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Find the sum and product of each of these pairs of numbers. Express your answers as a base 3 expansion. Hint: We can just add and multiply using the grade-school algorithms (working column by column starting at the right), using the addition and multiplication tables in base three (for example, 2 + 1 = 10 and 2 · 2 = 11). When a digit-by-digit answer is too large to fit (i.e., greater than 2), we "carry" into the next column. (10 points) (112)3, (210)3

Answer :

Answer:

[tex]112_3 + 210_3 = 1022_3[/tex]

[tex]112_3 \times 210_3 = 101220_3[/tex]

Explanation:

To find the sum of the two numbers, start summing from the right most numbers.

right most: 2 + 0 = 2

middle: 1 + 1 = 2

left: 1 + 2 = 3. Converting 3 to base 3, we have 1 r 0 = 10.

Therefore, [tex]112_3 + 210_3 = 1022_3[/tex].

To find the product, simply do

[tex](0 \times 112) + (1 \times 112) + (2 \times 112)\\[/tex] = [tex]000 + 112 + 1001[/tex] = [tex]101220[/tex].

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