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 find the number of distinct rational numbers that can be expressed in the form of a/b, where a and b are integers such that 1 ≤ a < b ≤ 10, we need to consider the number of possible values for both a and b.
First, let's consider the possible values for b. Since b should be greater than 1, we have 10 - 1 = 9 possible values for b.
Next, let's consider the possible values for a. a can take any integer value from 1 up to b-1. For each value of b, the possible values for a would be (b-1) - 1 = b - 2.
So, for the given range of b (1 ≤ b ≤ 10), we can calculate the number of possible values for a by adding up the number of possible values for each b:
(b = 2) => a = 2 - 2 = 0 (not within the range of 1 ≤ a ≤ b-1)
(b = 3) => a = 3 - 2 = 1
(b = 4) => a = 4 - 2 = 2
(b = 5) => a = 5 - 2 = 3
(b = 6) => a = 6 - 2 = 4
(b = 7) => a = 7 - 2 = 5
(b = 8) => a = 8 - 2 = 6
(b = 9) => a = 9 - 2 = 7
(b = 10) => a = 10 - 2 = 8
Adding up all the possible values for a, we have 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.
Therefore, there are a total of 36 distinct rational numbers that can be expressed in the form a/b, where a and b are integers such that 1 ≤ a < b ≤ 10.