For how many values of n where n is a positive integer less than 10 is n+1/2 an integer?

A) None
B) One
C) Three
D) Four
E) Five

Please I would like some help explaining how to get the answer :)

N+1÷2

N is less than 10, which means that we can take n=9
9+1÷2
=10÷2
=5
Answer is 5

I try to solve it but I couldn't get the answer

Well, I must say, this question is quite interesting! Let's dive into solving it, shall we?

To determine the number of values of n for which n + 1/2 is an integer, we need to consider that n should be a positive integer less than 10.

Now, let's take a closer look at the expression n + 1/2. For this expression to be an integer, the fractional part, 1/2, must be eliminated.

We can see that 1/2 can only be eliminated when n is an odd number. Why, you ask? Well, even numbers have a 0 in the ones place, meaning when you add 1/2, you will still end up with a fractional part.

Therefore, we need to find the number of odd positive integers less than 10. So, let's list them out: 1, 3, 5, 7, and 9.

Counting, we find that there are indeed five values (1, 3, 5, 7, 9) for n where n + 1/2 is an integer.

So, the answer is E) Five.

I hope that helps, and remember, math can be funny too!

To find for how many values of n, where n is a positive integer less than 10, the expression n + 1/2 is an integer, we can go through each option and check if the expression results in an integer.

Let's start with option A) None:
If there are no values of n for which n + 1/2 is an integer, then we need to check if any value of n between 1 and 9 satisfies this condition.

Calculating n + 1/2 for each value of n less than 10:
1 + 1/2 = 1.5 (not an integer)
2 + 1/2 = 2.5 (not an integer)
3 + 1/2 = 3.5 (not an integer)
4 + 1/2 = 4.5 (not an integer)
5 + 1/2 = 5.5 (not an integer)
6 + 1/2 = 6.5 (not an integer)
7 + 1/2 = 7.5 (not an integer)
8 + 1/2 = 8.5 (not an integer)
9 + 1/2 = 9.5 (not an integer)

None of these calculations result in an integer, so option A) None is the correct answer.

Therefore, the answer is A) None.

Let me know if I can help you with anything else.

To determine for how many values of n (where n is a positive integer less than 10) the expression n + 1/2 is an integer, we need to understand the concept of integers and how they relate to the given expression.

An integer is a whole number (both positive and negative) without any fractional or decimal parts. The expression n + 1/2 would only be an integer if the fractional part, i.e., 1/2, cancels out when added to n.

To solve this problem, we can consider each possible value of n from 1 to 10 (exclusive) and check whether n + 1/2 results in an integer.

1) For n = 1:
1 + 1/2 = 1.5 (not an integer)

2) For n = 2:
2 + 1/2 = 2.5 (not an integer)

3) For n = 3:
3 + 1/2 = 3.5 (not an integer)

4) For n = 4:
4 + 1/2 = 4.5 (not an integer)

5) For n = 5:
5 + 1/2 = 5.5 (not an integer)

6) For n = 6:
6 + 1/2 = 6.5 (not an integer)

7) For n = 7:
7 + 1/2 = 7.5 (not an integer)

8) For n = 8:
8 + 1/2 = 8.5 (not an integer)

9) For n = 9:
9 + 1/2 = 9.5 (not an integer)

Considering all the possible values of n, we can see that none of the calculations result in an integer.

Therefore, the correct answer is A) None, as there are no values of n (less than 10) for which n + 1/2 is an integer.