ࡱ> @ 6bjbjFF ,,r, $$$$T4====H>4 i2>$@*@*@*@;T;T;Thhhhhhh$RjRlzh;TgQ;T;T;Th$$*@*@=hZZZ;TT$*@*@hZ;ThZZr;eT6f*@> "=Uegh0 iezmWmf44$$$$mf;T;TZ;T;T;T;T;Thh4404$Z444Basic Math for Culinary Programs Culinary Arts and Restaurant Management Pastry Arts Fraction Basics: A fraction is a way of showing a relation between a PART and a WHOLE For example: If you cut a pie into 4 equal pieces    And you ate 1 piece Then you ate of the pie. 1 The top number represents the PART of the pie you ate 4 The bottom number represents how many pieces were in the WHOLE Pie The part is over the whole So would represent 1 piece of a pie that is cut into 2 equal pieces 2/8 would represent 2 pieces of a pie cut into 8 equal pieces EQUAL FRACTIONS Fractions can be different but equal = 2/4 = 4/8  Reducing Fractions To reduce a fraction to its lowest term Find a number that will divide equally into both the top and bottom number For example: You can see in the example above that 2/4 is the same as ( is the lowest term). To get the lowest term, divided both the top and bottom numbers by 2 2 ( 2) = 1 4 ( 2) = 2 * How would you know what numbers to use to reduce the fraction? Here are some tips. If both the numbers in a fraction end with an even number then each number can be divided by 2 If either or both the numbers in the fraction ends with a 5 or a 0 then each number can be divided by 5 5 ( 5) = 1 10 ( 5) = 2 Mixed Numbers and Improper Fractions A mixed number is a number that contains a whole number AND a fraction For example: 1  An improper fraction is a fraction in which the top number is larger than the bottom number For example: 3/2  To change a mixed number to an equivalent improper fraction Multiply the whole number by the bottom number of the fraction (called the denominator) 1 .. 1 x 2 = 2 Then take your answer and add the top number of the fraction (called the numerator)  2 + 1 = 3  The answer you get now becomes the top number of your new improper fraction and the bottom numbers stays the same as when you started 3/2 To change a fraction into a decimal The fraction sign means DIVIDE it is telling you to divide the top number by the bottom number For example: tells you to divide 1 by 2 On a calculator you put in the top number first 1 Then push the divide sign Then put in the bottom number 2 The answer will always be the decimal form of that fraction .5 So is equal to .5 is equal to .25 is equal to .75 1/3 is equal to .33 (the indicates a repeating number (3) that never ends) 1/8 is equal to .125 The names for decimal places are as follows: If an instructor wants you to give your answer to the nearest 10th it would mean to use only 1 number after the decimal point = .5 or 1/3 = .3 If an instructor wants you to give your answer to the nearest 100th it would mean to use only 2 number after the decimal point = .50 or 1/3 = .33 If an instructor wants you to give your answer to the nearest 1000th it would mean to use only 1 number after the decimal point = .500 or 1/3 = .333 To change a decimal into a percentage Simply move the decimal to the right two places For example: .25 becomes 25% .5 becomes 50% .125 becomes 12.5% Multiplying Fractions To multiply fractions you simply multiply the numbers straight across 1 2 2 --- X --- = --- 2 4 8 If you have a mixed number, you must first change it to an improper fraction before you multiply (see page 3) Dividing Fractions To divide fractions, take the fraction that immediately follows the division sign and turn it upside down 2 8 --- --- = 4 3 Then just multiply straight across 2 3 6 --- X --- = ---- 4 8 32 Remember, if you have a mixed number, you must first change it to an improper fraction before you multiply Adding and Subtracting Fractions To add or subtract fractions the bottom numbers must be the same (Called a common denominator) To find a common denominator you must find a number that