My son is very quick at mental calculations and is about to participate in a competition. He does not use an abacus or soroban — he calculates naturally in his head and enjoys it, so we didn’t want to interfere with his natural style.
He can add, subtract, multiply, and divide very quickly in his mind. He can also work with fractions quickly, but he has one problem: in the competition, answers must be given in simplified form to be counted as correct.
To simplify, he often needs to first calculate a large 4- or 5-digit denominator, then calculate the corresponding numerator. The issue is that while he’s working on the numerator, he sometimes forgets part of the denominator he just worked out.
In other words, he struggles to hold a large number in memory while computing another large number.
What are some mental strategies or training methods to help remember and hold large intermediate numbers in mind during multi-step mental math problems?