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52 votes

Proof of why BODMAS (or BIDMAS) works?

It's purely a matter of how we choose to define the notation. The main reason for it is that it lets us write polynomial expressions (which are extremely common) without parentheses, e.g., $x^3 + 3x^2 ...
Daniel Hast's user avatar
  • 4,893
11 votes

Proof of why BODMAS (or BIDMAS) works?

Perhaps it is worth pointing out that every programming language defines an operator precedence structure to avoid ambiguities. An example table for C and C++ can be found here. Ambiguities must be ...
Joseph O'Rourke's user avatar
10 votes

How to teach if calculations and algebraic manipulations are off limits

I highly recommend looking at the Calculus exams from the University of Michigan. These problems tend to focus on extracting relevant information for ...
Steven Gubkin's user avatar
9 votes

Proof of why BODMAS (or BIDMAS) works?

To build on other answers, you might show how other conventions exist. Use an H.P. calculator for example (postfix), the LISP family of languages (prefix), and the APL language (all right-associative),...
JDługosz's user avatar
  • 191
8 votes

Proof of why BODMAS (or BIDMAS) works?

I understand this is not a realistic suggestion, but can you avoid "teaching" "PEMDAS" or "BOMDAS" altogether, and teach your students just the math instead? As pretty much everybody already said, ...
zipirovich's user avatar
8 votes

Determining the first digit of the Quotient using hand long division efficiently?

The awkwardness of "guessing" in the division algorithm is an artifact of the base-ten representation of numbers. If you represent in binary, then your only possible "guess" is 1. In binary, your ...
user52817's user avatar
  • 11k
6 votes

If a computer could be programmed to do a math test, then should those tests be changed?

No. There is a sort of magical thinking implicit here that something needs to stay, be different between computers and people. At the end of the day, we are "meat" computers. And the ...
guest's user avatar
  • 85
3 votes

Student-friendly / efficient approach to computing Taylor coefficients of infinite binomial series expansions?

I think the bug can actually be a feature. Kids need work on the "muscles" of computation. It's not like this is the only setting where doing long calculations is needed (can be the norm in physics ...
guest's user avatar
  • 129
3 votes

Determining the first digit of the Quotient using hand long division efficiently?

Round. Check. Correct. What we need is $436\div48$. Rounding to remove the last digit reduces the problem to $44\div5$. This gives us an educated guess of either $8$ or $9$. From here we then ...
Simply Beautiful Art's user avatar
3 votes

Proof of why BODMAS (or BIDMAS) works?

It works by avoiding the ambiguity that 2 + 3 x 6 would otherwise have. If we simply said we calculate left to right, we'd have a result of 30. With the priority, multiplication higher, we have ...
JTP - Apologise to Monica's user avatar
2 votes

How to explain inverse modulo?

For the first, there are a number of apps out there, though I will recommend that you go somewhat non-simple and use Sage. Are you looking for additive or multiplicative inverse? In either case, it ...
kcrisman's user avatar
  • 5,976
2 votes

Proof of why BODMAS (or BIDMAS) works?

It is kind of arbitrary which operation goes first, but my guess is that our current system is just a little more concise in most problems. As an example imagine two systems: a system A that is like ...
Bram's user avatar
  • 21
1 vote

Resources for improving computational skills at the high school/university transition

The Art of Problem Solving has plenty of problems involving pre-calculus tools, some of them quite challenging. However, the best way forward might not be computationally challenging exercises. You ...
Mark Fantini's user avatar
  • 3,040

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