋯
!
!
!!"#$
!"#$%!!
!"#$%!!"!
!"#!!"#$%&#'(
!!"##
!!"#$%!! +!!"#$%!! +!!"#$%!! + ⋯ !!"#$%!!"! !!"#!!"#$%&#'(
!!"#$
$ ''''''''''''''''
$
!
!
In'order'to'find'the'total'resistance,'you'must'divide'1'into'the'
'to'get'!!"## .'
In'order'to'find'the'total'resistance,'you'must'divide'1'into'the''to'get'.
der'to'find'the'total'resistance,'you'must'divide'1'into'the'!"#$$
! 'to'get'!
!"#$$!"## .'
!
der'to'find'the'total'resistance,'you'must'divide'1'into'the'
'to'get'!!"##'to'get'!
.'
In'order'to'find'the'total'resistance,'you'must'divide'1'into'the'
!"#$$
!"## .'
!"#$$
!
!= ! ÷
!"## !
!!"## = !!÷
!' !!"##!!'
!!"## = ! ÷!!!"##=
!' ! ÷
!'
!!"##
!"##
!!"##
©"Math"&"Science"Center"WCCUSD""02/01/14
Example'1'('the'resistance'values'are'too'low'for'the'Christmas'tree,'the'power'consumption'
is'not'realistic)'
'
Let’s'calculate'the'total'resistance,'!
!"!#$ ,'if'we'are'given'the'following'information:''
' Example'1'('the'resistance'values'are'too'low'for'the'Christmas'tree,'the'power'consumption'
Let’s'calculate'the'total'resistance,'!
!"!#$ ,'if'we'are'given'the'following'information:''
!!"##$%!!"#$%&! ='.2'Ω'(100'yellow'lights),'''''''!
!"#!!"#$%&#'( =5Ω,'''''!!"#$ =6'Ω'''''''
is'not'realistic)'
Example'1'('the'resistance'values'are'too'low'for'the'Christmas'tree,'the'power'consump$on'
Example'1'('the'resistance'values'are'too'low'for'the'Christmas'tree,'the'power'consumption'
!!"##$%!!"#$%&! ='.2'Ω'(100'yellow'lights),'''''''!!"#!!"#$%&#'( =5Ω,'''''!!"#$ =6'Ω'''''''
'is'not'realis$c)
is'not'realistic)'
Let’s'calculate'the'total'resistance,'!!"!#$ ,'if'we'are'given'the'following'information:''
'
First-calculate-the-combined-resistance-for-the-yellow-lights.-The-yellow-lights-are-in-aLet’s'calculate'the'total'resistance,','if'we'are'given'the'following'informa$on:'
Let’s'calculate'the'total'resistance,'!
!"!#$ ,'if'we'are'given'the'following'information:''
!!"##$%!!"#$%&! ='.2'Ω'(100'yellow'lights),'''''''!
!"#!!"#$%&#'( =5Ω,'''''!!"#$ =6'Ω'''''''
series-circuit,-so-we-can-simply-add-each-resistance-together.-Since-the-resistance-forFirst-calculate-the-combined-resistance-for-the-yellow-lights.-The-yellow-lights-are-in-a!!"##$%!!"#$%&! ='.2'Ω'(100'yellow'lights),'''''''!!"#!!"#$%&#'( =5Ω,'''''!!"#$ =6'Ω'''''''
each-yellow-light-is-.2-Ω-and-there-are-100-lights,-we-can-add-.2-one-hundred-times-ORseries-circuit,-so-we-can-simply-add-each-resistance-together.-Since-the-resistance-for'''''
we-can-multiply-.2-by-100' each-yellow-light-is-.2-Ω-and-there-are-100-lights,-we-can-add-.2-one-hundred-times-ORFirst-calculate-the-combined-resistance-for-the-yellow-lights.-The-yellow-lights-are-in-awe-can-multiply-.2-by-100series-circuit,-so-we-can-simply-add-each-resistance-together.-Since-the-resistance-forFirst-calculate-the-combined-resistance-for-the-yellow-lights.-The-yellow-lights-are-in-aFirst-calculate-the-combined-resistance-for-the-yellow-lights.-The-yellow-lights-are-in-a- ! series-circuit,-so-we-can-simply-add-each-resistance-together.-Since-the-resistance-foreach-yellow-light-is-.2-Ω-and-there-are-100-lights,-we-can-add-.2-one-hundred-times-OR!"!!"#$"!!!"#!$"% = !!"#$%!! +!!"#$%!! +!!"#$%!! + ⋯ !!"#$%!!"" '
series-circuit,-so-we-can-simply-add-each-resistance-together.-Since-the-resistance-forwe-can-multiply-.2-by-100each-yellow-light-is-.2-Ω-and-there-are-100-lights,-we-can-add-.2-one-hundred-times-OReach-yellow-light-is-.2-Ω-and-there-are-100-lights,-we-can-add-.2-one-hundred-%mes-OR!!"!!"#$"!!!"#!$"%
=!