both the denominators will divide into evenly Sometimes the higher of the two denominators can be used as a common denominator 1 7 --- + --- = 2 8 In this example 8 can be used as the common denominator because 2 goes into 8, evenly four times 2 x 4 = 8 So The 7/8 stays the same BUT to change the into something over 8 we must multiply the top number by whatever number we use to change the 2 into an 8 ( 2 x 4 = 8)  1 (x 4) = 4 2 (x 4) = 8  4 7 11 --- + --- = --- 8 8 8 Now we can add the top numbers (THE BOTTOM NUMBERS STAY THE SAME) Sometimes a new number has to be used as a common denominator For example: 1 2 --- + --- = 4 5 Here the lower of the two denominators (4) does not divide evenly into the higher denominator (5) So we must find a number in which both denominators will evenly divide To do this you can multiply the two denominators 4 x 5 = 20 20 is the common denominator because both 4 and 5 go into 20 Now we multiply the top number exactly as we did to each of the bottom numbers to get 20  1 (x 5) = 5 4 (x 5) = 20  5 8 13 --- + --- = --- 20 20 20 The term percent means "part of a hundred". The use of percentages to express a rate is common practice in the food-service industry. For example, food and beverage costs, labor costs, operating costs, fixed costs, and profits are usually all stated as a percentage to establish standards of control. To indicate that any number is a percentage, the number must be accompanied by %  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/pexample.gif" \* MERGEFORMATINET  Example: If 34 percent of the customers in a restaurant favor nutritious entres, a part of the whole number of customers is being expressed. The whole is represented by 100 percent. In this example, all of the customers that enter the restaurant represent 100 percent.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/d_p.gif" \* MERGEFORMATINET  To convert any decimal to a percentage, multiply the number by 100 and add a percent sign.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/d_pexample.gif" \* MERGEFORMATINET  A shortcut would be to simply move the decimal point two places to the right and add a percentage sign.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/p_d.gif" \* MERGEFORMATINET  To convert percentages to decimal form, divide by 100 and drop the percent sign.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/p_dexample.gif" \* MERGEFORMATINET  A shortcut would be to simply move the decimal point two places to the left and drop the percent sign. Chefs may use percentages to calculate and apply a yield percentage or food cost percentage. It is helpful to remember the following formulas when working with percentages:  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/formulas.gif" \* MERGEFORMATINET  Helpful Hints: First determine what you are looking forpart, whole, or percentage. The number or word that follows the word of is usually the whole number the word is usually is connected to the part. The percentage will always be identified with either the symbol % or the word percent. The part will usually be less than the whole. Now it's time to put this knowledge to use. The bakeshop has an order for 10 dozen rolls. Forty rolls have been baked. What percentage of the rolls still have to be baked?  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/rolls.gif" \* MERGEFORMATINET What You Know:1 dozen = 12 rolls10 dozen rolls = 120 rolls40 rolls have been baked 80 rolls still need to be bakedPercent = Part/WholeTo find the percentage:  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Percentages/images/problem.gif" \* MERGEFORMATINET  1. Find the decimal equivalent of: a) 9.99% b) 0.5% 2. Change the following to a percentage: a) 0.0125 b) 2/5 3. If you order 300 lobster tails and you use 32 percent, how many do you have left? 4. You have 60 percent of a bottle of raspberry syrup remaining. If 10 ounces were used, how many ounces did the bottle originally hold? 5. Mr. Smith purchased $125.00 worth of spices and herbs. Because this was such a large order, the supplier charged Mr. Smith only $95.00. What percent discount did Mr. Smith receive? ____________________________________________ Answers 1. a) .0999 b) .005 2. a) 999% b) 40% 3. 