Question

insert two rational numbers between 1/3 and 1/4 , and arange in descending order
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Answer 1

Method 1:

$\frac{1}{3} and \frac{1}{4}$

LCM= 12 (no common factors)

$\frac{1}{3}$×$\frac{4}{4}$= $\frac{4}{12}$

$\frac{1}{4}$×$\frac{3}{3}=\frac{3}{12}$

(There are no rational no.s between these two. Usually it would end with this but if there are no rational no.s you gotta do the the following method or the method attached. I, myself, prefer this method over the one I attached. The other method would always give you numerous numbers tho.)

In the question, it said insert two rational numbers therefore-

2+1=3 (don't ask me why bcoz I have no idea why but that's how it usually is)

Then multiply the fractional no.s with 3, both the numerator and the denominator.

$\frac{4}{12}$×$\frac{3}{3}$=$\frac{12}{36}$

$\frac{3}{12}$×$\frac{3}{3}$=$\frac{9}{36}$

Therefore, the two rational numbers between $\frac{1}{3}$ and $\frac{1}{4}$ (always remember to put the initial no. in the final answer for this) in decreasing order are $\frac{11}{36} and \frac{10}{36}$