Answer
Regroup when: the first number is a whole number, or
the fraction in the first number is smaller than the fraction in the second number.
Work Step by Step
When subtracting two numbers, you need to regroup when:
(a) the first (or top) number is a whole number
or:
(b) the fraction in the first (or top) number is smaller than the fraction in the second (or bottom) number
Example of situation (a):
$\displaystyle 10-5\frac{1}{3}=9\frac{3}{3}-5\frac{1}{3}=...$
Example of situation (b):
$\displaystyle 10\frac{1}{3}-5\frac{2}{3}=9\frac{4}{3}-5\frac{2}{3}=...$