204 4. 25 ounces 5. 24%  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/bridge.gif" \* MERGEFORMATINET  The bridge method is the "recipe" for converting from one unit of measure to another. It can be used to convert ounces to pounds, quarts to pints, tablespoons to cups, grams to ounces, volume to weight, and so on. Example: teaspoons to cups Step 1: If the unit of measurement that you are converting is a whole number, put it over 1. If it is a fraction, first convert it to a decimal and then put it over 1.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/step1.gif" \* MERGEFORMATINET  Step 2: Place a multiplication sign next to this.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/step2.gif" \* MERGEFORMATINET  Step 3: Draw another fraction line.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/step3.gif" \* MERGEFORMATINET  Step 4: Put in the units of measurement. The unit of measurement to be removed is written on the bottom. The unit of measurement to be converted to is written on top. The units diagonal to each other (that are the same) cancel each other out.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/step4.gif" \* MERGEFORMATINET  Step 5: Enter the numbers to create the equivalency.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/step5.gif" \* MERGEFORMATINET  Step 6: Multiply straight across.  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/step6.gif" \* MERGEFORMATINET  Step 7: Reduce the resulting fraction (if needed).  INCLUDEPICTURE "http://www.ciakids.com/CulinaryMath1/Conversions/images/step7.gif" \* MERGEFORMATINET  Convert the following using the bridge method: 1. 5 gallons = ? qt 2. 78 cups = ? quarts 3. 18 tsp = ? cups 4. 2 pecks = ? gal 5. 9 tbsp = ? tsp  Answers: 1. 20 qt 2. 19.5 quarts 3. .375 cups 4. 4 gal 5. 27 tsp  PAGE 4 *** NOTICE that 1 and 3/2 are equal! 7 = 7 8 = 8 2 (x 4) = 8 5 (x 4) = 20 U.S Standard Ounces to Pounds Metric System 3tsp = 1 tbsp = oz 8 oz = # 1,000 ml = 1 L = 33.8 oz 16tbsp = 1 cup = 8 oz 16 oz = 1# 1,000 g = 1 KG = 2.21# 2 cups = 1 pint = 16 oz 32 oz = 1# 28.35 g = 1 oz 2 Pint = 1 quart = 32 oz 64 oz = 4# 4 quarts = 1 gallon =128 oz  !WXi    $ % & ' q ճtp_UMh&mh&m5h&mh&m5>* jh&m5>*UmHnHuh_jh UmHnHujh_UmHnHujhT"UmHnHu(jh 5>*CJ UaJ mHnHujhyhUmHnHuh&mh%h?&3h?&35h"h?&3h?&3h%5>*CJ aJ h?&3h?&35>*CJ aJ h?&35>*CJ aJ !"JVWXij   # $ q  gd_ & F$a$gd?&3r446q r s    $ % 4 5 8 : J K S U e g s t u v າʦʚʚʀxʚʚnjhG9 hG9 hG9 5>*h"h%;5jhl5UmHnHuh"h CJ aJ h"h 5CJ aJ hh 5CJ(aJ(h%;hTz25h%;h 5h%;h >*h jh[UmHnHuh%;hTz2h&mh&mh&m5jh&m5UmHnHu) 3 4 t u v   h i  ) @ gd_ 򿸪wog_[hY~7h7hl6h7h76h7CJ$aJ$h7hl5CJ$aJ$h7hl5h7hl hl5>*h<hTz2h h%;jhb*UmHnHu hG9 hG9 hG9 hX 5CJ aJ hr"hr"5CJ aJ hr"hr"5CJ,aJ,hr"5CJ,aJ, hr"5 hG9 5hG9 hG9 5#        ! ' ( ) 1 6 8 @ A B D T c d h i j n q r s u { } ǿܭܭ𦟕xjhEUmHnHuh<h<56>*h<h<h<5>* hl5>* hlhlh_6CJaJ h_>*h7h7h75 h_5h_hl>*h_h_6h_h_6CJaJh_h_>*h_h7hl5hl/@ A B > c d } {gd_gd78A]c,-.D./8=?bɿɪɅɓvrrjf\hT7hT75>*hC^0hRN9hEu5hEujh25UmHnHujh,CUmHnHuhRN9h|5jh,C5UmHnHu h|h| h>5>* hY~75>*hC^0h|5>*h|jh2UmHnHujhEUmHnHuh<h<56>*hY~7h<h2!{|-DE/3=>?cdgd| p^p`gd| Fgd2bcpu|"#@ABcd124ǕǕyql hRN95h>hY6hYhY5 hY5hYhYhYCJaJhRN9hRN95hRN9hRN9CJ aJ hT7hT7CJ aJ hRN9hT75hT7hT75CJ aJ hRN9hlhT75CJ$aJ$hlhT7CJ aJ hbhT7hT75hY~7hT7hT7hC^05>**$Cef2GHuv*+,-ghgd>gdRN9gd|45BGHdtuv*+-np(*h(+,9>Ϭˏ}u}me}]hh5hh>5hhs5hh{5hsh{h{hY5>*h{h{5>*hY~7hY~7CJaJhbCJaJhY~7CJaJhY~7h>CJH*aJhY~7h>CJaJh>hY~7h>5CJaJhY~7hY5CJaJhYhY5 hY5hYhYCJaJ$h,?@AWX  lyz$a$gd;gd|gd>>?