How many distinct rational numbers can be expressed in the form a/b, where a and b are integers such that 1 ≤ a < b ≤ 10?
To determine the number of distinct rational numbers that can be expressed in the form a/b, we need to consider all possible combinations of integers a and b within the given range.
Since 1 ≤ a < b ≤ 10, we have a total of 9 possible values for a (1, 2, 3, 4, 5, 6, 7, 8, and 9).
For each value of a, we need to consider all possible values of b. Since a must be less than b, we can start with a + 1 and go up to 10.
So, for each value of a, we have a total of (10 - (a + 1) + 1) = (10 - a) possible values for b.
To find the total number of distinct rational numbers, we sum up the number of possibilities for each value of a:
Total = (10 - 1) + (10 - 2) + (10 - 3) + (10 - 4) + (10 - 5) + (10 - 6) + (10 - 7) + (10 - 8) + (10 - 9)
Total = 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
Total = 45
Therefore, there are 45 distinct rational numbers that can be expressed in the form a/b, where a and b are integers such that 1 ≤ a < b ≤ 10.