14) You will likely want to have a calculator handy for this question. a) Create several three-digit natural numbers, reverse the digits, and subtract them. For example, subtract 794 − 497. b) In part a, you found several differences (the result of subtracting). Factor these differences into primes. What do you notice about the factors? Make a conjecture based on your observations. If you do not notice a pattern yet, try more examples. c) Let ? be a 3-digit natural number. Express ? in a generalized form using your place value knowledge. Let ? be the number in the hundreds place, ? be the number in the tens place, and ? be the number in the ones place. d) What are the possible values of ?, ?, and c? e) Now let ? be the number with the digits of ? reversed. Express ? generally using your place value knowledge. f) Now subtract ? − ? (using the generalized forms) and simplify the expression. What do you observe? What have you proven? Explain.
14) You will likely want to have a calculator handy for this question.
a) Create several three-digit natural numbers, reverse the digits, and subtract them. For example, subtract 794 − 497.
b) In part a, you found several differences (the result of subtracting). Factor these differences into primes. What do you notice about the factors? Make a conjecture based on your observations. If you do not notice a pattern yet, try more examples. c) Let ? be a 3-digit natural number. Express ? in a generalized form using your place value knowledge. Let ? be the number in the hundreds place, ? be the number in the tens place, and ? be the number in the ones place.
d) What are the possible values of ?, ?, and c?
e) Now let ? be the number with the digits of ? reversed. Express ? generally using your place value knowledge.
f) Now subtract ? − ? (using the generalized forms) and simplify the expression. What do you observe? What have you proven? Explain.
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