@AVWX   lxyz-.gzodYNYhhbCJaJh;h;CJaJh;hP-CJaJhbh`CJaJhCJaJhP-h" 5>*h" hh" 6hh6hbh;CJaJhbh7CJaJhbh" CJaJhbhRN9CJaJhbhRN95>*CJaJhbh75>*CJaJhbh>CJaJh>hhs5Egh234"*MN$a$gdgd] $a$gd;gd|gh 234 -?@*,yynyhhCJaJh;hCJaJhCJaJh1 h75h7h7h] 5h7h] 6hEk%h] h] h" 5>*h] h] 5>*hbh] CJaJhbh7CJaJh;h;h;CJaJh;CJaJhbhP-CJaJhP-+,:>MNO^_`_afghjkopqrstv|鬚}t}t}lh_h86h86CJaJh_h86CJaJh8h_h8>* h8>*"jh8CJUaJmHnHuh4CJaJh1 h1 5>*h1 h1 CJ aJ h1 h1 5h1 h75h4h7h75h7h1 hCJaJh;hCJaJ'NOfgi~HIJ$a$gd_o$a$gd8gd4gd8$a$gd4gd1 |}~ݻvkvhh8CJaJhRbh85CJaJh8h85h;h8CJaJh8CJaJh1 "jh8CJUaJmHnHuhRbh85 h85h_h86h86CJaJh_h86CJaJh8jh8UmHnHuhRbh85>* h85>**&FJV`.····ިިtktkthRb6CJaJh_hRb6CJaJh_hRb>* hRb>*jhRb>*UmHnHuhRbhRb5hRbh`hh_oCJaJh;h_oCJaJh_oCJaJh`h75h7h1 h1 5h1 h8h;h8CJaJh8h85 h8h8&jk-./)$a$gdRbgdRb$p^p`a$gdRb$a$gd_o"$)*V ̺~zlzhhex5>*CJaJhexhhRbCJaJhRbhRb5CJaJh;hRbCJaJhRbCJaJh`jhHx<UmHnHu"jhHx<CJUaJmHnHuhRbhRb5hRb6CJaJh_hRb6CJaJhRbhRb5>*hRbh_hRb6()VW !%"""[##-$~$$V%%&s&t&&&A''''t( & Fdd[$\$gdexgdex$a$gdexgdex !!!!%"&"""""""W#X#Y#Z###)$*$+$,$~$$$$$$V%%&&o&p&q&r&&&&&''?''t(u((((((󯩠jr'hexUhex0J6] hex0JhexCJOJQJ^JaJjhexUh{Ehex>*jChexUj?hexUj> hexUj#hexU hex0JhexjhexU4t((((()\kdQ2$$IfT-40Cp634-apT $$Ifa$gdex $Ifgdex(((()))!)")=)>)?)_)`)a)v)w)))))))))**++, ,!,N,,,,,,--- --޸޸ޖއ|mjFh]hexCJUaJh]hexCJaJjh]hexCJUaJh`h-hex6CJaJ hmOhexh{EhexCJaJhexCJaJj5hexUjhexUhexCJOJQJ^JaJhexhexCJaJ)hex5B*CJOJQJ\^JaJph33*)))!)")#)0\kdy3$$IfT-40Cp634-apT $$Ifa$gdex $Ifgdex\kd2$$IfT-40Cp634-apT#)=)>)?)_) $$Ifa$gdex $Ifgdex\kd 4$$IfT-40Cp634-apT $$Ifa$gdex_)`)a)v)w)0\kd55$$IfT-40Cp634-apT $$Ifa$gdex $Ifgdex\kd4$$IfT-40Cp634-apTw))))#*.*6*8*=*h*t*|****b+g++!,N,V,j,~,,, ^`gdex ^`gdexgdex$a$gdexgdex,,,,, ---./A///=00111=2>2?2@2c2223p3$a$gdex\$gdexgdex ^`gdex---... / / ////A/B/////////90:0;0<0=0D001111111111192:2;2<2=2H2c2d222222233l3m3n3o344)4޾޶ޮަjhexUmHnHujihexUjdhexUj^hexUjLZhexUjThexUjNhexUjKhexUjhexU hex0Jhexhex5B*CJ\aJph4N4\4f4p4q4r4}4~444444444444gdRbgd4gd2$a$gd_ ^`gdexgdex)4p4r4s4y4z4{4|4~4444444444444444444444444ºҮҊ~tjf~f~^~Y hRb>*h8h45h8h8h45>*h8h85>*h4h_h4>* h8>*h2CJ aJ hEuh25CJaJh|h2CJ aJ h|h25CJ aJ h2CJ4aJ4h|h2CJ4H*aJ4hEh2hE0JmHnHu h20Jjh20JUhexhhyhexCJaJ 444444444444444444444555555#5$5666󺲮h$ h6ghexhexhhex5hhex5>*hRbhRb5hRbhRb5>*h_hRb6hRb6CJaJh_hRb6CJaJhRbh_hRb>*44$5%5c55556666gdex 1h/ =!"#$%? 01h:pex/ =!"#$% P0xx) 01h:pex/ =!"#$%? 01h:pex/ =!"#$% P0xx6 01h:pex/ =!"#$%0x@=*NV;$͵,\<  &&*x=+떞}}m @um?2f`;P*:p183' (L"gLgs4WRIU<UϷt:3?~tmoΗA_txwCO~AO}R?o{/L>yw?~yӏ~;ǏSzO~3|矗K%Ϸ-8 郇zٯ=hXdN&ǎ7HѣHBMv&Hz-u:z%bnfWVGv۷orqa' x<͆ $NKz)a!D^=zY?O?}+Zrr$, I^O~Jż'jK _'Y+WyxYTQ@'ezE:L 辆ɓ-6}Ə@a/gh;cDz͞@UV>s+F#|fh+b(mFuhֺooo8p\.ydn]\=U^JmJr,ODA}Ht2+WG 1MJzAdxo;"/UAhZ^NZJgmnw_^^J>uay)^%^CBy|*7XFBW*z-<==V+IC^W3R ےh]r({1|™', y~-g3h HCݒ11 {+*$Bli .禌b2 p5{$M& B;^#PfOqJ\|Γ߾}&5͞^cpHu<U@7by}||li)7).NnzNDJ"ID\Dl6=&,4R|7"4zDC2:ñjǒ^mɁ%m5Jfe[`p>ا"NuZuR"ʪw:gChy['[%?<;Iwu^nJPg['Oׂ^^MgB5Y}zx- IrLT%ًqc̫3f~͖'zۖ`:ttGޢ5R9dOr X6 "E' ?Bf y5NYb3 -+(BS&8 zXVyǔ8քlh^VA[2\R\N͖=EkKԘc*m@Wf$ۼ4m}(VF4O_~!ظG((y~~Wof#-3+,mFy5ułS~Ch9-{֗IvH_D?EcnW䑗 ͶTvNcDf!ϝ{||杜p846I@]j-Nι[R1uh֟ ŗH~2l[EdDT'v}?#i似Ssh1g0$w^ [Ni^8qh%4C9T Ypr+㒔/ f=ęJCvzyf[g;3vhs)xy^1h6PYnܟڹ0 h+vs'=mPp:VYC9'xf9hu5`vEPh68=yETǧs.\^XS4Zg[h6;,RfR]yhLmUswhiG1EcdzB~:~,l"6Π;4+zLpƁsY@idgn`d,|@,;dMQxl|8LϣZ+cl:8\edCDޖE93ä,Q69h6nWj.h6M˷{Q]f6A,M*FMkbפiM<I9lRX5L fZ  ͂pZbY[Ͳ,[3BݔJ6NSFgdh6YKηA#hN=e:fi14fb!MgعjB hΰd1jqmb2W@P)mZJ@-fMs*nChcU,1or.3B1e~hכXApOcfgElնi*3/*o`I2hnVYF,Y(]^i eY 4 ~,Y9 e'4 P4>ꎕY4 6M (FY<,܈mbNMzY ɨhֺ!~,J/ e* =hάX.HaپzCfBԱs1Y(N;i7ۼCw*@v EIuȶ$уfrGݮVa2zhB)f跎{d=a4fv:*6tGpG5(6Kl3ɀfZYG)GhQf^\P%f.!uYVT4 aiB@fmmh|֬bJ4 >k֖<1q͂Ϛ4Y?;,8qZlfb2=>>r&ְ2 ͂vK)Y(ױ ^q~lZUpY(:C>fNF4[dq&B-h[l4 ַVylq͂4jZ?1gÂӍ4FԴ7tl=[@Icdl1ψ<48_Ja#M|;lsfSv]hBnh6M솕YI:'W0͒}:-nQfszx΅ZƊN-V{3,'lFv\z{Τ+,Fgͦld}9嘨ͦid}Z4 ԲVfS[ %;ExqFق2ͦcd!dd1h6)F}^c:_>(Ƅ &{ϖh6&dFGDh6b#;˧ajlFg&TlkHYliC7OgMmP g"h>!٘ROYQ}Ls8!8F[dYbfih|]\U f;M;g5TfCy<* 4^[k8Idf}ƹSF^!=znv†~r/4Ӑ5fEgi4tyY̜36 z,-27^ ucw]f[ǙͪR,,l8Yܩ6#EmZWR  j E^l)s4نl6 ؒCRd4 ιAݻVG> 6@Pxz"=4[y."