+!!"#$%!! +!!"#$%!! + ⋯ !!"#$%!!"" '
. !!Ω.
+!!Ω + !Ω +!"#$%!!
⋯ !Ω'='.!!Ω×!""'='!"Ω'
we-can-multiply-.2-by-100we-can-mul%ply-.2-by-100
. !!Ω.
+!!Ω
+ !Ω + ⋯ !Ω'='.!!Ω×!""'='!"Ω'
' !!"!!"#$"!!!"#!$"% = !!"#$%!! +!!"#$%!! +!!"#$%!! + ⋯ !!"#$%!!"" '
' We-can-plug-in!!"Ω-into-our-total-resistance-formula,-as-well-as-the-resistance-of-the!!"!!"#$"!!!"#!$"% = !!"#$%!! +!!"#$%!! +!!"#$%!! + ⋯ !!"#$%!!"" '
. !!Ω. +!!Ω + !Ω + ⋯ !Ω'='.!!Ω×!""'='!"Ω'
red-ornaments-and-the-starWe-can-plug-in!!"Ω-into-our-total-resistance-formula,-as-well-as-the-resistance-of-the--------. !!Ω. +!!Ω + !Ω + ⋯ !Ω'='.!!Ω×!""'='!"Ω'
red-ornaments-and-the-star'
-We-can-plug-in-into-our-total-resistance-formula,-as-well-as-the-resistance-of-the-red'
- ornaments-and-the-star
We-can-plug-in!!"Ω-into-our-total-resistance-formula,-as-well-as-the-resistance-of-the!
!
!
!
=
!
+
+
'
red-ornaments-and-the-starWe-can-plug-in!!"Ω-into-our-total-resistance-formula,-as-well-as-the-resistance-of-the!!"##
!!"#$%!! +!!"#$%!! +!
!
! !"#$%!! + ⋯ !!"#$%!!"" !!"#!!"#$%&#'(
!
!!!"#$
=!
+
+
'
red-ornaments-and-the-star!!"##!!"#$%!! +!!"#$%!! +!!!"#$%!! + ⋯
!
!
!
!"#$%!!""
!"#!!"#$%&#'(
!"#$
!
!
!
=
!
+
+
'
!!!"## !!"!Ω!
! !Ω ! !Ω
!
!
!
!
=!
+
+
'
=
!
+
+
!!!"##
! !"#$%!!!Ω
!
!!!"#$ '
!!"##
!"!Ω!
!Ω
!!"#$%!! +!
+!
+
⋯
!
!
!"#$%!!
!"#$%!!""
!"#!!"#$%&#'(
'
=!
+
+
'
!!"##
!!"#$%!! +!!"#$%!! +!!"#$%!! + ⋯ !!"#$%!!"" !!"#!!"#$%&#'( !!"#$
! '
!
!
!
Now-we-have-to-add-the-three-fractions:-=
!
+
+
!!!"## !!"!Ω! ! !Ω ! !Ω'
Now-we-have-to-add-the-three-fractions:-=!
+
+
'
Now-we-have-to-add-the-three-frac%ons:First,-find-the-lowest-common-denominator-by-breaking-down-each-denominator-to-a!!"##
!"!Ω! !Ω !Ω
'
multiplication-of-prime-numbers.First,-find-the-lowest-common-denominator-by-breaking-down-each-denominator-to-aFirst,-find-the-lowest-common-denominator-by-breaking-down-each-denominator-to-a'
multiplication-of-prime-numbers.mul%plica%on-of-prime-numbers.
Now-we-have-to-add-the-three-fractions:-Now-we-have-to-add-the-three-fractions:-First,-find-the-lowest-common-denominator-by-breaking-down-each-denominator-to-a!
!
!
!
=
!
+
+
'
First,-find-the-lowest-common-denominator-by-breaking-down-each-denominator-to-amultiplication-of-prime-numbers.!
! ! !!×!
!×!×!!!
-------------------------------------------- !!!"##
=!
+ +
'
multiplication-of-prime-numbers.!
!×!×!!!
!
!×!
!"##
The-lowest-common-denominator-is-!×!×!×!-=-60-because-it-has-all-the-numbers-inall-three-denominators.The-lowest-common-denominator-is-!×!×!×!-=-60-because-it-has-all-the-numbers-in!
!
!
!
