Write a program or a function that takes two non-empty lists of the same length as input and does the following:

• uses elements of first list to get numerators,
• uses elements of the second list to get denominators,
• displays resulting fractions after simplification (2/4=>1/2), separated by "+"s,
• displays "=" and result of addition after last fraction.

## Example:

### Input

[1, 2, 3, 3, 6]
[2, 9, 3, 2, 4]


### Output

1/2+2/9+1+3/2+3/2=85/18


• elements of lists will be positive integers,
• elements can be separated by spaces, eg: 1/2 + 2/9 + 1 + 3/2 + 3/2 = 85/18 is ok,
• trailing newline is allowed,
• lists can be taken in other formats than above, eg.: (1 2 3 3 6) or {1;2;3;3;6}, etc.,
• 1 can be expressed as 1/1,
• instead of printing you can return appropriate string,
• you do not need to handle wrong input,
• shortest code wins.
• What range of values does it have to support? – Brad Gilbert b2gills May 19 '17 at 12:26
• @BradGilbertb2gills I would say at least -30 000 to 30 000, but then I don't know whether it would be extra problem for some languages. So maybe just standard integer range of your language of choice. – user65167 May 19 '17 at 12:36
• @PrzemysławP saying "standard integer range of your language of choice" is not a good idea, some languages have standard integer as booleans – Felipe Nardi Batista May 19 '17 at 12:37
• Thank you! @BradGilbertb2gills Then at least -30 000 to 30 000. – user65167 May 19 '17 at 12:40
• Can we get fractions as [1, 2] [2, 9] [3, 3] ... instead? – Olivier Grégoire May 19 '17 at 12:42

# M, 12 11 bytes

÷µFj”+;”=;S


This is a dyadic link. Due to a bug, it doesn't work as a full program. F is also required due to a bug.

Try it online!

### How it works

÷µFj”+;”=;S  Dyadic link. Left argument: N. Right argument: D

÷            Perform vectorized division, yielding an array of fractions (R).
µ           Begin a new, monadic chain. Argument: R
F          Flatten R. R is already flat, but j is buggy and has side effects.
j”+       Join R, separating by '+'.
;”=    Append '='.
;S  Append the sum of R.

• I like how more than a quarter of the program is to append the '='. :) – Computronium Jul 19 '17 at 10:19

# Ruby 2.4, 54 53 characters

->n,d{a=n.zip(d).map{|n,d|n.to_r/d};a*?++"=#{a.sum}"}


Thanks to:

• Value Ink for the Ruby 2.4 specific version (-3 characters)
• Value Ink for optimizing the Rational initialization (-1 character)

### Ruby, 5857 56 characters

->n,d{t=0;n.zip(d).map{|n,d|t+=r=n.to_r/d;r}*?++"=#{t}"}


Sample run:

irb(main):001:0> puts ->n,d{t=0;n.zip(d).map{|n,d|t+=r=n.to_r/d;r}*?++"=#{t}"}[[1, 2, 3, 3, 6], [2, 9, 3, 2, 4]]
1/2+2/9+1/1+3/2+3/2=85/18


Try it online!

• a=n.zip(d).map{|f|(f*?/).to_r};a*?++"=#{a.sum}" in Ruby 2.4 saves you 3 bytes. – Value Ink May 19 '17 at 18:46
• Thanks @ValueInk. I suspected that may be possible, just had no 2.4 neither locally nor on TIO. – manatwork May 20 '17 at 16:13
• Yeah, I installed 2.4 specifically so I could test out solutions with sum haha. Also I just remembered that .map{|i,j|i.to_r/j} is shorter by 1 byte – Value Ink May 22 '17 at 20:25
• Doh. I tried various approaches through .to_f and division, but didn't thought to dividing Rational with Fixnum. Thanks again, @ValueInk. – manatwork May 24 '17 at 19:54

## Mathematica, 33 bytes

Row@{Row[#/#2,"+"],"=",Tr[#/#2]}&


input

[{1, 2, 3, 3, 6}, {2, 9, 3, 2, 4}]

• Isn't Row@@{#/#2,"+"} the same as Row[#/#2,"+"]? – feersum May 19 '17 at 13:57
• yes! you are right! – J42161217 May 19 '17 at 14:04
• Fantastic! I didn't realize Row was so convenient for things like this :) – Greg Martin May 19 '17 at 18:08

# Python 3, 104 bytes

9 bytes thanks to Felipe Nardi Batista.

from fractions import*
def f(*t):c=[Fraction(*t)for t in zip(*t)];print('+'.join(map(str,c)),'=',sum(c))


Try it online!

