Question

Question If n is divided by 7, the remainder is 5. What is the remainder when (n + 3) is divided by 7 ? 5 3 2 1

Answer 1

The remainder when n is divided by 7 and the remainder is 5, and then (n + 3) is divided by 7, is 1.

Step-by-step explanation:

When a number n is divided by 7 and the remainder is 5, we can write this as n = 7k + 5, where k is some integer. To determine the remainder when (n + 3) is divided by 7, we add 3 to the expression for n, resulting in n + 3 = 7k + 5 + 3. Simplifying this, we get n + 3 = 7k + 8.

Now, 7k is divisible by 7, so we only need to consider the remainder when we divide 8 by 7, which is 1. Therefore, the remainder when (n + 3) is divided by 7 is 1.

Now, let's find the remainder when (n + 3) is divided by 7. We substitute the value of n into the expression: (7k + 5) + 3 = 7k + 8.

To find the remainder, we divide 7k + 8 by 7. The remainder will be the same as the remainder of 8 when divided by 7.

When 8 is divided by 7, the remainder is 1. Therefore, the remainder when (n + 3) is divided by 7 is 1.

Answer 2

When n is divided by 7 and yields a remainder of 5, adding 3 to n and then dividing by 7 gives a remainder of 1, because the sum of the remainder and 3 must still respect the bounds for a remainder in division by 7.

Step-by-step explanation:

If n is divided by 7, and the remainder is 5, then when (n + 3) is divided by 7, the remainder can be determined by simply adding 3 to the initial remainder of 5. However, since the result of a division by 7 must have a remainder between 0 and 6, we see that 5 + 3 equals 8, which is more than 6. So we subtract 7 from 8 to get the remainder when (n + 3) is divided by 7, which is 1.

Here's the mathematical explanation: If n % 7 = 5, then n = 7k + 5 for some integer k. So, (n + 3) = (7k + 5) + 3 = 7k + 8. Dividing this by 7 gives us 7k + 7 + 1. The 7k + 7 part is divisible by 7 and we're left with a remainder of 1.