&-m2*\քs,Wllc[[x4٢W%˖ih>fe\ʶ"[4{ BGc9O}xx+ 4[L^O4,b$קsU2x`[gD>ҩ"ؚ(0OOOۢ<:=OLUk~薢ZE3ii1y@̼V\4&IsTNc;:E`IL!%OR YV-2S֬ y'+fu߆QDer-8e$mV**|0q (+xxfGuшSpY)Ukv\:Ge@RiN^X"#2Ngl6KOU&ժY ImN;BZNpOۂpR72GcpclyRL!jVj-y:ۂf,{ż&^eǼih,ˋqk|xyy,^^'nnXFdK$^cbЩxUV jV5owug`)N]&qJ/Փfۂɳ+)WW!.G4{E 2&@rIw)O4-\gat:kCljVWR҈ӕfdJ.@9=^YV4n偌F'%w|Ku3'>5YrkK'g3#R2yBlUT\%լdEW HR+:[ޕݼ\fITʳ Szz2 ߤ5AQ:-;[0xxE={*wDz5mwfw|EU5l ^LiA'/Z2 q-ÙhVj:KBGS|&[,7TMѲYTfhYiGֹOS h_K"b} UmB5͐*Do߾ݒzmE7wd^Vt vz\R'_e635"Jj\jr?s_CyT2i\xl0 uDZrsj葝ʶf˿~?9AL$ݸ}(&XK !r8֓\놘sGg|ɟ~__5BRB1InxWGz~l6;vYTQ@'ezE:L 辆ɓ-6}Ə@a/gh;cDz͞@5^5h mE2Z͈ZM=%O4̍bK u[IݺM"VW.UE(Nf*?0[h}!IwTWI/̴-<`pG$2:>HV@KnKɧNB?,/Âv> ]q~F eوQA^%^CBy|*7XFBW*z-<==V+IC^W3R ےh]r({1|™', y~-g3h HCݒ11 {+*$Bli .禌b2 p5{$M& B;^#PfOqJ\|Γ߾}&5͞^cpHu<U@7by}||li)7).NnzNDJ"ID\Dl6=&,4R|7"4zDC2:ñjǒ^mɁ%m5Jfe[`p>ا"NuZuR"ʪw:gChy['[%?<;Iwu^nJPg['Oׂ^^MgB5Y}zx- IrLT%ًqc̫3f~͖'zۖ`:ttGޢ5R9dOr X6 "E' ?Bf y5NYb3 -+(BS&8 zXVyǔ8քlh^VA[2\R\N͖=EkKԘc*m@Wf$ۼ4m}(VF4O_~!ظG((y~~Wof#-3+,mFy5ułS~Ch9-{֗IvH_D?EcnW䑗 ͶTvNcDf!ϝ{||杜p846I@]j-Nι[R1uh֟ ŗH~2l[EdDT'v}?#i似Ssh1g0$w^ [Ni^8qh%4C9T Ypr+㒔/ f=ęJCvzyf[g;3vhs)xy^1h6PYnܟڹ0 h+vs'=mPp:VYC9'xf9hu5`vEPh68=yETǧs.\^XS4Zg[h6;,RfR]yhLmUswhiG1EcdzB~:~,l"6Π;4+zLpƁsY@idgn`d,|@,;dMQxl|8LϣZ+cl:8\edCDޖE93ä,Q69h6nWj.h6M˷{Q]f6A,M*FMkbפiM<I9lRX5L fZ  ͂pZbY[Ͳ,[3BݔJ6NSFgdh6YKηA#hN=e:fi14fb!MgعjB hΰd1jqmb2W@P)mZJ@-fMs*nChcU,1or.3B1e~hכXApOcfgElնi*3/*o`I2hnVYF,Y(]^i eY 4 ~,Y9 e'4 P4>ꎕY4 6M (FY<,܈mbNMzY ɨhֺ!~,J/ e* =hάX.HaپzCfBԱs1Y(N;i7ۼCw*@v EIuȶ$уfrGݮVa2zhB)f跎{d=a4fv:*6tGpG5(6Kl3ɀfZYG)GhQf^\P%f.!uYVT4 aiB@fmmh|֬bJ4 >k֖<1q͂Ϛ4Y?;,8qZlfb2=>>r&ְ2 ͂vK)Y(ױ ^q~lZUpY(:C>fNF4[dq&B-h[l4 ַVylq͂4jZ?1gÂӍ4FԴ7tl=[@Icdl1ψ<48_Ja#M|;lsfSv]hBnh6M솕YI:'W0͒}:-nQfszx΅ZƊN-V{3,'lFv\z{Τ+,Fgͦld}9嘨ͦid}Z4 ԲVfS[ %;ExqFق2ͦcd!dd1h6)F}^c:_>(Ƅ &{ϖh6&dFGDh6b#;˧ajlFg&TlkHYliC7OgMmP g"h>!٘ROYQ}Ls8!8F[dYbfih|]\U f;M;g5TfCy<* 4^[k8Idf}ƹSF^!=znv†~r/4Ӑ5fEgi4tyY̜36 z,-27^ ucw]f[ǙͪR,,l8Yܩ6#EmZWR  j E^l)s4نl6 ؒCRd4 ιAݻVG> 6@Pxz"=4[y."&-m2*\քs,Wllc[[x4٢W%˖ih>fe\ʶ"[4{ BGc9O}xx+ 4[L^O4,b$קsU2x`[gD>ҩ"ؚ(0OOOۢ<:=OLUk~薢ZE3ii1y@̼V\4&IsTNc;:E`IL!%OR YV-2S֬ y'+fu߆QDer-8e$mV**|0q (+xxfGuшSpY)Ukv\:Ge@RiN^X"#2Ngl6KOU&ժY ImN;BZNpOۂpR72GcpclyRL!jVj-y:ۂf,{ż&^eǼih,ˋqk|xyy,^^'nnXFdK$^cbЩxUV jV5owug`)N]&qJ/Փfۂɳ+)WW!.G4{E 2&@rIw)O4-\gat:kCljVWR҈ӕfdJ.@9=^YV4n偌F'%w|Ku3'>5YrkK'g3#R2yBlUT\%լdEW HR+:[ޕݼ\fITʳ Szz2 ߤ5AQ:-;[0xxE={*wDz5mwfw|EU5l ^LiA'/Z2 q-ÙhVj:KBGS|&[,7TMѲYTfhYiGֹOS h_K"b} UmB5͐*Do߾ݒzmE7wd^Vt vz\R'_e635"Jj\jr?s_CyT2i\xz$ȷ-0P D0>gs^ҶU_ճj^ZgOp`/orW;ͯ\?o^XW?ѯ??޿??~}?7?~?՛_}z'/O֧>IoyէlnWן\D䈰$’K",K",$’$’K",K",$",$’K"’K", [Ԗ%rbIAY~37nT ~-ؿ%kYu ’<2{6%Nd'hX:u`mنmg[,Qm( R(H!KKn,QQ,1JDKq)I K5.o)GpNkЍWv h?K- H,:\7j SsK|,͚BXj7m\.sΒki¥g:tHKnV `nK,e/U =[uRܱ:^H=Bޞk_Ʌԛӄ)7[ݛ+RcN=4͕+fZEH_=Jߏ/E>: fZαOjN\WN:qj]Ajé߳SwfЕ_:}ϳ&ӪV?SIunq5ͩG )Stz-*!&fE;ceMDN}5hnVľple֜>8!Q8%yx%kyvTh4W3sV4v4D[P:j ' s]a!KFFRnnM)QR|(QJprm"ʒR+ ndun-_ej8q:6יZDeM`ϨlV}qχv|-]b 级fC|Y5פT<#𘥚cHXIg6 .ҥW2dr-0Knl0m| ;hKwkAjvHі AvHі fVG{!1+*WkKri~!RZ՟ iuyW3Z*c!シQR?jJG*R{H,)u9bPBgQ*kJ? RKK^WQZz/UYs"SUiz[zo'%sM%3oW$Qԟ%aI%aI%D%DXaIDXaI%D%DXDXaI%aI%DXDXaIDZzaԿw|r|?|Z翼\~~ǯ]??}^?{?\?_X?7~jcEXaIDXaI%D%DXDXaI%aI%DXDXaI%%8wڲD],I1}>uRÒ4w)8K:}Rm!7ZJ͒<)KYm<:_)2Kr'+fInL,8}hR[䙜@bIT%yf ?4ADK"^W,N ʝ%9Kr،DK|H/$GĒC$?G‰%y* KH@h@b@zѲX ̰-HY©HqZy!K!K!-dI%Y}CK,%Az%Ӗ:{7-p:yRb:X09ґ&sb GLN'z [Tұ`'@Zs8uNc@*biRiHw 8&pb ,津i&TRcN[RiH'Xi~v5H5-5㴫!,tsN,RNp8H-5qY* iϘ崹n7r9m.K!mʉX8N'-M)R39K!UJj0H)srH X*Ω0KAS|+ K59:l)\Il/HYjVB3RzנS8K8Kr3i _mq;+^) %Z8+^c)E)fKMOZQ$ {T7j!^[{KѐVZǠ[ Rz[؍-5t`mN>`-H)C?c!H)ұ2V4 h4$fEUꃴuymIZNU!/D [KU!.{FRET,񽗷4*rUJgBZM_h"PE[j9.G *@H,=J%x-bVAji0 J? RWKe 1/tR|jsJ? RoK} >giUr@b KivReqpbi4lK;c 'k[;&K DT[K#4>`tN]n_z+K DTI[x֤%BE,]<_/2X%X.AKDuDKy(b n-"`"%"-zKDmoRQU]KsTǏ9iaG}X>$D9,$",$’$’K",K",$’$’K"’K",$",$’K"’K",[KZ_|~}gZwHZc#Dd(sV  S 2ApexamplebyrDCD/sϽWUDenMrDCD/sϽWPNG  IHDR!`PLTE??oo__﯏//OOkkbKGDH cmPPJCmp0712HsrIDATXGr D$vxSv624x˛{˒|HOѧmNn hip)FhI {䟨\IvEݤSA ߬_'a3|b׉ DTrC>G3e]˧+tLW>P|p䡟 w72q͒j 1T ]B-ckiN*&k&ݙOC./ oEmϪt ѧ9d|^S!>u 0f3~Qy l|+݂eVZpЇyҝ=4t#/s#8v^sق4>;v 5*3`e_ٟ~L3>CSo[X6|pMgz(vVXV^5Ga)в0IZ>#0-Y<)"}!