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Let the smaller number be x, and the larger number be 5x
the difference in their reciprocals would be:
(1/x) - (1/5x) = 1/10
if we combine the 2 fractions, we would get:
(5/5x) - (1/5x) = 4/(5x) = 1/10
Taking the reciprocal, 5x/4 = 10
x = 8
smaller number = x = 8
larger number = 5x = 40
the difference in their reciprocals would be:
(1/x) - (1/5x) = 1/10
if we combine the 2 fractions, we would get:
(5/5x) - (1/5x) = 4/(5x) = 1/10
Taking the reciprocal, 5x/4 = 10
x = 8
smaller number = x = 8
larger number = 5x = 40