[BlindMath] middle school math part 2

[John]

Hello,
> Thank you for your feedback about assisting with middle school math.
> 
> Including myself there are 3 individuals on this list that have a school-aged child somewhere between grade 1 and grade 8.
> 
> I got out my Cranmer abacus from APH to do another middle school math problem.
> 
> I just checked. APH sells the Cranmer abacus for $43.34 and have 17 in stock.
> 
> If you want an abacus, it is in stock.
> 
> If everyone on the blind math list rushed out and ordered one, the staff at APH sure would be surprised.
> 
>  
> 
> I did the problem on the abacus really well although I have not done an abacus problem since 2019 or earlier.
> 
> It can really help with keeping track of place value.
> 
> The approach can work typing out each step without the abacus but you do not get the rigor of the built-in columns of the abacus keeping all the numbers aligned.
> 
>  
> 
> Here is a problem that my son got right on a unit test.  I wanted to duplicate his work to build my confidence.
> 
> I could not do this problem in my head.
> 
>  
> 
> Mary sells each cup of hot chocolate for 65 cents of profit.
> 
> If she makes $23.40 in profit, how many cups of hot chocolate did she sell?
> 
> This problem can be restated as 65 times x = 2340.
> 
> It then becomes
> 
> x = 2340 divided by 65.
> 
>  
> 
> With the abacus you set up the divisor 65 in the left 2 columns and the dividend 2340 in the right 4 columns.
> 
> Now I assert that the first digit of the answer is 3.
> 
> I write 3 two columns to the left of the first column of the dividend.
> 
> So I write 3 in column 6.
> 
> I proceed to subtract 65 * 3 from the first 3 digits of the dividend.
> 
> I start with 234 and move from left to right subtracting 195.
> 
> The interim step of 234 minus 195 = 39.
> 
> After performing this subtraction starting in the one thousands column the answer is 39 in the hundreds column.
> 
> Examining the last 3 columns the answer is 390.
> 
> Now I look at what the ones digit of my answer might be.
> 
> Now I assert that 65 goes into 390 6 times.
> 
> I set 6 in the column to the right of the 3 that is the first digit of my answer.
> 
> So I set 6 in column 5.
> 
> If correct then this means my answer is 36.
> 
> The 36 is in columns 6 and 5.
> 
> I proceed to find out if 36 is correct.
> 
> I now subtract 65 * 6 from 390.
> 
> Working on the tens digit I have 60 * 6 = 360
> 
> Subtracting 360 from 390 I have the remainder 30.
> 
> Now working on the ones digit subtracting 5 * 6 from 30 I have 30 - 30 = remainder 0.
> 
> A valid answer will have remainder in the range of 0 through 1 less than the divisor.
> 
> So 0 through 64 would be fine.
> 
> Now on the abacus the left 2 columns show 65.
> 
> Columns 6 and 5 show the answer 36.
> 
> Columns 4 and 3 are blank.
> 
> Columns 2 and 1 show the remainder 0.
> 
>  
> 
> The answer is correct.
> 
> Dividing 65 cents into $23.40 results in 36 cups of hot chocolate sold with no remainder.
> 
>  
> 
> Very best,
> 
> John
> 
>