Subtract the following in base five Show all your work 2 2 1

Subtract the following in base five. Show all your work. 2 2 1_five - 4 2_five Use your work in to explain how the way we regroup in base five subtraction is similar to the way that we regroup in base ten subtraction.

Solution

If we are using base five notation to express numbers, then the only symbols we have for digits are 0, 1, 2, 3, and 4 .

221 five

- 42      five

Since 2 is greater than 1, we have to borrow from the second column. Since the numbers are written in base five notation we are borrowing five so the 2 in the third column becomes 1 and adding 5 to 1 gives us 6 in the first column. Then,

           221      five

4             (as 6 – 2 = 4)

Again, since 4 is bigger than 1, we have to borrow from the third column. Since the numbers are written in base five notation we are borrowing 5 so the 2 in the third column becomes 1 and adding 5 to 1 gives us 6 in the first column. Then,

             221     five

- 42      five

4   (as 6 – 2 = 4)

Again, since 4 is bigger than 1, we have to borrow from the third column. Since the numbers are written in base five notation we are borrowing 5 so the 2 in the third column becomes 1 and adding 5 to 1 gives us 6 in the second column. Then,

             221     five

- 42      five

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