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Given a sorted ascending sequence of fractions, if I add a constant $c$ to each fraction's numerator and denominator, how is the sequence affected?

For example, if I have a sequence in ascending order:

$$\frac12, \frac38, \frac57, \frac ab,\ldots$$

if I add a constant $c=1$

$$\frac{1+c}{2+c}, \frac{3+c}{8+c}, \frac{5+c}{7+c}, \frac{a+c}{b+c},\ldots$$

will my sequence still be sorted in ascending order?

Thank you!

1 Answers 1