Let

x = the number

3x = thrice the number

The sum of their reciprocals is 4:

1/x + 1/(3x) = 4

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click here to see the equation solved for x

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x = 1/3

1/x = 1/(1/3) = 3

3x = 3*(1/3) = 1

1/3x = 1

The reciprocals are 3 and 1.