The-lowest-common-denominator-is--2-x-2-x-5-x-3-=-60-because-it-has-all-the-numbers-in=
!
+
+
all-three-denominators.!!
!
! ! !!×!'
!×!×!!!
!"##
=!
+ +
'
all-three-denominators.
!!"##
!×!×!!! ! !×!
The-lowest-common-denominator-is-!×!×!×!-=-60-because-it-has-all-the-numbers-inThe-lowest-common-denominator-is-!×!×!×!-=-60-because-it-has-all-the-numbers-inall-three-denominators.all-three-denominators.©"Math"&"Science"Center"WCCUSD""02/01/14
Second,-multiply-each-denominator-with-the-number(s)-that-will-make-theSecond,-multiply-each-denominator-with-the-number(s)-that-will-make-theSecond,-mul%ply-each-denominator-with-the-number(s)-that-will-make-theSecond,-multiply-each-denominator-with-the-number(s)-that-will-make-thedenominator-60.-Consequently,-you-must-multiply-the-numerator-with-the-sameSecond,-multiply-each-denominator-with-the-number(s)-that-will-make-thedenominator-60.-Consequently,-you-must-multiply-the-numerator-with-the-samedenominator-60.-Consequently,-you-must-mul%ply-the-numerator-with-the-samedenominator-60.-Consequently,-you-must-multiply-the-numerator-with-the-sameSecond,-multiply-each-denominator-with-the-number(s)-that-will-make-thenumber-because-that-way-you-are-nor-changing-the-fraction’s-value-since-you-aredenominator-60.-Consequently,-you-must-multiply-the-numerator-with-the-samenumber-because-that-way-you-are-nor-changing-the-fraction’s-value-since-you-arenumber-because-that-way-you-are-nor-changing-the-frac%on’s-value-since-you-arenumber-because-that-way-you-are-nor-changing-the-fraction’s-value-since-you-areSecond,-multiply-each-denominator-with-the-number(s)-that-will-make-thedenominator-60.-Consequently,-you-must-multiply-the-numerator-with-the-samemultiplying-the-fraction-by-1.number-because-that-way-you-are-nor-changing-the-fraction’s-value-since-you-areSecond,-multiply-each-denominator-with-the-number(s)-that-will-make-themultiplying-the-fraction-by-1.mul%plying-the-frac%on-by-1.
multiplying-the-fraction-by-1.denominator-60.-Consequently,-you-must-multiply-the-numerator-with-the-samenumber-because-that-way-you-are-nor-changing-the-fraction’s-value-since-you-aremultiplying-the-fraction-by-1.denominator-60.-Consequently,-you-must-multiply-the-numerator-with-the-same!×!×!
!
!×!
number-because-that-way-you-are-nor-changing-the-fraction’s-value-since-you-aremultiplying-the-fraction-by-1.!!! = ! !!!
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The-total-resistance-of-the-Christmas-tree-isΩ-or-2.4!Ω'
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The-total-resistance-of-the-Christmas-tree-isΩ-or-2.4!Ω'
!!!
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©"Math"&"Science"Center"WCCUSD""02/01/14
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Problem'1
Problem'1'
It’s'your'turn'to'put'your'knowledge'to'prac$ce.'Calculate'the'total'resistance,','if'you'are'
It’s'your'turn'to'put'your'knowledge'to'practice.'Calculate'the'total'resistance,'!!"!#$ ,'if'you'
given'the'following'informa$on:'
are'given'the'following'information:''
!!"##$%!!"#$%&! ='.03'Ω'(200'yellow'lights),'''''''!!"#!!"#$%&#'( =4Ω,'''''!!"#$ =12'Ω'''''''
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Congratula$ons,'you'have'applied'addi$on'of'ra$onal'frac$ons'to'a'real'life'engineering'
Congratulations,'you'have'applied'addition'of'rational'fractions'to'a'real'life'engineering'
situa$on!'If'you'want'to'challenge'yourself'and'use'other'concepts,'go'onto'the'“Next'Steps”
situation!'If'you'want'to'challenge'yourself'and'use'other'concepts,'go'onto'the'“Next'Steps”'
'
Next'Steps:'After'you'have'found!!!"!#$ ,'the'total'resistance,'you'can'calculate'how'
much'electric'power,'(W)'that'is'measured'in'Watts,'is'needed'to'light'the'entire'
tree.'if'you'know'the'electric'current,'I,'in'the'city'of'San'Francisco.'
! = !!×!!! '
Calculate'the'power,'W,'given'the'following'additional'information:'
''Calculate'the'power,'W,'given'the'following'addi$onal'informa$on:
I'='15'Amp'
''I'='15'Amp
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