Don, Can you identify which ones of the twenty five items in the pairs don't work?
%/~ 1r3%i.5 |NaN error | %/~1r3%i.5 Linda -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Don Kelly Sent: Monday, November 16, 2015 12:59 AM To: [email protected] Subject: Re: [Jprogramming] Why is subtraction and division of rational numbers so hard? Could it be that 1r3 % i.1 =(1/3)%0 so the result of the summation is infinity + some numbers? try -/~ 1r3 %1 +i.5 0 1r6 2r9 1r4 4r15 _1r6 0 1r18 1r12 1r10 _2r9 _1r18 0 1r36 2r45 _1r4 _1r12 _1r36 0 1r60 _4r15 _1r10 _2r45 _1r60 0 or -/~ 1r3 %1r1000000+i.5 0 1000000000000r3000003 2000000000000r6000003 1000000000000r3000001 4000000000000r12000003 _1000000000000r3000003 0 1000000000000r6000009000003 2000000000000r9000012000003 1000000000000r4000005000001 _2000000000000r6000003 _1000000000000r6000009000003 0 1000000000000r18000015000003 2000000000000r24000018000003 _1000000000000r3000001 _2000000000000r9000012000003 _1000000000000r18000015000003 0 1000000000000r36000021000003 _4000000000000r12000003 _1000000000000r4000005000001 _2000000000000r24000018000003 _1000000000000r36000021000003 0 Don Kelly On 11/15/2015 1:05 AM, Linda A Alvord wrote: > How would you explain to a 4th grade student why subtraction and division > of fraction is so difficult for J. Here is a dialog I wrote to review all > the big ideas students should remember from third grade. Tables show how > some verbs like + and times are commutative and * and % are not. If the verb > is commutative you need only "master" a little more than half of the table. > > > > > > > > +/~i.5 > > > i. > 0 1 2 3 4 > > 1 2 3 4 5 > > 2 3 4 5 6 > > 3 4 5 6 7 > > 4 5 6 7 8 > > > > > > > > -/~i.5 > > > > 0 _1 _2 _3 _4 > > 1 0 _1 _2 _3 > > 2 1 0 _1 _2 > > 3 2 1 0 _1 > > 4 3 2 1 0 > > > > > > > > */~i.5 > > > > 0 0 0 0 0 > > 0 1 2 3 4 > > 0 2 4 6 8 > > 0 3 6 9 12 > > 0 4 8 12 16 > > > > > > > > %/~i.5 > > > > 0 0 0 0 0 > > _ 1 0.5 0.333333 0.25 > > _ 2 1 0.666667 0.5 > > _ 3 1.5 1 0.75 > > _ 4 2 1.33333 1 > > > > > > > > 1r3%i.5 > > > > _ 1r3 1r6 1r9 1r12 > > > > > > > > +/~ 1r3%i.5 > > > > _ _ _ _ _ > > _ 2r3 1r2 4r9 5r12 > > _ 1r2 1r3 5r18 1r4 > > _ 4r9 5r18 2r9 7r36 > > _ 5r12 1r4 7r36 1r6 > > > > > > -/~ 1r3%i.5 > > > > |NaN error > > | -/~1r3%i.5 > > > > > > */~ 1r3%i.5 > > > > _ _ _ _ _ > > _ 1r9 1r18 1r27 1r36 > > _ 1r18 1r36 1r54 1r72 > > _ 1r27 1r54 1r81 1r108 > > _ 1r36 1r72 1r108 1r144 > > > > > > > > %/~ 1r3%i.5 > > > > |NaN error > > | %/~1r3%i.5 > > > > > > > > t=: 13 :'>:/~i.y' > > > > t 5 > > > > 1 0 0 0 0 > > 1 1 0 0 0 > > 1 1 1 0 0 > > 1 1 1 1 0 > > 1 1 1 1 1 > > > > > > > > (t 5)*+/~i.5 > > > > 0 0 0 0 0 > > 1 2 0 0 0 > > 2 3 4 0 0 > > 3 4 5 6 0 > > 4 5 6 7 8 > > > > > > > > (t 5)**/~i.5 > > > > 0 0 0 0 0 > > 0 1 0 0 0 > > 0 2 4 0 0 > > 0 3 6 9 0 > > 0 4 8 12 16 > > > > > > > > (t 5)*+/~ 1r3%i.5 > > > > _ 0 0 0 0 > > _ 2r3 0 0 0 > > _ 1r2 1r3 0 0 > > _ 4r9 5r18 2r9 0 > > _ 5r12 1r4 7r36 1r6 > > > > > > > > (t 5)**/~ 1r3%i.5 > > > > _ 0 0 0 0 > > _ 1r9 0 0 0 > > _ 1r18 1r36 0 0 > > _ 1r27 1r54 1r81 0 > > _ 1r36 1r72 1r108 1r144 > > > > > > > > Linda I > > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
