Final answer:
The answer involves calculating distinct fractions between 0 and 1 with a whole number denominator less than 6. By listing out all possibilities and eliminating duplicates, we can count the number of unique fractions.
Step-by-step explanation:
The student has asked about the number of distinct numbers between 0 and 1 that can be expressed as a fraction a/b where a and b are whole numbers and b is less than 6. To solve this, we must consider all the possible fractions with denominators ranging from 1 to 5.
For example, when b is 2, the possible values for a are 0 and 1, yielding the fractions 0/2 and 1/2. When b is 3, we could have 0/3, 1/3, and 2/3 as the possible fractions. We continue this process for denominators 4 and 5. It is important to note that we should only count each distinct fractional value once, even if it can be created with different pairs of a and b.
For each denominator, we end up with the following fractions:
- b=1: 0/1, 1/1
- b=2: 0/2, 1/2
- b=3: 0/3, 1/3, 2/3
- b=4: 0/4, 1/4, 2/4, 3/4
- b=5: 0/5, 1/5, 2/5, 3/5, 4/5
After eliminating duplicates and the fraction equal to 1, we count the remaining fractions to get the final answer.