[Jprogramming] J TECH Grade 3 <<Multi[plication and Division

[Linda Alvord]

Just as in Grade 2 there are two tables of arithmetic facts that are the
focus of the year. In third grade those two areas are multiplication and
division within the range from 0 to 100. One process is the inverse of the
other.  The journey toward division is first to create improper fractions
with only single digit denominators in the range from 0 to 9. Then find the
whole portion and finally the residue in reduced form.  The final result in
J would be:

  96 % 9x

32r3

 

This is 10 6/9 or 10 2/3 for a correct answer in mixed fractions. Numbers
are not converted to decimals this year. The decimals are used in relation
to money $3.45    

Since I am a long way from third grade, I was surprised at how formidable
this might be for a third grade student.  Here are the two tables they must
master.  They might expose patterns to help them understand the process
better.

 

load 'viewmat'

GRB=:1 0 2{"1 (#:i.8){0 255

T=:(i.11)*/i.11                       NB. Times 

]TT=:(i.11) * table i.11              NB. Times table

W=:<.IF=:(i.101x)%/>:i.9              NB. Whole portion of improper
fractions fractions 

R=:1|IF                               NB. Remainder or residue 

MF=: <"1 W,"0 R                       NB. Mixed fractions

A=:<' MF '

B=:<"0 >:i.9

C=:<"0 ,.i.101

]MFT=: (A,B),"2 C,. MF                 NB. Table of mixed fraction results

 

GRB viewmat T

GRB viewmat 10*0.1*W+R                 NB. Strategy to convert mixed

                                       NB. fractions to decimals    

 

If you are aware of easier ways to make these tables please let me know.

 

Linda