-y8a[9\Qn@NC~'@Cl3>o>qgn\\g{ck(@XCjJryfGgCd[T"oi\`5ȼLZ@gYM~P~ݑ_P/t p/XTȮW(t_id!D2B#-.ʉC9:ls/äXh_Sןuཾe +L{O+6wq5U?|zS揠vm|\]v$-C=2'8]T[^ʔ" _jn{M~~F+R&_IENDB`DdwL  S (Ad_pb{R$# 9.)LvWgenOR$# 9.)LvPNG  IHDR<b`PLTE{{OO??߿//``S~bKGDH cmPPJCmp0712HstIDATXGWk NKb]Vɇ]L3=1׸ <}M= VWH>]|lԉ; |&7$cx3\64o9B@{ Y%`pUcWNldX}OՌ=؄$}ȫPju u7uNCBYW.VC6F̽;V uW9' 'W2.sG6od;qzl 'lf]F~&?٤W9:&zA#ɣ @}H!՞繘 fy>6o/Ik(ڬ9,|<5xK x# +yP&택ez"|ty5DiW/Yi&5^_l#| 튏ml<ָݬ1AI#Buo9Nmr@kEGh$bt7h#of#Tbwp*O=onn5CnJApjx*UN5RwȿHhW^@TmZU5oD Jhi7}nEhc=yl<ѿ{^ԣfn.GFېk$NuRVϣXZKx-EoIJƉ3i͓ ydUϻ<CNoW!o(UEݭ}4v@5=4"28WZL2TZeZJ2̊6jY}ˊE*\kOoVb8okdMR9iw-F_5.~q,_IENDB`Dd=Z  S 6Ad_pexamplebS7kQ<:/ en'7kQ<:PNG  IHDR!;m)`PLTE??ߟ쟏鏯__//ooOOܑSbKGDH cmPPJCmp0712HsLIDAThCW: }k +- MX"9!yAߵmWfq}x*)=ǔՓšk.KG|c> s<\A`4.$ܱ}UPT"tѰ:0b̋$R1/=SQof2l\'cQ}q<[$1EP( q.^c'vIX pZG#O,il*^;fU3*,)1 l1+Tz$ph]u{e {xYB@RX5SQ )Ut̰7L9)c,X*p$b.2EqrP,Sh7ۢ. %󡺣UU\DGT7,y{(HXPw>fk0UyEe87kUgğ ֯B=EʬY|>Ya`[}Gw'7!O?Ư0Oo_Sv>oB/`|x]+Η?6IENDB`Dd4WL  S (Ap_dbd҃ї+x V@en8҃ї+x VPNG  IHDR6`PLTE{{OO??߿//``S~bKGDH cmPPJCmp0712Hs]IDATXGWr $!.ȒV4~$6ww`c.V7dߴ( 5]θ ƪ ?SgpxbC߻-r.? F8~vRrxQ-vf8| v( Ί'W|‡T[4N|u,R+PAy*__X{44Oz* j[l^ZXgmќqA! "M7 < _8T>!Aj{E4xi}?Y#jF}p.p0T[Blg9ùrF#;k+lP 66*dVE;![qc`{IV:.CGZJ>c^  Z6c%y8t;4>5(VҎ[UCf3cfvl'|` "cU"1I^LP&LYe 4 6g`i6s}JwkV+lgcg $*l8 #D6 x$5 /X}M{m:YwvكnE@ 0l c;Nr.Rl?Զ4jw5ZJǵ2 CkIm5l| `‰꫃^MKe6 #:Y !, ǚ1v]]@|ZhQKUjsl{Օ&Y7ڞz`crMD#Ƴ<qo[dϦ \8d*2mWIwJ[?(X)M}gq FPeemAMmh!lV, iPPV(s3hc֤L@Wzns6!ƜNFީ8 SiRqsaWhAj^c]J4z mm7XLz Y:膃UJU2͐¢ߤQϒك顗[GwXׯE\V$/RK%ۈV2#x?vơ6..>o$U,^AIENDB`DdLsZ  S 6Ap_dexampleb# _*8B+een# _*8B+ePNG  IHDR!;m)`PLTE??ϟ//__ooOOWbKGDH cmPPJCmp0712HsIDAThCVv j ƖkwFėK9mF363 AZK+{\߯wK>){| nQk*:Ok|^G!-ЃD<3\3%Uݗ: 60G_mB8ۏ<5V ŹE&33W#2}xg&: HH9Zx6sw=I2ocNR thuAC28 *1Cƌ.}$"[ְ%,Zqm> e0,ڦ ϭ?"tfKMZX4zBeϔpOHb0-Da5j68f40Z7R1g^gḥ붦i>HE,h0YgwO4"w zvݤQ+KdY 7W8YL$܁ؑ n܌؁Pùnavy0e yĂBPDDĬ&&i\n63 !s,}hxV#%! EϦc E WG,iPNO3\'f wf c>Xh.wkh}0 ɓ7o/vc֣OjEk>9%[+l\osUo`,O0} Rdq9Vv VhHl`›3 8΀3"1ŏ~cMh}x:,DKC2d}ceyT1/^ǧN8p֢yя2?r2 h\꺁/S+XBO&&EH /Lc0m_lj)znn6LWv[0!2w֥Rt&NgS< )KvTK.mkrlrnjbyS7o%9SKNQɴNpzL.t#?G.V K# .%Jlwgy U flSt/jfO}~gmmXû1`y 31-qg=پ7#HH]Ɩ89V'|y1N]쳋enq^ʧ'7N3\€]',3*O J*ѐOFB}5{K oÉβI~ yDoMKͥңMW٘06Qn4hGCT(/MK8M Sm Yz-pΤ)6ߛr1>UO#OlaFV5cp"ed^k\lLLeK?gNP֔pXG /ѫ5sǞf8r 0vdjS=Po[g 1"*I"َք%gP}}iIW2(S™r<R|TEH,!uNLEޥmAV)K D243}:]O]jmSggD$eE`\Mebܳ/H7'qgl]K0$gmܺ[`-e푫Vt<`3efE939hU*g4b|S}Nehr#Mwf?Iyv?̴n,݌#HM_Ȯ;GgpgpgpgpgpgpcBg++YZx}wPi؅^_-7W/sUd/F(P< 8(k׍c&{v: ƝLBS'ȂbSE`A"F"Oɚ1* 1xҙv~N+hfr=QѮ,D P[q^WQ3Vt>πeaU&ci]MشIF*5w~&~}1̈kN\HW/S $9Oz'ѧA#I͹Zs ;y㇁)RL fJ~BFu e`P6%ۑ̄ŐC@*HH? %"r3Q?! G'WH3Q;b3En{z!=aӃAH&;q 9J%S{u?FV6-0dZdI\bS$,NxM>)0YzT/ R{Y DOREDRѹ`2Ya[! d؍xy ̛9C8€Qx G LI0@hw K|Y/N6aH=;(ʏrn;IH "mNUmk6ݱv,CF=N ^nT 9k1S G2f8g#K9TFV0T':V7%1wQ˓KO 2Xɍf&-Tn Onj*l옪 )6R&k\ت1{ܤ&"a3 Ȫ7F~ 8[dCYh" U_|>AkGmE|%d%5S7JH P'nEP~-r%^)HJ F9![iT3oI Ajox(bAWbޤo71mx.4-//铭SR4tȔۓK]KPVJrXnԚh0֙r0B%k3_b[qLnŪ1\z?GKVxp'2:Ӎ9GյrEj,uX|dنy~g[ ihkSh `>ORvrTxN%'@\EU,MKX n9fd4$Nvd]Ha'-KL8||ҍLBj*)} w2#yƨ8j$X:mUb4u+)#!i;;j㥪52ػg ;0ćvD ŐquXb4=Z.?(}&M*hXQEz<4$Վ6d K O~Df~)7?7a]gK~Tyj@XB[0`4w}{`lDjrD^;X[YkRh`l !WZj/-Nh ¢QĪ?i{]XUcbeQU.ob6B;Umze!D"iR1lplaە}>{tt͢9cY|K{}W{mwC{:EI'R7u`#=e{#lnhVzydBT&E30w 0CJLPMv!C6#`l@iR|n1f҉bMn~T&{ 2>5kpkYlE_kXY"pUֿ>/syqOywڎ2N z֎q>Oׯa;JON# ON;R_M&,FKL9=ɩ#KN` ǻ1[ H.vIc%{s"\:oC,#!VO7c J@Sp-1͒Tr3uHXբd m8sw1Wx8yLj-qr_>{l! #;~hc_8IZgOw 肏ۿƸzz0IENDB`$$If!vh55w#v#vw:V -4p6+,5534-pT$$If!vh55w#v#vw:V -4p6+,5534-pT$$If!vh55w#v#vw:V -4p6+,5534-pT$$If!vh55w#v#vw:V -4p6+,5534-pT$$If!vh55w#v#vw:V -4p6+,5534-pT$$If!vh55w#v#vw:V -4p6+,5534-pTDd0T  S 0AproblembJac9o 6enJac9oPNG  IHDR^`PLTEKK44nn爙!!ڮbKGDH cmPPJCmp0712HsIDATx^]v \<&ۤ i C;4MMUUUU@ʊ&V{5FpmMujMGuj+kvu&s;(I6 6oMjڍYFQj͆-!VGeBgkȘir/XDa6%Ygnɔ粌J ӈ>u1EdhXt=d`&İv`צh OG+FFm>^8ԷUpcN H6RG/|pbx– d݅V~ł! v_!78{^c*i@@@ho5ӥ{j["k:+q۫/n 5 |DT|ͼQac-,@MD a諻pY2@mEez0"3%fxԷYYTp175Yܲ_P|R@+jm6?