# Perl 6,  77  73 bytes

{join('+',($/=[@^a Z/ @^b]).map:{.nude.join('/')})~"="~$/.sum.nude.join('/')}


Try it

{($/=[@^a Z/@^b])».nude».join('/').join('+')~'='~$/.sum.nude.join('/')}


Try it

## Expanded:

{  # bare block lambda with two placeholder params ｢@a｣ and ｢@b｣

(
$/ = [ # store as an array in ｢$/｣ for later use

@^a Z/ @^b        # zip divide the two inputs (declares them)

]

)».nude\              # get list of NUmerators and DEnominators
».join('/')           # join the numerators and denominators with ｢/｣

.join('+')            # join that list with ｢+｣

~
'='                   # concat with ｢=｣
~

$/.sum.nude.join('/') # get the result and represent as fraction }  ## Clojure, 71 bytes #(let[S(map / % %2)](apply str(concat(interpose '+ S)['=(apply + S)])))  Yay for built-in fractions! # Mathematica, 61 bytes t=#~ToString~InputForm&;Riffle[t/@#,"+"]<>"="<>t@Tr@#&[#/#2]&  ## JavaScript (ES6), 111 bytes Takes the lists in currying syntax (a)(b). let f = a=>b=>a.map((v,i)=>F(A=v,B=b[i],N=N*B+v*D,D*=B),N=0,D=1,F=(a,b)=>b?F(b,a%b):A/a+'/'+B/a).join++'='+F(A=N,B=D) console.log(f([1, 2, 3, 3, 6])([2, 9, 3, 2, 4])) # Java, 225 bytes int c(int a,int b){return b>0?c(b,a%b):a;} (N,D)->{int n=0,d=1,i=0,g;String s="";for(;i<N.length;g=g(N[i],D[i]),N[i]/=g,D[i]/=g,s+=(i>0?"+":"")+N[i]+"/"+D[i],n=n*D[i]+N[i]*d,d*=D[i++],g=g(n,d),n/=g,d/=g);return s+"="+n+"/"+d;}  N and D are both int[], contextualized. I reused Kevin Cruijssen's GCD function. See it and test it online! ## Julia v0.4+, 66 53 bytes -13 bytes thanks to Dennis a^b=replace(join(a.//b,"+")"=$(sum(a.//b))","//","/")


Try it Online!

Alternately, if fractions can be displayed using // rather than /, the following works for 35 bytes:

a^b=join(a.//b,'+')"=$(sum(a.//b))"  # setlX, 103 bytes f:=procedure(a,b){i:=1;l:=[];while(i<=#a){l:=l+[a[i]/b[i]];i+=1;}s:=join(l,"+");return s+"="+eval(s);};  Creates a function called f where your insert two lists. ungolfed: f := procedure (a,b) { i:=1; l:=[]; while(i<=#a){ l:=l+[a[i]/b[i]]; i+=1; } s:=join(l,"+"); return s+"="+eval(s); };  with named variables and annotations: setlX doesn't provide a comment feature so let's just pretend that we can comment with % f := procedure(firstList,secondList) { count := 1; list := []; while(count <= #firstList) { % calculate every fraction and save it as a list list := list + [firstList[count]/secondList[count]]; count += 1; } % Seperate every list entry with a plus ([2/3,1] -> "2/3+1") str := join(list, "+"); % eval executes the string above and thus calculates our sum return str + "=" + eval(str); }; • What if #firstList is different from #secondList? – user58988 May 21 '17 at 19:05 • you mean differnet size? The question states that first list is used by enumerator and wrong input can be ingored – BlueWizard May 21 '17 at 20:04 • but other than that: if the second list is longer, the remaining entries will be ignored. If the list is shorter a runtime error will occur. – BlueWizard May 21 '17 at 20:05 # Perl 6, 72 bytes 65 bytes Native and automatic rationals should make this easy, but default stringification is still as decimal, so we have to .nude (numerator and denominator) which kills our score and makes the 1 ugly :( my \n = 1,2,3,3,6; my \d = 2,9,3,2,4; (n Z/d)».nude».join("/").join("+")~"="~([+] n Z/d).nude.join("/")  Update: Removed unneeded brackets, kill more space and use smarter map. Saves characters over Brad's solution at the cost of no not being a lambda sub. • Welcome to the site! Nice first answer! – programmer5000 May 19 '17 at 13:13 # 05AB1E, 35 34 bytes ‚øvyy¿÷'/ý'+}¨'=¹.¿©¹÷²*O®‚D¿÷'/ýJ  Try it online! # Jelly, 31 bytes ,:gj”/ ṙJ$ṖP×Sç⁸P¤,ç@"j”+$¥Ṛj”=  Try it online! # PHP>=7.1, 190 Bytes <?function f($x,$y){for($t=1+$x;$y%--$t||$x%$t;);return$x/$t."/".$y/$t;}[$n,$d]=$_GET;for($p=array_product($d);$x=$n[+$k];$e+=$x*$p/$y)$r[]=f($x,$y=$d[+$k++]);echo join("+",$r)."=".f($e,$p);  Online Version +14 Bytes for replacement return$x/$t."/".$y/$t; with return$y/$t>1?$x/$t."/".$y/$t:$x/$t; to output n instead of n/1 # F#, 244241 239 bytes let rec g a=function|0->abs a|b->g b (a%b) let h a b=g a b|>fun x->a/x,b/x let s,n,d=List.fold2(fun(s,n,d)N D-> let(N,D),(n,d)=h N D,h(n*D+N*d)(d*D) s@[sprintf"%i/%i"N D],n,d)([],0,1)nom div printf"%s=%i/%i"(System.String.Join("+",s))n d  Try it online! # setlX, 62 bytes [a,b]|->join([x/y:[x,y]in a><b],"+")+"="++/[x/y:[x,y]in a><b];  ### ungolfed: [a,b]|-> define a function with parameters a and b join( [ x/y : using set comprehension, make a list of fractions [x,y] in a><b from the lists zipped together ], "+" ) join them with "+" + "=" concat with an equals sign + concat with +/[x/y:[x,y]in a><b] the sum of the list ; # Google Sheets, 83 81 bytes =ArrayFormula(JOIN("+",TRIM(TEXT(A:A/B:B,"?/???")))&"="&TEXT(sum(A:A/B:B),"?/???"  Saved 2 bytes thanks to Taylor Scott Sheets will automatically add 2 closing parentheses to the end of the formula. The two arrays are input as the entirety of columns A and B. Empty rows below the inputs will throws errors. • you should be able to drop 2 bytes by dropping the terminal )) – Taylor Scott Sep 5 '17 at 16:17 # R, 109 bytes f=MASS::fractions;a=attributes g=function(n,d)paste(paste(a(f(n/d))$f,collapse='+'),a(f(sum(n/d)))\$f,sep='=')


requires the MASS library (for its fractions class). the function g returns the required output as a string.

# TI-BASIC, 100 bytes

:L₁⁄L₂                                              //Creates a fraction from Lists 1 & 2, 7 bytes
:toString(Ans→Str1                                  //Create string from list, 7 bytes
:inString(Ans,",→A                                  //Look for commas, 9 bytes
:While A                                            //Begin while loop, 3 bytes
:Str1                                               //Store Str1 to Ans, 3 bytes
:sub(Ans,1,A-1)+"+"+sub(Ans,A+1,length(Ans)-A→Str1  //Replace "," with "+", 33 bytes
:inString(Ans,",→A                                  //Check for more commas, 9 bytes
:End                                                //End while loop, 2 bytes
:Str1                                               //Store Str1 to Ans, 3 bytes
:sub(Ans,2,length(Ans)-2                            //Remove opening and closing brackets, 13 bytes


Note the ⁄ at the beginning, different from /. This makes the fractions hold their forms. It does work with negative fractions.

Sigh. TI-BASIC is horrible with strings. If all we had to do was print the fractions, and then their sum, the code would be:

### TI-BASIC, 12 bytes

:L₁⁄L₂    //Create fractions from lists, 7 bytes
:Disp Ans //Display the above fractions, 3 bytes
:sum(Ans  //Display the answer, 2 bytes


That means that 88 bytes of my code is spent just formatting the answer! Hmph.

