![]() Likewise, 111 is the same as 0-7 in Octal (not covered in this phase). The 1111 binary count-0-15-is the same as 0-9A-F in a single Hexidecimal digit.After solidifying counting on decimal-after sufficient study and practice on addition and subtraction-we return to the Suan Pan to discuss Hexidecimal.This avoids the student's mind basing on a solid world view of everything being nice, even parts. We can also show that of five parts you have to double that to get the decimal number, and indicate to the student that we'll cover the methods for this in further and more-complex arithmetic. It is sufficient to show that a whole is made up of 10 parts and that 3 and 7 parts is 0.3 and 0.7 of one whole. Introducing decimals requires introducing division, but not introducing the computation of division.11.5 is the same operation with a different position for the decimal place. Thus 100 + 15 is just 1 moved left two bars, plus 15 based at the base, and it's 115. The concept of a decimal place is inherent, and so fractional components are introduced immediately at counting.The Soroban will be the calculator of choice here.No friendly numbers, because everything is mechanical and direct and thus a lot faster than preprocessing. One is so subtract 3, 4-3=1, you're adding and so you overflow one to the left, the answer is 11. Multiplication, on the other hand, can be done digit by digit-which is why we memorize single-digit multiplication tables. I have never encountered any mathematical approach to division which was simple and linear. That said, division with multiple-digit numbers is…not simple. Teaching this early (instead of the Friendly Numbers thing) by digit-wise columnar addition and subtraction (Soroban and Anzan use this strategy) avoids developing the perception that math is complex and hard. Applying this prior to division happens to apply it to every operation ahead of time. ![]() You could say that the 5 was one column left of the 4 and the decimal point was two columns left, so the 5 shifts to three columns left to give 50 that's valid, and it's required when carrying out multiplication. ![]() People do this all the way down to addition, and will convert (6 + 7 + 4) to (5 + 5 + 7) to (10 + 7) to (17)-having carried out three additions, one subtraction, and a strategic analysis instead of only one subtraction and one addition (7-3 and 3+4). My point here is that you're looking at the operation as a sort of complex thing which requires an approach strategy because there's a decimal point. The answer is 50: decimal points are meaningless and shift in the same direction in division, so just move it two columns right (200 / 4). The 2 was two columns left the 20 was one column left, so you get 0.5. 4 isn't a factor of 2 the next digit is 0, thus 20 / 4.
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