\JX )=t/>Z_“L̛wc WVf1ݘm̓ aZra\&2^& Rqb`-L1-Huad)ox\SGCR}2潗`Ռ@èBYK0y-P)8Q! . {d+E./Rg>8u>ǻ,P[2R4ui~R$+#D\T}s_XvC?iRlnRjz`/ ~, PP5`sVd %/lE t,ĘkW E n82[Wf̏8@n$'VvM瀫U-|.rbR| ݈9.7/pNiPǘs^M ^`"]Bp*#r>e   ZW3: +-',QDU;i0 ^u 7U9=aMj O =9xP(GYr[ rR "8¶p@2̨w",țhw!|a$/7I:Ic  觊J[7 [8NKiW 7u|B/ΑaҢR8S2i@*:<<8Vյ6Xp#4"8JYe>6ʱ"IaS a=j<@o{rD1{=L8sd݋e\{j^6cf Йxc;\@υU 0- tUڲ9)_2pp Ma$_,,OH0Dˣ a:@K4 Fl(%ΙRSORG(tX|Gaqԧ0 "vٜBE>3'q}E:3s__VPo:~7Ͽ-lf~{/6. ( 97ibնW |ꨨh 1IQ;H8B A;v4Vጬ]H;1a\/an]0qjP!Irћ1ذ'wƹ+LGͲo[WxLƍ+64')FқauNdDU7a2p/dD9sX1:=& 4I]S󙢐ug>.kLcڡ9<`Q+W ;A_p1NqޡU>"PXXQ?luH^ x37 b*$lg튖^IֶT T T T T |"4B~H]ڎ̙P+oH=D dK2~l|Lsm'}S(d1muP+@ߕj,k4"(W(Ωϵ2_,8?Pׇ<^[b7|}mBVC聶:U@ D=OBI PR~A(6RNj,(^_ NnsTsT LoZL*6A oi3njAilz ԅ-O9/[Koܱ4>)9s}-Ut3`-{y6z^QՉhaq}L? ;7& ^=o19oKҖ/H$c>pEFL?謘~>/hpyϘwDnG̒ ѰGE2Ho&֖Q\I$B{w%o)y< @A;) wߴ+~@q`*&F ޲d?Jȣ hI0)le%lѭ^RIxrn *5pdA+F߈K#:~'/5Ɂ3X" {ƌRũ/ 68s6IENDB`"DdA wR   S .A bridgeb|2= Lhߤ͍XFenP2= Lhߤ͍PNG  IHDRpߎ/`PLTE??//OO__oo쟯Wg@bKGDH cmPPJCmp0712HsuIDATXGVْ v%qfDʗCYh~ ^DGg9 %6Ϯ_"³fP úY'РPтsf+!䋎X4͈7\.C'_M 5'dZ:o δjӲWwƗC8#0ݽ[B \!Fc ~4TםogZR:rgOQLE>Yq8sߗ@lvV "?V |(D:lW~ ,eH Rh:okyuoW#)\LUP/ڎ;d\Bqn! %jtMъ0Z,&.A[Rd/Y#WH=fߴ(rQ *cl+z_?#,cBxF`J_~DJgxJ؆,LMh@;_nco1>IENDB`Dd8P   S ,A  step1 bOwc>UA^+*)+Ken#wc>UA^+*)PNG  IHDRH2Ȋm`PLTEߞ//__??OOpp*bKGDH cmPPJCmp0712HsHIDATHKmo VPk; 4M&פ=/(j/qmCv(a [X|1vHb2c6&!:pouΙ‰T/6Az@&*y!is `ڋ lkj ȉܚ"ũI0d ,^2ؐ 2ٌ 9B3[PKkYN [zXdXo᭺f-=L3߫C ޿!wBl֟ݵܳbge7hHPd25.4 1?:b܈_uIENDB`*Dd P   S ,A  step2 bFe!IFubNenZFe!IFuPNG  IHDRdΈ0J`PLTE||XX??Ϯ﮿//u<"bKGDH cmPPJCmp0712HsIDATx^[r#) $klڽžaPU*4HQjf`3 l6fgw{a*\bÙXsR0qij`cJlTJIkT5: cWHى&PsO3ߜ;  2%c>҆ dEhmzU*skpL5>|Ұ:9V)k}AX)zSkRn-^a-bREK@2ڴg61Ss^D!z@EJ=%"Uܕ#jM~~-f3V"-,6k ;+|wO-7N]h.QޑMR5~?9䬣_"Qگ%ޣ_7ҭ-8־ ]jk7V{> y h` #X9}0–g=zk8#5t# GL=Rbl;`Z$b*-NJ$kщb#Ј"UX<"f/bAGO3IyvuݔJ\*k՜]],yw3l ѠV4v*W*Nte|qG kM3[R~, m{\ݎytYc{W+ѢЌ( t4бz.){>l `,h0e4`M`X +{ٿZԩ9vAhc֌oʆ:Pb 3MDsi[bi<[x W3V7Gk1 1K%tPޕњ貑y~#@#sӡõ+>UU N+"RvyZ4Mf]nO 7ƉivQnjM֫Brz,Tz kjKrнzqz ^?/ږ|Hy NsD!n)8zR=XqɦWٽXiH0h$N: f]h<:{9'cJMy< p3 l60qA]tIENDB`DddP   S ,A  step3 bK3D ^G UenK3D ^GPNG  IHDRA?I`PLTE::{{WWbKGDH cmPPJCmp0712HsIDATx^Zn0 $$+_+`,KZuꈆ [1Ⱥ M[ڷ6V"fӿaopMd=coS-D,r՝!]Fl ohfX`#e|d&_~~e2wE8uP^P-cLJ2qG\:Aoĩ0j'Y0iaVxW)zQIn)(/# +t\;Tϱdv&xKu  _!x+c(L̝(@ LuV- 0[QꏉyEj8P傽b]K-w,k 1WuZ{Xk]t3@,?Vwת| [qfBxJ+,pSE.ȷ@09NƂXrt:n2?c!tG4͍2t|n@ut/š2x8M9@6aZ)DԙD5Bw(:Sԗ#W! SRvQT ηfLr h|@o@3wRv*. _ȗ:E*w%ꈱ1̘'$dQ}}^LMͼJ^]n|nY@q|w.Eز@+K; QYSp&|?Jfp-Q8,sE2Q-` ٚpTZ('?CڹC3N.h}f{TCTdM/F^='Ⱥ>W y`|-צ}s-``0k KZ&{E+^-. q{ͨsM>~ŨuTv`j9o[ ``00 ?XʹIENDB`Dd P   S ,A  step4 b6xD⁶D~(dmVqr0J^p{m1)$67Չ@bMQo/Fl# 9T_O?["&q,:@2D YdD@ HUR S_ֺ$rX,% v_IJl VXIIm-lˊNC@iE}_Za>%ǘOf"NńbklZfҜϰ0%c 6*YҸ$R/%$'8t`0AF#m> $~vA/nġA=[f)G4!p>ɖ~7ik;wÖv]csTS ==(z̊Vjwc5=spyl\",PU"ࣅcCN!ɯz!O! _$ˠJ8!i=xv ,oEDfW4 4r9Hв;^5'wk9g<~'" v*0 L?T? (WJmIENDB`ADd P  S ,A step5 b Ws~2qFZy_enq Ws~2qFZPNG  IHDRAhB`PLTE{{XX??//vvdbKGDH cmPPJCmp0712HsIDAThCXْ W8i {x&!l`4Pnf`3 l6_`:Ts<7aY"Z,jK,HeyOYȴ ؜D HONo ZTu87;'fk3ؠsLLz#2UHŋL27Ct|ETOZ1Ќi')Uۃ6`ӐZu'HX]8Ȑ R|R=2 ?;HK*㙒dM~YM4)`tf8vYe&kgqR0@z\&32\)aRivD7=qT2 MSOzEÍQ|2_Mph$X%/18! ˤK"a#=*?膣5>k7U7Ҝ8[}8!z0G@8ⰄOm_.?Ƣ%p5sU79Uue(.㚋16=Apؗw'5> Vm5To5I97ڵo0p Gj&^q\)ȍIa`^ơ$%-ve,JHQ>:&oeEU> ĥ9ڡ#nQv9^~I` vZl0K T=FOROgךOl f2A9$gP(PLs9AGtsA|5%649 o*p,e-Tt[&Ehe3MUٝ;.Aڞj3 l6 ?IGIENDB`DdP  S ,A step6b"x+݆A~7$7^denx+݆A~7$7PNG  IHDRAF`PLTEWWϝ띿??//oo]bKGDH cmPPJCmp0712HsIDATx^r0 - /2t7mXnE00uԐA`A`A`A`^&m;_?t*Y&a(K5b}]||K,7^JMDZS0Ca>fĪ)uBf(MRTX,N4q}[иw NvwI3aZ!7"ٙi^pfJ\ { ڟ` 'Hzrᠸo?Qn%>RI- 6>Reb{졣"%VTGe;OBd 0a9L+%0V;q|qNpIyRZy.$ELEeRGǁ~ld- bm D&%B,H |e)lƖM`!D'󬼃K _ aCZye0fi?WOfnO35ߘ5nO Q3 !|IU]qc) rtɤHFg -ޟV)žI.S9&Yi|X9C8 rge(. [-ب:6:_.~-xYї Dfq=tFb'jLi;&+~ѯ3 Gg5-!d[~ $A4$!LnD9+|} 2AC, nEmCqe(Eކ"ͤ`߁l8qU,L]'/\L6؁N0%'o#C[:ו[1&+Q~Am/6C 0  0  0 w68wIENDB`DdaP  S ,A step7b=x֕p"$jenx֕p"PNG  IHDRA_e`PLTE??//ߎ鎯__ooOObKGDH cmPPJCmp0712Hs6IDAThCXۮ04ZjM|tVZR+ ԘaCP`(0  P#͎!xv"VYzYDZ(mPx^8|j",1 IOUL[; @'U^j-4u'Ib$vD=QQ3UQ~6@ $ANlWԐE岬nōEfLpźݕyM./!yK,.2yf ~pt*>y d`Kq!,O2x}>;".BSnM$^Acȟq]|f,cC A7 |vg'SG/&xkJgh2_;0/l#4/̦o$<ႜSXe͘(wR{I]5l伔Mnu"N>|&(Q4 ЇO3>-^AAmhv=㯄st#E5S\31gˎ|VhV.7Ehu<׀ CP`( | ٟ'/IENDB`@@@ NormalCJ_HaJmH sH tH DA@D Default Paragraph FontRi@R  Table Normal4 l4a (k(No List4@4 `Header  !4 @4 `Footer  !.)