1. A number leaves remainder 6 when divided by 10. What is the remainder when the number is divided by 5? Justify your reasoning.
When divided by 10, these numbers will leave a remainder of 6.
16, 26, 36, 46, 56, etc.
What is the remainder when these numbers are divided by 5?
To find the remainder when a number is divided by 5, we can use the concept of modular arithmetic.
Given that the number leaves a remainder of 6 when divided by 10, we can represent it as:
Number = 10k + 6, where 'k' is an integer.
Now let's apply modular arithmetic to find the remainder when this number is divided by 5.
We know that any integer can be represented as the sum of its quotient and remainder when divided by any divisor. So,
Number = 5(2k) + (10k + 6) % 5
Since 10k + 6 is fully divisible by 5 (as it leaves a remainder of 0 when divided by 5), we can simplify the expression to:
Number = 5(2k)
The remainder when 5(2k) is divided by 5 is 0.
Therefore, the remainder when the given number is divided by 5 is 0.