Question

insert 6 rational numbers between _2/3 and 3/4​

Answer 1

Answer:

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Answer 2

Answer:

19/28, 29/42, 59/84, 3/7, 61/84 and 31/42

Step-by-step explanation:

First, we find the LCM of the denominators= 12

Then we multiply 2/3 with 4/4 to get 12 in the denominator. 2/3*4/4=8/12

Then we multiply 3/4 with 3/3 to get 12 in the denominator. 3/4*3/3=9/12.

Now, since we are not getting any rational numbers by this two steps, we again multiply the LCM by n+1, where n is the number of rational numbers to be found.

Multiply 12 with n+1=7, that will give 84.

Now, multiply 8/12 with 7/7=56/84, and 9/12 with 7/7=63/84.

The 6 rational numbers are: 57/84=19/28, 58/84=29/42, 59/84=59/84, 60/84=3/7, 61/84=61/84 and 62/84=31/42. (NOTE: Every numbers needs to be simplified to its simplest form.