@. _ Page NumberV^@"V ex Normal (Web)dd[$\$CJOJQJ^JaJTO1T ex boldtitlegr1#5CJOJQJ\^JaJo(ph33dOBd ex boldtitlegrdd[$\$#5B*CJOJQJ\^JaJph33@OQ@ exbodytxt1CJOJQJ^JaJo(*Hu.45D*Hu!$+,."cτ!"JVWXij#$q34tuvhi)@AB>cd}{|-DE/3=>?cd$ C e f 2 G H u v * + , - g h    , ? @ A W X  lyzEgh234"*MNOfgi~HIJjk-./)VW%[-~VstAt !!!!!"!#!=!>!?!_!`!a!v!w!!!!#"."6"8"="h"t"|""""b#g##!$N$V$j$~$$$$$$$ %%%&'A'''=(0)))=*>*?*@*c***+p+q+r+s++++++++++,,,,,,,, ,!,",#,$,%,&,',(,),4,>,N,\,f,p,q,r,},~,,,,,,,,,,,,,$-%-c----...000 0 00000000000000000000000000000000000000x0000 000 000 00x0x0x0x0x00000000000000000000000000000000000 000000000x0x0x0x0x000x000x00x000x0x00x0x0x0x0x0x0x0x000000000000000 000 0 00 000x0x0x0x0x000x00x0x0x00x0x0x0x0x0000000x0x0x0x0x0x0x0x0x0x0x0x0x0 0x00000 0 080 0x0 00x0x0x0x0x0x00x0x0x000x0x0x0x0x00x0x0x0x0x0x0x0x0x0x0x0x0x0x0x0x0x0x0x0x0x00x00x0x0x0x0x000x0x00x0x0x00000000x0x0x0x0x0x0x00000x00000000x 0 0x 0x 0x0x0x0H 0H 0L 0H 0H 0L 0H 0H 0L 0H 0H 0L 0H 0H 0L 0H 0H 0L 0000000000000000000000000000 0 000 000 0 0 0(0 0 00 0x0x0x0x0x0x00x0x00x0x00x00(0(0(0(0(0(000(@0000(0(0(00(0(0(0(@0x0000(000000000000000000000000 000 @0@004R0P000P0x0x00P0x0x00P000000@0 oVW%[-~VsAt !!!!!"!#!=!>!?!_!`!a!v!w!!!$ %%%&'A'''=(0)))=*>*?*@*c***+p+p,.00#00@000#0000#00#00#0000@000000000#00#0000@000#0000#00#00 0000#00 0000#0 00000#000000#000000#00 00@0 @0p000 0$K; 000000000000000000000000000000#000000 @0 0Q, q b4>g,| (-)446!"$&(*,-/0246<?@ @ {hN)t()#)_)w),p3&446 #%')+.135789:;=>A6%WY)+~oqt !!!$%%& ' 'A''''9(;(0))))9*;*c***+l+n+.CCCCCCCCCCCCCCCC !Y]/X"$NV;$͵,\*"$Z8YY;հf)ɯ@,\2(  NB "@ S D P2   3 jJ"`NB  S DNB  S D TB   c $DTB   c $DNB  S DHB  C DV  # "`  HB ( C DNB + S D\ 4 3 4"` \ 5 3 5"` NB ; S DNB < S DHB ? C D NB B S DNB C S DB D   N T3`'9 E  \ F 3 A "`T3\ 9Z T3P9 G T3P9\ H 3 A "`T3P9`B I c $D1$6$6ZB J S D1$6$6Pn !2(8 K #"  !T3`'9\ L 3 A "`!2(8`B M c $D1!5$5fB N s **D1"6%6fB O s *9D1#2#5ZB P S D1$5j'5`B Q c $:D1%,3%5`B R c $%6D1%R5%7P S 3 A "`P T 3 A "`$N T(V. U  b2 V C jJ"`T%( -\ W 3 A "`(V.N T4: X  \ Y 3 A "`4:4Z T4 m: Z T4 m:b2 [ C jJ"`T4 m:`B \ c $DjJ$ 4$ \:B S  ?$q4-g~,. Bt Bttt th8th&8&tT" !NtS c!tEX _tULtXL7yt&t?dt" 0t($t+t4p]tC,tBTm t5$ Dt<xTt;T $tD/$ t49:?@I!"* "$r,|,~,,..3u"59=>Brv> B k t $ .  mpswGI)q,r,|,~,,,,,,,,,..333333333333333333333333333333458A-.DDuu* - @ @ lx-.ffgII)q,r,|,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,..3345st$p,r,~,,,..GHxͼ2Vei^J.mlFiu$^`o(   ^ `hH.  L ^ `LhH. xx^x`hH. HH^H`hH. L^`LhH. ^`hH. ^`hH. L^`LhH.^`OJPJQJ^Jo(^`OJQJ^Jo(hHopp^p`OJQJo(hH@ @ ^@ `OJQJo(hH^`OJQJ^Jo(hHo^`OJQJo(hH^`OJQJo(hH^`OJQJ^Jo(hHoPP^P`OJQJo(hH808^8`0o( ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.^`CJOJQJo(^`CJOJQJo(opp^p`CJOJQJo(@ @ ^@ `CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(PP^P`CJOJQJo(VeiGH^J.miub                 *J        sr2Q&m~e1 j " p G9 sP bc _o] "T"r"%Ek%b*/v+J,:-P-C^0Tz2?&3y5x6Y~78 8RN9;!;%;Hx<I}?TgGpHnI_J@QsWZX S[b^#hyhGilon}`rsEuHz{17$AU{[wI!5,C 7[:ex|lpwkRb#v$%.D _mD< ^`X `T7$YrE]4q)>b<"W t !!!!!"!#!=!>!?!_!`!a!v!w!.@M".P@UnknownGz Times New Roman5Symbol3& z Arial?5 z Courier New;Wingdings"1hޢ&¨O%P%P!4d\,\,2QH ?:- Basic Math for Culinary Programsdplchuov    Oh+'0 , H T ` lx!Basic Math for Culinary Programsicrasidplplpl Normal.dotfchuov.d30oMicrosoft Word 10.0@ΏR@@@~>"%՜.+,0 hp|  YTIP\, !Basic Math for Culinary Programs Title  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`acdefghijklmnopqrstuvwxyz{|}~Root Entry F"Data bm1Table:mWordDocumentSummaryInformation(DocumentSummaryInformation8CompObjj  FMicrosoft Word Document MSWordDocWord.Document.89qRoot Entry Fcd<}Data bm1Table:mWordDocumentSummaryInformation(DocumentSummaryInformation8CompObjj  FMicrosoft Word Document MSWordDocWord.Document.89q՜.+,D՜.+,L hp|  YTIP\, !Basic Math for Culinary Programs Title4 $,