Yes, rational and irrational numbers can be negative. Te only thing that is desired is that they could be mapped to a place on a real number line. Negative numbers are to the left of #0# on number line.
By definition, rational numbers are a ratio of two integers #p# and #q#, where #q# is not equal to #0#. Hence, if #p# is negative and #q# is positive (or vice versa but #q!=0#), #p/q# could be negative.
Examples of negative rational numbers are #-3.14159#, #-17/4#, #-2/3# or #-3.bar(142857)# (here #bar(142857)# indicates these numbers are repeating infinitely). These are equivalent to #-314159/100000#, #-17/4#, #-2/3# or #-22/7# (in form #p/q#).
Similarly there could be negative irrational numbers too like #-pi#, #root(3)(-80)#, #-sqrt2# etc. These are equivalent to their positive irrational numbers like #pi#, #root(3)(80)#, #sqrt2# but towards left of #0# on real number line.
Similarly, there could be irrational numbers like #6-3pi# which are #3pi# units to the left of #6#, but as this would lie to the left of #0#. Some other such numbers are #1-sqrt3#, #root(3)2-sqrt5#, #-sqrt17+2# and #-7.239135113355111333555.....#. (The last number is non-terminating non-repeating decimal number and hence an irrational number.)
