Numbers on the Board

The following numbers are written on the board:`1/3,1/2,1,2,3`. In each step, you are allowed to choose any two numbers written on the board and replace each of them with their product.
Can you reach a quintet of numbers in this way whose sum is `4 1/4`?

Difficulty level (1 very easy - 10 very hard): 3

Topics:
Algebra -> Sequences Arithmetic -> Fractions
Sources:
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