Question

How many fractions between and inclusive can be written with a
denominator of 15?

Answer 1

There are a total of 15 fractions that can be written with a denominator of 15, corresponding to each numerator from 1 to 15 inclusive.

Step-by-step explanation:

To determine how many fractions can be written with a denominator of 15, we must consider all the possible numerators. Since a fraction consists of a numerator divided by a denominator, and in this case, the denominators are fixed at 15, we only need to vary the numerator to generate different fractions.

For a denominator of 15, the possible numerators that yield valid fractions range from 1 to 15, because if we use 0 as the numerator, it results in the fraction 0/15, which is equal to 0, and if we used numbers greater than 15, they could be simplified to a fraction with a smaller denominator or be equal to a whole number.

Counting from 1 to 15, we can represent the number of fractions that can be written with a denominator of 15 as follows:

1. 1/15
2. 2/15
3. 3/15
4. 4/15
5. 5/15
6. 6/15
7. 7/15
8. 8/15
9. 9/15
10. 10/15
11. 11/15
12. 12/15
13. 13/15
14. 14/15
15. 15/15

Therefore, there are 15 possible fractions that can be written with a denominator of 15.

Answer 2

The number of fractions between 0 and 1 (inclusive) with a denominator of 15 can be found using the formula (n-1)/n, where n is the denominator.

So, to answer your question, we can use the formula and plug in 15 for the value of n:

(15-1)/15 = 14/15

Therefore, there are 14 fractions between 0 and 1 (inclusive) with a denominator of 15.