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What is the number of distinct numbers 0 ≤ r ≤ 1 that can be expressed as a/b where a and b are whole numbers and b < 6?

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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.

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