# C, 171 bytes

Try Online

i;t;x;y;f(int s,int*a,int*b){x=*a;y=*b;while(++i<s)x=(y-b[i])?(x*b[i])+(a[i]*y):(x+a[i]),y=(y-b[i])?(b[i]*y):y;for(i=1;i<=(x<y?x:y);++i)t=(x%i==0&&y%i==00)?i:t;x/=t;y/=t;}


# Axiom, 212 bytes

C==>concat;S==>String;g(a)==C[numerator(a)::S,"/",denom(a)::S];h(a:List PI,b:List PI):S==(r:="";s:=0/1;#a~=#b or #a=0=>"-1";for i in 1..#a repeat(v:=a.i/b.i;s:=s+v;r:=C[r,g(v),if i=#a then C("=",g(s))else"+"]);r)


test

(5) -> h([1,3,4,4,5,6], [2,9,5,5,6,7])
(5)  "1/2+1/3+4/5+4/5+5/6+6/7=433/105"
Type: String
(6) -> h([1,3,4,4], [2,9,5,5,6,7])
(6)  "-1"
Type: String


# Casio Basic, 161 Bytes

Dim(List 1)->A
for 1->I to A step 1
3*I-2->B
List 1[I]->C
List 2[I]->D
locate 1,B,C
locate 1,B+1,"/"
locate 1,B+2,D
C/D+E->E
next
locate 1,B+3,"="
locate 1,B+4,E


Explanation:

• Number of input is saved in A
• A iterations
• B acts as a counter for correct displaying
• I'th item of List 1 and 2 saved in C and D
• Displaying of Variable C / Variable D
• save C/D+E in E
• After last number locate = and E

# Haskell (Lambdabot), 9491 86 bytes

t=tail.((\[n,_,d]->'+':n++'/':d).words.show=<<)
a#b|f<-zipWith(%)a b=t f++'=':t[sum f]


Try it online!

Thanks @Laikoni for -8 bytes!

### Ungolfed

-- convert each fraction to a string (has format "n%d", replace '%' with '/' and prepend '+' ("+n/d"), keep the tail (dropping the leading '+')
t = tail.((\[n,_,d]->'+':n++'/':d).words.show=<<)
-- build a list of fractions
a # b = let f = zipWith(%) a b in
-- stringify that list, append "=" and the stringified sum of these fractions
t f ++ "=" ++ t [sum f]

• Your missing a import Data.Ratio for % which is not in Prelude. – Laikoni Jul 19 '17 at 14:16
• You can save some bytes by replacing "?"++ with '?':. – Laikoni Jul 19 '17 at 14:21
• The shortening also works for "/"++d and "="++. – Laikoni Jul 19 '17 at 14:25
• Rearranging saves some more bytes: tail(f>>=t)++'=':(tail.t.sum)f – Laikoni Jul 19 '17 at 14:46
• Putting tail and =<< into t saves some more: Try it online! – Laikoni Jul 19 '17 at 14:55

# MATL, 32 bytes

/YQv'%i/%i+'wYD3L)61yUYQVwV47b&h


Try at MATL online!

### Explanation

Consider [1, 2, 3, 3, 6], [2, 9, 3, 2, 4] as input.

/         % Implicit inout. Divide element-wise
% STACK: [0.5 0.222 1 1.5 1.5]
YQ        % Rational approximation (with default tolerance)
% STACK: [1 2 1 3 3], [2 9 1 2 2]
v         % Conctenate all stack elements vertically
% STACK: [1 2; 2 9; 1 2; 3 2; 3 2]
'%i/%i+'  % Push this string (sprintf format specifier)
% STACK: [1 2; 2 9; 1 2; 3 2; 3 2], '%i/%i+'
wYD       % Swap, sprintf
% STACK: '1/2+2/9+1/1+3/2+3/2+'
3L)       % Remove last entry
% STACK: '1/2+2/9+1/1+3/2+3/2'
61        % Push 61 (ASCII for '=')
% STACK: '1/2+2/9+1/1+3/2+3/2', 61
y         % Duplicate from below
% STACK: '1/2+2/9+1/1+3/2+3/2', 61, '1/2+2/9+1/1+3/2+3/2'
U         % Evaluste string into a number
% STACK: '1/2+2/9+1/1+3/2+3/2', 61, 4.722
YQ        % Rational approximation
% STACK: '1/2+2/9+1/1+3/2+3/2', 61, 85, 18
VwV       % Convert to string, swap, convert to string
% STACK: '1/2+2/9+1/1+3/2+3/2', 61, '18', '85'
47        % Push 47 (ASCII for '/')
% STACK: '1/2+2/9+1/1+3/2+3/2', 61, '18', '85', 47
b         % Bubble up in stack
% STACK: '1/2+2/9+1/1+3/2+3/2', 61, '85', 47, '18'
&h        % Concatenate all stack elements horizontally. Implicitly display
% STACK: '1/2+2/9+1/1+3/2+3/2=85/18'