Question

Find10 Rational numbers between 2/3 and 5/4​

Answer 1

Hey friends,

Hope it helps.

Question:

Find 10 Rational numbers between 2/3 and 5/4​

Answer:

7/10, 5/7, 8/11, 3/4, 7/9, 4/5, 5/6, 1/1, 8/7, 7/6, 13/11, 6/5, 17/14, 11/9 and 16/13 are 15 rational numbers between 2/3 and 5/4​

Step-by-step explanation:

So we have 2/3 and 5/4

Now, we need to find 10 Rational numbers between them.

To do that, add both the numerators and the denominators with each other.

2/3, 5/4

= 2/3, 2+5/3+4, 5/4

= 2/3, 7/7 , 5/4

= 2/3, 1 , 5/4

(note: 7/7 =1)

• So we found 1 rational number between 2/3 and 5/4​, which is 1. But we will take that as 1/1 in the next step as it means the same.

= 2/3, 2+1/3+1, 1/1 , 1+5/1+4, 5/4

= 2/3, 3/4, 1/1, 6/5, 5/4.

= 2/3, 2+3/3+4, 3/4, 3+1/4+1, 1/1, 1+6/1+5, 6/5, 6+5/5+4, 5/4.

= 2/3, 5/7, 3/4, 4/5, 1/1, 7/6, 6/5, 11/9, 5/4.  

• You must have noticed that until we get 10 rational numbers, we keep adding numerator-and-numerator, just like how we do for the denominator.

= 2/3, 2+5/3+7, 5/7, 5+3/7+4, 3/4, 3+4/4+5, 4/5, 4+1/5+1, 1/1, 1+7/1+6, 7/6, 7+6/6+5, 6/5, 6+11/5+9, 11/9, 11+5/9+4, 5/4. (since you want 10, you can add only few of them, but for your ease

= 2/3, 7/10, 5/7, 8/11, 3/4, 7/9, 4/5, 5/6, 1/1, 8/7, 7/6, 13/11, 6/5, 17/14, 11/9, 16/13, 5/4.

Thus, we get 15 rational numbers between 2/3 and 5/4.

Which is, 7/10, 5/7, 8/11, 3/4, 7/9, 4/5, 5/6, 1/1, 8/7, 7/6, 13/11, 6/5, 17/14, 11/9 and 16/13.

Hope it helps!