You eat 310 of a pack of hot dogs. Your friend eats 15 of the pack of hot dogs. What fraction of the pack of hot dogs do you and your friend eat? Write your answer as a fraction in simplest form.
You and your friend eat a total of 310 + 15 = 325 hot dogs.
The pack of hot dogs has a total of 325 hot dogs.
Hence, you and your friend eat the fraction 325/325 = 1/1 = $\boxed{1}$.
To find the fraction of the pack of hot dogs that you and your friend eat, we need to add the number of hot dogs you ate to the number of hot dogs your friend ate, and then divide that sum by the total number of hot dogs in the pack.
You ate 310 hot dogs and your friend ate 15 hot dogs, so the total number of hot dogs you both ate is 310 + 15 = 325.
Let's assume the pack of hot dogs contains x hot dogs.
The fraction of the pack of hot dogs that you and your friend ate is (325/x).
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD) which is 5.
So, the simplified fraction is 325/5x, which can be further reduced to 65/x.
Therefore, the fraction of the pack of hot dogs that you and your friend ate is 65/x, where x represents the total number of hot dogs in the pack.
To find the fraction of the pack of hot dogs that you and your friend eat, we first need to determine the total number of hot dogs in the pack. Let's call this value "x".
We know that you eat 310 hot dogs, and your friend eats 15 hot dogs. So the total number of hot dogs consumed by both of you is 310 + 15 = 325.
Now, we need to compare the total number of hot dogs consumed to the total number of hot dogs in the pack. This can be expressed as:
(325 hot dogs consumed) / (x total hot dogs in the pack)
Since we want to write the answer as a fraction in simplest form, we need to find the greatest common divisor (GCD) of 325 and x. This can be done by prime factorizing both numbers:
325 = 5 * 5 * 13
x = a * b * c * ... (prime factorization of x)
The GCD of 325 and x will be the product of the common prime factors raised to their lowest exponent. In this case, since 325 only has 5 and 13 as the prime factors, the GCD will be 5 * 13 = 65.
Therefore, the fraction of the pack of hot dogs that you and your friend eat is:
325/65
Simplifying this fraction by dividing both the numerator and the denominator by their GCD (65) gives us:
5/1
So the answer is 5/1, which is equivalent to the whole number 5.