Find a number between #-2 4/5# and #-3 1/5#?

Question

Nova Allen · Accepted Answer

There are umpteen numbers less than #-2 4/5# and greater that #-3 1/5#. One such number is #-3#.

First of all observe that as the two numbers are negative, #-2 4/5# is the greater than the other number #-3 1/5#. Hence, a number less than #-2 4/5=-14/5# and greater than #-3 1/5=-16/5# means a number between these two numbers. We can have umpteen numbers between any two such numbers. Say we have two numbers #a# and #b#, then a number #(ma+nb)/(m+n)#, where #m# and #n# are any two positive numbers, lies between #a# and #b# and we can have infinite such numbers by choosing variety of #m# and #n#. Let us choose #m=1# and #n=1#, then this number is #(a+b)/2#. As we have #a=-14/5# and #b=-16/5#, this is #(-14/5-16/5)/2=-30/5xx1/2=-15/5=-3# Observe that as in #(ma+nb)/(m+n)# all numbers #m,n,a# and #b# are rational numbers, #(ma+nb)/(m+n)# will give only rational numbers between #a# and #b#. In fact there could be infinite irrational numbers between #a# and #b# e.g. #(a^m*b^n)^(1/(m+n))#.

Zoe Adams · Answer

undefined A number between $-2 \frac{4}{5}$ and $-3 \frac{1}{5}$ is $-3$.