What is #2 1/7 div 2 1/2#?

Start by writing the problem as fractions.

#(2 1/7) / (2 1/2) = (2/1+1/7)/(2/1 + 1/2)#

Working with one set of numbers at a time, multiply to get a common denominator. The easiest and fastest route is usually to multiply one of your fractions by #1/1# using factors from the other fraction, so that you don't change the equation from the original value. Since our denominator in #2/1# is 1, we can multiply that denominator by the other fraction's denominator, to get our common denominator.

First the numerator of the original problem.

#((2/1*7/7)+1/7)/(2/1 + 1/2)=(14/7+1/7)/(2/1 + 1/2)#

Then we'll do the denominator of the original, multiplying #2/1# by #2/2#, which we got from the other fraction's denominator.

#(14/7+1/7)/((2/1*2/2) + 1/2)=(14/7+1/7)/(4/2 + 1/2)#

Now that all the addition fractions are over a common denominator and are all equal slices of the same pie, we can add numerators together.

#((14+1)/7)/((4+1)/2)=(15/7)/(5/2)#

Dividing by a fraction is the same as multiplying by the inverse of that fraction. Flip the numerator and denominator of the original denominator and multiply that against the original numerator.

#(15/7)*(2/5)#

Multiply numerators by numerators and denominators by denominators.

#(15/7)*(2/5) = 30/35#

From there you could see both top and bottom are divisible by 5, so you can pull out 5 from the top and bottom, which is just one, and simplifying your problem to #6/7# .

#30/35=5/5*6/7=1*6/7=6/7#

Alternatively, you can cancel: 15 divided by 5 from the second fraction which leaves 3 in the numerator of the first, and then multiply numerators and denominators.

#15/7*2/5=3/7*2/1=6/7#

First change the mixed numbers into improper fractions.

#2 1/7 div2 1/2#

#=15/7 xx 5/2#

Multiply by the reciprocal:

#15/7 xx2/5#

#cancel15^3/7 xx2/cancel5#

#=6/7#

Note that by multiplying by #2/5#, you are first finding how many 'halves' there are in #2 1/7# and then by dividing by #5#, you are finding how many 'groups of '#5 # halves' there are .... which is what #div 2 1/2# actually means,