For this assignment, I created a table of numbers that multiply to forty-five in base 60. At first, I found it helpful to warm up with simple integer factors, but then I challenged myself to include base 60 fractions (and even repeating ones) in some of my pairs.
What I found most interesting was working with fractions. For example, in the pair (5,30 – 8,10,54,32,43,38 repeating), I experimented with a repeating expansion. Getting there required some long division, which gave me the chance to relive how I first developed an intuition for why the algorithm works. Another fun challenge was adding numbers with “decimals” in base 60, which stretched my comfort zone in thinking beyond base 10 habits.
Some pairs were straightforward because I could think of the fraction as a mixed number and then quickly convert the fractional part into a denominator of 60. Others, like the repeating decimal expansion, required much more patience. I noticed how quickly simple integer pairs gave way to more complex fractional relationships, which showed me the depth and flexibility of base 60 arithmetic.
Overall, this assignment not only gave me a chance to practice with base 60 fractions, but also reminded me of the value of exploring multiple representations of numbers in relation to learning. Sometimes the cleanest path was converting directly into mixed numbers, and other times it was grinding through long division. Both processes deepened my understanding of how the system works.
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