What is the result of the subtraction 41_5 - 23_5 in base 5? — JAMB UTME

What is the result of the subtraction $41_5 - 23_5$ in base 5?

13_5

The answer

13_5

is correct because borrowing 1 from the fives place contributes 5 to the units place, making the calculation

(1 + 5) - 3 = 3

for the units place and

3 - 2 = 1

for the fives place.

Set up column subtraction for

41_5 - 23_5

in base 5.

In the units position, we evaluate

1 - 3

Since 1 is smaller than 3, a borrow operation from the fives column is required.

Borrow 1 from the fives column (reducing 4 to 3) and add the base value 5 to the units digit 1.

Units column value becomes

1 + 5 = 6

. Fives column value becomes 3.

When borrowing in base

n

, the borrowed amount is equal to

n

, which is 5 for base 5.

Subtract digits in each column.

Units column:

6 - 3 = 3

. Fives column:

3 - 2 = 1

. The result is

13_5

Completing the column subtraction yields the final digits in base 5.

Subtraction in Non-Decimal Number Bases

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