Find a rational number between - 1/3 and - 1/4?

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Answer 1 · 2018-04-22T05:48:25

#-4/15,-5/18# and #-4/13# are all between #(-1)/3# and #(-1)/4#

If #a/b# and #c/d# are two rational numbers

the number #(ma+nc)/(mb+nd)# lies between the two rational numbers #a/b# and #c/d#, where #m# and #n# are two positive integers.

Here we have #(-1)/3# and #(-1)/4#

and selecting #(m,n)# as #(1,3)#, #(2,3)# and #(3,1)#, we get

#(1*(-1)+3*(-1))/(1*3+3*4)=-4/15#

#(2*(-1)+3*(-1))/(2*3+3*4)=-5/18#

#(3*(-1)+1*(-1))/(3*3+1*4)=-4/13#

and #-4/15,-5/18# and #-4/13# are all between #(-1)/3# and #(-1)/4#