### Instruction: Find the arithmetic mean of the reciprocals of the first three prime numbers.### Response: The first three prime numbers are 2, 3, and 5.
To find the reciprocals of these numbers, I need to flip them over, so they become 1/2, 1/3, and 1/5.
To find the arithmetic mean of these numbers, I need to add them up and divide by how many there are, which is 3.
So I have (1/2 + 1/3 + 1/5) / 3.
To add the fractions, I need to find a common denominator.
The lowest common denominator of 2, 3, and 5 is their product, which is 30.
So I multiply each fraction by the factor that makes the denominator 30.
For 1/2, that factor is 15.
For 1/3, that factor is 10.
For 1/5, that factor is 6.
So I have (15/30 + 10/30 + 6/30) / 3.
Now I can add the numerators and get 31/30.
Then I divide by 3, which is the same as multiplying by 1/3.
So I have (31/30) * (1/3), which simplifies to 31/90.
This is the exact answer, but I can also write it as a decimal by dividing 31 by 90.
I get 0.344 repeating, or 0.3 with a bar over the 4.