Find rational number between 3÷4 and 5÷6?

just in the middle is (18/24+20/24)/2 = 19/24

The rational number 4/5 is between 3/4 and 5/6

3/4 + 5/6 = 3x6+5x4/24 = 18+20/24 = 38/24
38/24 divided by 2 =19/24
so (3/4 + 5/6)/2 = 19/24
The rational no. is 19/24.

3/4_______________5/6
18/24____19/24____20/24

A possible answer is 19/24

19/24

e.g take the average =(1/2)(3/4 +5/6)=(1/2)(38/24)=19/24

So you have 3/4 and 5/6.

First, you want to have a common denominator. The smallest one turns out to be 12.

Thus, if you multiply the first fraction by 3 on both top and bottom you get 3(3/4) = 9/12

For the second fraction you can multiply by 2 on top and bottom to get 2(5/6)=10/12.

So you see that you have 9/12 and 10/12. Well there is no fraction with a denominator of 12 that fits between 9 and 10.

So the next step is to find the next biggest common denominator. we can see that we can use 24.

so multiplying 9/12 and 10/12 by two gives us 18/24 and 20/24. Here we can see that now there is a rational number between these two fractions which is 19/24.

We can see that the more our denominator increases, the more rational numbers we will have between these two fractions. In reality, you can increase the denominator to infinity and thus will have an infinite number of rational numbers between the fractions.

Hope this helped :)

Well,

3/4 = 6*3 / 6*4 = 18/24
and
5/6 = 4*5 / 4*6 = 20/24
therefore
19/24 is suitable

hope it' ll help !!

4/5 will be a rational number between 3/4 and 5/6, as will an infinity of other numbers.

[3/4 + 5/6 ] / 2 is one answer